A linguistic decision support model for QoS priorities in networking

Knowledge-Based Systems 32 (2012) 65–75

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Knowledge-Based Systems journal homepage: www.elsevier.com/locate/knosys

A linguistic decision support model for QoS priorities in networking q Sergio Gramajo a,⇑, Luis Martı´nez b a b

Artificial Intelligence Research Group, National Technological University, Resistencia, Chaco 3500, Argentina Computing Department, Jaén University, Jaén 23071, Spain

a r t i c l e

i n f o

Article history: Available online 3 September 2011 Keywords: Quality of Service Traffic engineering 2-tuple linguistic model Decision support Fuzzy linguistic approach Extended linguistic hierarchy

a b s t r a c t Networking resources and technologies are mission-critical in organizations, companies, universities, etc. Their relevance implies the necessity of including tools for Quality of Service (QoS) that assure the performance of such critical services. To address this problem and guarantee a sufficient bandwidth transmission for critical applications/services, different strategies and QoS tools based on the administrator’s knowledge may be used. However it is common that network administrators might have a nonrealistic view about the needs of users and organizations. Consequently it seems convenient to take into account such users’ necessities for traffic prioritization even though they could involve uncertainty and subjectivity. This paper proposes a linguistic decision support model for traffic prioritization in networking, which uses a group decision making process that gathers user’s needs in order to improve organizational productivity. This model manages the inherent uncertainty, imprecision and vagueness of users’ necessities, modeling the information by means of linguistic information and offering a flexible framework that provides multiple linguistic scales to the experts, according to their degree of knowledge. Thereby, this decision support model will consist of two processes: (i) A linguistic decision analysis process that evaluates and assesses priorities for QoS of the network services according to users and organizations’ necessities. (ii) A priority assignment process that sets up the network traffic in agreement with the previous values. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction Nowadays network technologies are crucial to develop efficiently essential tasks in most organizations. Internet based networks provide a service so-called best effort delivery that means the network does not provide any guarantee that either data is delivered or that a user is given a guaranteed Quality of Service level or a certain priority. Therefore, in a best effort network all users obtain best effort service, i.e., they obtain the best possible service without planning from the network. Moreover depending on the current traffic load, unspecified variable bit rate and delivery time are obtained [1–3]. This type of network service together the commercial use of Internet and its increasing demand of resources make require the companies a higher guarantee of quality for their relevant and critical services. The use of QoS leads to improve the trustworthy of networks facing problems like delivery delays, loss of data packets, low bandwidth, quality of content and so on [1,2,4,5]. The throughput of these features plays a key role in the achievement of quality for the network traffic. q This paper has been partially supported by the research projects TIN200908286, P08-TIC-3548 and Feder Fonds. ⇑ Corresponding author. Address: French 414, Resistencia, Chaco, Argentina. E-mail addresses: [email protected] (S. Gramajo), [email protected] (L. Martı´nez). URL: http://www.ujaen.es (L. Martı´nez).

0950-7051/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.knosys.2011.08.016

The previous premises help to provide an overall view of the problems that networking QoS are facing up within the companies [1,2,4]:  Network administrators need to design networks able to achieve maximum efficiency for critical applications satisfying users’ needs.  The routers must be set up to provide different services to different types of network traffic.  Network administrators must have a wide knowledge of QoS techniques and their application scope.  The process of traffic prioritization to users and/or network applications is complex and subjective where there may be many points of view and different opinions about problem at hand. Consequently, a necessity to increase the control and provide intelligence to local networks for prioritizing critical and useful network services for organizations is needed. Thus, traffic prioritization is becoming more and more common and demanded in the corporate market. For instance, companies with remote offices are connected via Internet and their applications tend to become centrally hosted but with a demand of good remote performance. It is noteworthy that control network traffic is an essential component in organizations and it could provide flexibility to

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accommodate emerging real-time applications and critical services. The processes of priority allocation and planning of network traffic are complex and often involve subjective tasks. Such processes can be solved by using different techniques such as traffic shaping [5–8], DiffServ [9], and so on. They facilitate the control and prioritization of the traffic network by marking and delaying packets that are not important and sending first priority packets, using any leftover bandwidth space to send packets in descending order of importance. In this scenario, network administrators or network engineers need to make decisions about the design of networks to achieve maximum efficiency in critical applications because well-organized networking traffic not only helps to improve productivity in organizations, but also helps users to develop their tasks more efficiently. This decision process implies the assignation of traffic priorities to users and/or network applications, planning traffic engineering, set up and implement QoS parameters to improve the network user’s perception. The complexity of such decisions is increased because of in the real world, the scenario, objectives, constraints and results of feasible choices for the design of networks are not usually precisely known, but rather than are uncertain and vague. Additionally the only view of a network administrator can be biased regarding the real needs of users and organization. Even more, several network administrators might have different views and provide different solutions for the same problem. Hence the use, in the decision process for networking QoS, the users’ opinions that work transversally across the organization and have a clear view about useful networking services might help to administrators to improve network traffic. Therefore, the use of tools that support the administrator/s to make these decisions and capable to manage users’ knowledge dealing with its inherent uncertainty and subjectivity might be very useful to obtain successful results in the quality of traffic network. Decision Support Systems (DSS) have supported complex decision making problems in different topics and environments since the early 70s [10–12]. Notwithstanding the great number of DSS proposed in the literature it is clear that still different challenges that they should achieve such as capturing and representing knowledge from experts, that is not a trivial task because of its imprecision, subjectivity and uncertainty. The application of fuzzy sets theory and fuzzy linguistic approach to decision making under uncertainty is a major topic that have provided very interesting results[13–15]. Therefore, this paper proposes a linguistic decision support model for QoS Priorities for Network Traffic that follows a MultiExpert Decision Making (MEDM) scheme. It includes relevant opinions from expert users regarding their necessity of QoS for each networking service. As far as we know there are not previous researches to deal with QoS techniques and MEDM in networking. Due to the fact that, the proposed decision support model will deal with information provided by different sources (administrators, users), related to human perceptions and qualitative aspects that involve uncertainty and vagueness, an appropriate tool to represent and manage this type of information is the linguistic modeling based on the fuzzy linguistic approach that provides a direct tool to model qualitative information by means of linguistic variables, but it implies processes of computing with words (CW) [16]. In the problem considered, different sources of information could have different degrees of knowledge, experience or ability regarding the problem alternatives. We propose a flexible expression framework in which various linguistic scales can be used by the different sources according to their degree of knowledge. This framework is based on the use of extended linguistic hierarchies [17] (ELH) which facilitates the processes of CW dealing with multiple linguistic scales and keeps the accuracy of the results.

The proposed decision support model consists of the following phases: 1. A linguistic decision analysis phase for assessing QoS. It analyses different alternatives, either types of network traffic or group of users and by applying a MEDM process computes the necessary QoS value for each alternative according to users’ necessities [18–22]. The alternatives are independent for each organization and its necessities. 2. A priority assignment process. The QoS values obtained in the previous phase will be used to filter the services of network traffic and prioritize them. This paper is organized as follows. Section 2 reviews basic concepts, classifications and uses of QoS in networking; Section 3 provides a linguistic background used to manage uncertain information in the proposal. Section 4 presents the linguistic decision support model for QoS priorities in network traffic, its application and architecture. In Section 5 is then proposed an illustrative example. Eventually Section 6 points out some concluding remarks. 2. QoS in networking Quality of Service (QoS) is a generic name for a set of techniques that seeks for providing different quality levels to different types of network traffic [1,2]. All the basic Internet technology has been developed or refined in the Internet Engineering Task Force (IETF). IETF working groups which developed the routing, management, and transport standards have contributed to current development and use of Internet. Additionally it has proposed different models of standards and mechanisms to meet the demand for QoS that are applied to specific solution domains. In this way, the most well-known are:  Resource Reservation Protocol (RSVP) [23]. It is a protocol created by the IETF and is based on signaling for resource reservation through bridges and routers on IP networks. Its main goal is to establish and maintain resources for user’s applications. It is also called the integrated services model  The differentiated services model (DiffServ) [9]. It is a QoS protocol proposed by IETF to distinguish different classes of service by marking and labeling packages in the IPv4 and IPv6 headers and afterwards prioritizing them.  The multiprotocol label switching technique (MPLS) [24]. It is a protocol proposed by Cisco Systems and standardized by IETF. It operates between link and network layer with high-speed switching and forwarding traffic functions by labeling traffic in the routers, and it can also operate with different protocols simultaneously.  Subnet Bandwidth Manager (SBM) [25]. It is a signaling protocol that operates at the link layer and enables communication and coordination between network nodes and protocols related to higher layer QoS.  802.1p and 802.1D standards [26]. They are IEEE standards created to work on the link layer and its function is to classify and prioritize traffic in Local Area Networks (LAN).  Traffic engineering [2]. It is a method of performance optimization for telecommunications network by dynamically analyzing, predicting and regulating the behavior of data transmitted over that network.  Traffic shaping [5–8]. It is a set of tools that provides control traffic achieving optimization, performance guarantee and/or prioritization by delaying packets. They are applicable at local, global, end-to-end networks [1,2] and often related to physical transmission media.

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with vague and imprecise knowledge. Therefore a more realistic approach may be used to manage this kind of information providing linguistic assessments instead of numerical values, i.e., by assuming that the variables involved in the problem are assessed by means of linguistic terms [30–32]. The fuzzy linguistic approach uses variables whose values are natural language words and it has been successfully applied to different fields such as: decision model [18,33–36], performance appraisal [21,22], sensory evaluation [19,20], recommender systems [37,38] and so on. We have to choose appropriate linguistic descriptors for the term sets and their semantics to describe the vague or imprecise knowledge. One possibility of generating the linguistic term set consists in supplying the term set directly by considering all the term distributed on a scale on which a total order is defined. For example, a set S of five linguistic terms could be:

S ¼ fs0 : Very  Low; s1 : Low; s2 : Medium; s3 : High;s4 : Very  Highg

Fig. 1. Scope of application.

Recently, different researches [27–29] have been conducted to describe the strengths and weaknesses related to each of these mechanisms and point out the benefits of QoS for organizations, allowing network administrators to take control of the use of these resources. Due to the large number of QoS techniques and their different application targets, the area of interest and application that we consider in this paper is focused on the traffic shaping technique that plans and prioritizes the network traffic by reducing or eliminating less important packages, leaving large bandwidth for important packages reach their destination as quickly as possible. An intelligent use of traffic shaping improves bandwidth utilization and network performance increases productivity. Therefore, it would be a good technique for companies to manage their resources prioritizing traffic instead of best-effort traffic. For example, it is assumed that an organization needs to control network traffic and allocate resources according to the importance of network services used. It requires implementing a control mechanism at the boundary of the organization’s local network. The point to perform control is done by a traffic shaper which offers different types of services for local network to access external networks or use Internet services. Fig. 1 outlines on the bottom side of traffic shaper the local network of the organization that will obtain a differenced service for the different users and/or network traffic. On the top side other networks out of the organization such as Internet is represented. 3. Linguistic background

In the linguistic approach an important parameter to be determined is the granularity of uncertainty that indicates the degree of discrimination given by a term set, so that the more knowledge about the variable, the more granularity can be used to assess it. Quite often different experts have different degree of knowledge about the items, in those cases several linguistic terms sets with different granularity of uncertainty may be useful [35,39]. Once it has been defined the descriptors is then necessary to establish the semantics of the linguistic terms, being the approach based membership function the most widely used. Thus, the semantics is given fuzzy numbers in [0, 1] (see Fig. 2). In this paper, we shall use triangular membership functions as semantics of linguistic terms whose representation is defined by three parameters (a, b, c), where b indicates the point in which the membership function value is 1, a and c indicate the left and the right limits of the definition domain of the membership function [40,41]. The midterm have an assessment of ‘‘approximately 0.5’’, with the rest of the terms being placed symmetrically around it. 3.2. The 2-tuple linguistic representation model Even though there are different methods to carry out processes of CW in decision making [16], the proposal of this paper will use the 2-tuple model. This model was presented in Ref. [41], for overcoming the drawback of the loss of information presented by the classical linguistic computational models: (i) The semantic model[42], (ii) and the symbolic one [43]. The 2-tuple model is a symbolic model that extends the use of indexes modifying the fuzzy linguistic approach representation by adding a parameter to the basic linguistic representation in order to improve the accuracy of the linguistic computations. It takes the concept of Symbolic Translation as the base of its representation [44,45]. Definition 1. The Symbolic Translation of a linguistic term. si 2 S = {s0, . . . , sg} is a numerical value assessed in [0.5, 0.5) that supports the ‘‘difference of information’’ between a counting of

Due to the fact that our QoS Decision Support model will deal with linguistic information and multiple scales, we shall review tools to manage this kind of information. We review briefly the fuzzy linguistic approach and how to manage multi-granular linguistic information by means of fuzzy 2-tuple linguistic model and extended linguistic hierarchies. 3.1. Fuzzy linguistic approach Many aspects of different activities in the real world cannot be assessed in a quantitative form, but rather in a qualitative one, i.e.

Fig. 2. A set of five terms with its semantics.

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information b assessed in the interval of granularity [0, g] of the term set S and the closest value in {0, . . . , g} which indicates the index of the closest linguistic term in S(si). From this concept a new linguistic representation model was developed, which represents the linguistic information by means of a linguistic 2-tuple. It consists of a pair of values namely, ðsi ; aÞ 2 S  S  ½0:5; 0:5Þ, being si 2 S a linguistic term and a 2 [0.5, 0.5) a numerical value representing the symbolic translation. This representation model defined a set of transformation functions between numeric values and linguistic 2-tuples to facilitate linguistic computational processes. Definition 2. Let S = {s0, . . . , sg} be a linguistic terms set and b 2 [0, g] a value supporting the result of a symbolic aggregation operation. The 2-tuple set associated with S is defined as S ¼ S  ½0:5; 0:5Þ. A 2-tuple that expresses the equivalent information to b is then obtained as follow:

DS : ½0; g ! S  i ¼ roundðbÞ si ; DS ðbÞ ¼ ðsi ; aÞ; with a ¼ b  i; a 2 ½0:5; 0; 5Þ

ð1Þ

being round () is the usual round operation, i the index of the closest label, si, to ‘‘b’’, and ‘‘a’’ the value of the symbolic translation. It is noteworthy to point out that Ds is a one to one mapping 1 [44] and D1 S : S ! ½0; g is defined by DS ðsi ; aÞ ¼ i þ a. In this way the 2-tuple of S is identified by a numerical value in the interval [0, g]. Remark 1. The transformation of a linguistic term into a linguistic 2-tuples consists of adding value 0 as symbolic translation: si 2 S ) ðsi ; 0Þ 2 S. On other hand, DS(i) = (si, 0) and D1 S ðsi ; 0Þ ¼ i; 8i 2 f0; 1; ::; gg. If b = 3.25 is the value representing the result of a symbolic aggregation operation on the set of labels, S = {s0 = Nothing, s1 = VeryLow, s2 = Low, s3 = Medium, s4 = High, s5 = VeryHigh, s6 = Perfect}, then the 2-tuple that expresses the equivalent information to b is (medium,.25). See Fig. 3. This model has a linguistic computational technique based on the functions DS and D1 S , for a further detailed description see Ref. [41].

Fig. 3. A 2-tuple linguistic representation.

 Rule 2: to obtain an ELH a new level, l(t⁄, n(t⁄)) with t⁄ = m + 1, should be added. This new level must have the following granularity:

nðt  Þ ¼ ðL:C:M:ðnð1Þ  1; . . . ; nðmÞ  1ÞÞ þ 1

being L.C.M. the Least Common Multiple. ELH building process then consists of two processes: (i) it adds m linguistic scales used by the experts to express their information. And (ii) then it adds the term set l(t⁄, n(t⁄)), with t⁄ = m + 1, according to Eq. (2). Therefore, the ELH is the union of all levels required by the experts plus the new level l(t⁄, n(t⁄)).

ELH ¼

t¼mþ1 [

ðlðt; nðtÞÞÞ

ð3Þ

t¼1

Sn(t) denotes a linguistic term set of thenELH corresponding to the leo nðtÞ nðtÞ vel t and a granularity of nðtÞ : SnðtÞ ¼ s0 ; . . . ; snðtÞ1 The use of multi-granular linguistic information makes the processes of CW more complex. In Ref. [17] an accurate computational model for ELH based on linguistic 2-tuples and the computational model for linguistic hierarchies was proposed [18]. ELH computational model needs to make a three-step process showed in Fig. 4, that consists of: 1. Unification phase. The multi-granular linguistic information is conducted into only one linguistic term set, that in ELH is  always Snðt Þ , by means of a transformation function TF ab ðÞ:

3.3. Extended linguistic hierarchies The proposed decision support model will offer to the experts a flexible expression framework with several linguistic scales according to their degree of knowledge about the problem. Different approaches dealing with multi-granular linguistic information have been proposed [17,18,35,39]. The decision support model shall use the ELH approach [17] to model and manage multi-granular linguistic information because of its features of flexibility and accuracy in the processes of CW. An ELH is a set of levels, where each level represents a linguistic term set with different granularity from the remaining levels of the ELH. Each level belongs to an ELH is denoted as l(t, n(t)) being t a number that indicates the level of the ELH and n(t) the granularity of the terms set of the level t. To build an ELH have been proposed a set of extended hierarchical rules [11]:  Rule 1: A finite set of levels, l(t, n(t)) with t = 1, . . . , m, that defines the multi-granular linguistic framework required by experts to express their preferences are included.

ð2Þ

Fig. 4. Computing with words processes in ELH.

S. Gramajo, L. Martı´nez / Knowledge-Based Systems 32 (2012) 65–75

n o n nðaÞ nðaÞ nðbÞ and SnðbÞ ¼ s0 ; . . . ; Definition 3. Let SnðaÞ ¼ s0 ; . . . ; snðaÞ1 nðbÞ snðbÞ1 g be two linguistic term sets, with a – b. The linguistic transformation function is defined as: TF ab : SnðaÞ ! SnðbÞ !     D1 ðsnðaÞ ; anðaÞ Þ  ðnðbÞ  1Þ j nðaÞ nðaÞ nðbÞ nðbÞ a ¼ sk ; a k TF b sj ; aj ¼ DS nðaÞ  1

ð4Þ

2. Computational process. Once the information is expressed in  only one expression domain Snðt Þ , the computations are carried out by using the linguistic 2-tuple model [17]. 3. Expressing results. In this step the results might be transformed into any level, t, of ELH in a precise way by using Eq. (4) to improve the understanding of the results if necessary. Remark 2. In the processes of CW with information assessed in an ELH, the linguistic transformation function, TF ab , performed in the unification phase, a, might be any level in the set {t = 1, . . . , m} and the computational processes are carried out in the level b that it is always the level t⁄ (see Eq. (4)). 4. Linguistic decision support model for QoS In this section, our proposal of a linguistic decision support model for QoS in networking is introduced. Usually, the building of a support model requires a management process within organization because of the complexity of providing prioritized traffic control and its inherent subjectivity. The proposed model consists of two phases: initially a decision analysis model which obtains global assessments about the alternatives (QoS assessments) and then a priority allocation process classifies the alternatives in differentiated traffic groups. Fig. 5 shows graphically both phases, that are further detailed below. 4.1. Linguistic decision analysis of networking services This phase aims to define the alternatives considered in the problem and analyze them to obtain QoS assessments that will be used for filtering and prioritizing network traffic and services. Such results will be implemented in the prioritization process of network services. It consists of the following three steps (see Fig. 6). 4.1.1. Evaluation framework In this step the decision framework is defined, i.e. it determines the structure and representation of the problem. The framework for the decision model about network services will consider a finite set of experts, E = {e1, . . . , ep} that express their preferences regarding a set of alternatives, X = {x1, . . . , xq}, for a specific organization in order to increase its productivity.

Fig. 5. Model phases.

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The set of alternatives will be formed by layering network services used within the organization. The identification process of alternatives is independent for each organization, depends on their necessities and consists of accomplishing preliminary studies about relevant network services and important users or group of users. Both users and services might be used as alternatives. The network administrators must be able to identify them. For a better understanding the set of alternatives is divided in five classes according to the network model layers (see Fig. 7).  1. User-Group Alternatives (UGA): The alternatives, X UGA ¼ xUGA 1 ; . . . ; xUGA g, are users or group of users that ought to be treated a in different way according to their relevance for the organization. 2. Application Layer  Alternatives (ALA): The alternatives,  ALA X ALA ¼ xALA , are applications that can be identified 1 ; . . . ; xb by regular expression of the protocol headers. 3. Transport Layer Alternatives (TLA): Such alternatives are services   TLA identified by TCP or UDP ports, X TLA ¼ xTLA , belong to 1 ; . . . ; xc transport layer in TCP/IP protocol stack. 4. IP and Link Layer  Alternatives  (ILA): They are lower-level alternaILA tives, X ILA ¼ xILA , which identify physical and IP 1 ; . . . ; xd addressing that can be useful. 5. Combination of Traffic belonging to any level (CTL): These alterna  CTL tives, X CTL ¼ xCTL , are formed by filters corresponding 1 ; . . . ; xe to two o more layers. Therefore, the decision framework considers the set of alternatives, X, as the union of the different types of alternatives belonging to each layer:

0

fxUGA;1 ;    ; xUGA;a g

1

C B fxALA;1 ;    ; xALA;b g C m B [ C B B fxTLA;1 ;    ; xTLA;c g C; X¼ C B C B x¼1 @ fxILA;1 ;    ; xILA;d g A fxALM;1 ;    ; xALM;e g

ð5Þ

where q = a + b + c + d + e. This framework will also offer the experts a multi-granular linguistic domain for expressing their preferences, v ij 2 SnðtX Þ , by using an ELH. Being n(tX) the granularity of the linguistic terms set used by expert, ei, to express his/her preferences regarding the alternative xj 2 X. Therefore the ELH defined in the evaluation framework contains m term sets used by different experts to expressn their preference o  nðt  Þ nðt  Þ for each alternative and a new term set Snðt Þ ¼ s0 ; . . . ; snðt Þ1 whose granularity is computed by Eq. (2).

Fig. 6. Steps of the decision analysis phase.

S. Gramajo, L. Martı´nez / Knowledge-Based Systems 32 (2012) 65–75

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nðt Þ p Gw i ! hSnðt Þ i X : hS   v ðxj Þ ¼ GwX v 1j ; v 2j ; . . . v pj 2 hSi

Being Gw the aggregation operator used to combine the information provided by the experts about the alternative xj. There exist different suitable aggregation operators for this process [46–48]. In our proposal the Ordered Weighted Averaging (OWA) [47] operator is used. Definition 4. An OWA operator of dimension n is mapping: F : Rn ? Rn that has an associated weighting vector W of dimension Pn n having the properties wj 2 [0, 1] and i¼1 wj ¼ 1 and such that Pn Fða1 ; . . . ; an Þ ¼ i¼1 wj bj where bj is the jth largest of the ai Fig. 7. Alternatives divided in layers.

Consequently, the ELH associated to the decision framework is defined as:

8n o9 XÞ XÞ t¼mþ1 = [ < Snðt ; . . . ; Snðt m 1 ELH ¼ : : ; nðt  Þ t¼1 fS g

ð6Þ

4.1.2. Information gathering Once the evaluation framework has been fixed, the experts will provide their opinions which indicate the QoS desired regarding each alternative by means of a linguistic preference vector, V, assessed in the n different o scales in the ELH. Let V i ¼ v i1 . . . v iq be a vector of preferences given by the expert ei and v ik 2 SrnðrÞ 2 ELH his/her preference about the alternative, xk. 4.1.3. Computing QoS assessments After the elicitation of experts’ preferences about the alternatives, the decision analysis phase will compute QoS assessments for each alternative according to their opinions. First, the linguistic information is transformed to linguistic 2-tuples by using the function H (see Remark 1):

H : SnðtÞ ! SnðtÞ where

v

i j

¼ Hðv 2 S i jÞ

Once the linguistic information is expressed by linguistic 2-tuples, the QoS assessments are computed following the computational scheme presented in Fig. 4. (i) Unification of multi-granular linguistic information. All the preferences provided by the experts in different linguistic scales of the ELH, are conducted into a unique expression domain, so called t⁄ and the transformation function TF tt is applied as follows (see Definition 3): Þ

where

TF tt

 

v ij

Definition 5. Let ððl1 ; a1 Þ; . . . ; ðlm ; am ÞÞ 2 hSim be a vector of linguistic 2-tuples, and w = (w1, . . . , wm) 2 [0, 1]m be a weighting vector P such that m i¼1 wi ¼ 1. The 2-tuple OWA operator associated with w is the function Gw : hSim ! hSi defined by: w

G ððl1 ; a1 Þ; . . . ; ðlm ; am ÞÞ ¼ Ds

m X

! wi bi

ð7Þ

i¼1

where bi is the ith largest element of fD1 ðl1 ; a1 Þ; ::; D1 ðlm ; am Þg. S S A natural question in the definition of the OWA operator is how to obtain the associated weighting vector. There are different ways to obtain such weights, in Ref. [46] an interesting proposal was introduced to obtain, w, according to the concept of fuzzy majority represented by means of non-decreasing linguistic quantifier, Q, that makes the aggregation process more flexible. Therefore the weighting vector W is computed with [47–49]: Definition 6. A relative linguistic quantifier on a numeric scales is a function Q : [0, 1] ? [0, 1] defined by:

Q ðxÞ

8 > < 0;

if x 6 a

xa ; > ba

:

1;

if a < x < b if x P b

where a, b 2 [0, 1] and a < b. Q(x) P Q(y) whenever x P y. The weights are determined by:

nðtÞ

TF tt : SnðtÞ ! Snðt

Remark 3. OWA operators satisfy some interesting properties as compensativeness, idempotency, symmetry and monotonicity[47]. Bearing in mind that the information is expressed by means of linguistic 2-tuple. Therefore to aggregate them the 2-tuple OWA operator is used [44].

    nðt Þ ¼ sj ; aj 2 Snðt Þ

wi ¼ Q

    i i1 Q ; m m

i ¼ 1; ::; m

Some examples of non-decreasing relative linguistic quantifiers are:  ‘‘Most’’ with (a, b) = (0.3, 0.8).  ‘‘At least half’’ with (a, b) = (0, 0.5).  ‘‘As many as possible’’ with (a, b) = (0.5, 1). After the quantifier is selected, the process proceeds to calculate the weighting vector, w, used in the aggregation process. According to Definition 5, the 2-tuple OWA operator associated with w is the  nðt  Þ p function Gw i ! hSnðt Þ i is obtained by: X : hS



v ðxj Þ ¼ GwX v 1j ; v 2j ; . . . v pj



¼ Ds

p X

! wi bi

ð8Þ

i¼1

(ii) Aggregation of information. When the information has been  conducted into Snðt Þ an aggregation process is carried out to obtain a QoS assessment,vj, for each alternative, xj, by aggregating its individual assessments:

where b is the ith largest element of n   i    o p 1 1 1 1 2 ðDS v j ; DS v j ; . . . ; DS v j . Therefore it is obtained the QoS assessments,v(xj), for each alternative, xj, by aggregating individual assessments of p experts. Each alternative will be then allo-

S. Gramajo, L. Martı´nez / Knowledge-Based Systems 32 (2012) 65–75

cated according to its QoS assessment in the priority vector in the next phase.

71

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ~; n ~ Þ ¼ ð1=3Þðjy1  n1 j2 þ jy2  n2 j2 þ jy3  n3 j2 Þ d2 ðy which is the Euclidean distance. Eventually the assignment process assigns a priority to each alternative according to the following algorithm:

4.2. Priority assignment process The decision support model aims to prioritize the alternatives to filter and assign a correct bandwidth regarding their necessity in the organization. This phase will assign to each alternative, xj, a priority, pk, based on QoS assessment, v(xj), obtained previously. This assignment is calculated by a classification algorithm based on the closeness between each alternative and the priorities used in the problem. The QoS system will prioritize the traffic of each alternative according to priority assigned.

Algorithm 1: Priorities Allocation to Alternatives 1. function Allocation () 2. load Input (Po);// Priorities considered   p p 3. do P o ¼ po1 ¼ ðap1 ; b 1 ; cp1 Þ; ::; pok ¼ ðapk ; b k ; cpk Þ 2 SP ; o o //It assigns a TFN to each pi 2 P . 

Remark 4. Traffic recognition and classification is done by different technologies that can have different capabilities and benefits. Therefore, classification process in many commercial products or free software may change depending on the standards used [1– 5,50]. The model presented in this contribution supports decision makers regardless the technology used, although we recommend its applicability in Traffic Shaping or DiffServ technologies. First, assignment process defines the priority vector  the priority  P o ¼ po1 ; ::; pok which represents the priorities supported by the QoS system of the organization ‘‘O’’. Each Alternative, xj, will be assigned to a priority, poi 2 Po . The previous assignment is based on the closeness between networking traffic priority and the QoS assessment, v(xj). So far we have used linguistic information to represent the QoS information. The priorities used by the decision support model will be also represented by linguistic terms because it is suitable for this type of problems, e.g., PO 2 SP (e.g., Po = {VeryLow, Low, Medium, VeryHigh, Total}). Second, the assignment process computes the closeness between the QoS assessment, v(xj), and the linguistic priorities, poi . Our proposal uses distance measures between the Triangular Fuzzy Numbers (TFN) that represent both the QoS assessments and the priorities. Different distances could be used like Euclidean [51] and Minkowski [52]. distance. In our proposal we use the latter dealing with TFN distances: ~ ¼ ðy1 ; y2 ; y3 Þ; n ~ ¼ ðn1 ; n2 ; n3 Þ two TFN, the MinDefinition 7. Let y kowski distance is defined as follows:

~; n ~Þ ¼ dp ðy

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p ð1=3Þðjy1  n1 jp þ jy2  n2 jp þ jy3  n3 jp Þ;

ð9Þ

where p P 1 is a distance parameter. It is easy to see that Eq. (9) is a weighted average distance. Moreover, we can draw the following properties: ~ and n ~ are real numbers, (i) If both triangular fuzzy number y ~ ¼ ðy; y; yÞ and n ~ ¼ ðn; n; nÞ, then the Minkowski disi.e., y ~; n ~ Þ is identical to the Euclidean distance, tance dp ðy ~; n ~ Þ ¼ jy  nj. dp ðy ~ and n ~ are identical if (ii) Two both triangular fuzzy numbers y ~; n ~ Þ ¼ 0. and only if Minkowski distance dp ðy ~ be triangular fuzzy numbers. n ~; n ~ and k ~ is closer to y ~ (iii) Let y ~ ~ ~; n ~ Þ 6 dp ðy ~; kÞ. than k if only if dp ðy Eq. (9) may have some common specific forms. For p = 1, it can be rewritten as follows:

~; n ~Þ ¼ ð1=3Þðjy1  n1 j þ jy2  n2 j þ jy3  n3 jÞ d1 ðy which is Hamming distance. For p = 2, Eq. (9) can be rewritten as follows:

TF ttC ðv ðxj ÞÞ;//QoS assessments obtained in 4. transforms V C the decision analysisa. . . 5. for each vC(xj) 2 VC do 6. for each poi 2 Po do

 7 distVector = distanceCalculation poi ; v C ðxj Þ ; 8. end for each 9. allocationTable = min (distVector);//the priority, poi 2 Po , with the shortest distance is assigned to xj 10. end for each 11. end function a In order to calculate distances the results of QoS assessments,v(xj), are transformed to anyoolevel, tc, of original linguistic term set in ELH ¼ St¼m nn nðtX Þ XÞ S1 ; . . . ; Snðt . m t¼1

The output of this algorithm is a table that shows the alternatives correspondent to n o each priority, as Table 1. Being xzwi ; . . . ; xzwj a set of alternatives whose priority is, poz . This classification will be implemented in a traffic shaper (see Fig. 1) to prioritize the network traffic and improve its productivity by ordering its networking traffic. 5. An illustrative example This section shows a simple example about how a company could use the decision support model presented to assign priorities to different network services. 5.1. Application scenario and decision analysis Let us suppose a Company that tries to improve its productivity in networking services. Many times its network has over-requests for resources causing saturation of networking services. Therefore, the use of the proposed decision support model to manage its resources by prioritizing traffic will support the network admin to solve such a problem. 5.1.1. Evaluation framework A set of experts and useful network alternatives in such company are selected. In order to simplify the computations and results without loss generality, let us consider a set of seven experts, E = {e1, e2, e3, e4, e5, e6, e7} that express their preferences regarding a set of alternatives, X = {x1, x2, x3, x4, x5, x6, x7, x8, x9, x10} according to the network model layers (see Fig. 7):

Table 1 Priority allocation for each alternative. P O0

P O1

...

P Ok

fx0wi ; . . . ; x0wj g

fx1wi ; . . . ; x1wj g

...

fxkwi ; . . . ; xkwj g

S. Gramajo, L. Martı´nez / Knowledge-Based Systems 32 (2012) 65–75

72

  CTL (1) UGA. X UGA ¼ xCTL : Differentiated group of users by 1 ; x2 their relevance in the company. (a) xCTL 1 : A group of users who perform important tasks in local network. (b) xCTL 2 : Single users in a local network that make VoIP calls to foreign offices.   ALA (2) ALA. X ALA ¼ xALA Network applications that users must 1 ; x2 use to work. (a) xALA 1 : Messaging services could be taken in different way. (b) xALA 2 : An application like ‘‘remote desktop’’ that is useful to many  management tasks.  TLA 3) TLA. X TLA ¼ xTLA : Here, networking administrator 1 ; x2 could identify TCP-UDP well-known ports to classify network traffic. Usually, the counting of this kind of alternatives might be bigger. (a) xTLA 1 : Let consider FTP remote connections. (b) xTLA 2 : Let consider traffic which destination port is 5432 that is useful toconnect remote databases.  ILA (4) ILA. X ILA ¼ xILA ; x . Many times is necessary to connect 1 2 organization network to other networks by IP addressing. (a) xILA 1 : Let consider traffic with destination is IP 10.10.10. 10/32. (b) xILA 2 : Let consider traffic with destination is IP-Subnet 11.11.11.0/24.   (5) ALM. X ALM ¼ xALM ; xALM . Often, alternatives for layer are not 1 2 enough to classify network traffic in a real case. (a) xALM : Traffic caused by a particular group of users (UGA), 1 destination www.example.org (ALA), TCP port is 80 of internet browsing (TLA) and IP source address is 12.12.x.x (ILA). (b) xALM : Traffic originated by a single user (UGA), destina2 tion www.example2.org (ALA), TCP port is 110 of mail reception (TLA) and IP address be 10.10.x.x (ILA). Therefore a set of alternatives will be;

0

fxUGA;1 ; xUGA;2 g

B fxALA;1 ; xALA;2 g 10 B [ B B fxTLA;1 ; xTLA;2 g X¼ B x¼1 B @ fxILA;1 ; xILA;2 g

1 C C C C C C A

fxALM;1 ; xALM;2 g Note that, the number of alternatives in a real organization would be bigger and they should be correctly explained to users. Each expert will provide their assessments of each alternative. Let us suppose that the experts of E have different degree of knowledge about the alternatives and express their assessments in different linguistic term sets, such as:

Therefore, the ELH that defines the evaluation framework is built as follows:

ELH ¼

4 [ t¼1

(

S5 ; S7 ; S9 ;

)

fS25 g

being t⁄ = 4 the added term set with 25 terms (see Fig. 8) according to ELH rules. The use of the ELH guarantees the accuracy of the CW processes. Thus final results might be expressed in any linguistic term set used by the experts in accurate way.

  S5 ¼ s50 ; s51 ; s52 ; s53 ; s54 ¼

8 5 s0 VeryLowð0; 0; :25Þ > > > > 5 > > < s1 Lowð0; :25; :5Þ

s52 Mediumð:25; :5; :75Þ > > > > s53 Highð:5; :75; 1Þ > > : 5 s4 VeryHighð:75; 1; 1Þ

  S7 ¼ s70 ; s71 ; s72 ; s73 ; s74 ; s75 ; s76 ¼

8 7 s0 Noneð0; 0; :17Þ > > > > s7 VeryLowð0; :17; :33Þ > > 1 > > > 7 > > < s2 Lowð:17; :33; :5Þ s73 > > > > s74 > > > 7 > > s5 > > : 7 s6

Mediumð:33; :5; :67Þ Highð:5; :67; :83Þ VeryHighð:67; :83; :1Þ Perfectð:83; 1; 1Þ

8 9 s0 > > > > s9 > > 1 > > > 9 > s > 2 > > > 9 > s >   < 3 S9 ¼ s90 ; s91 ; s92 ; s93 ; s94 ; s95 ; s96 ; s97 ; s98 ¼ s94 > > > > s95 > > > > > s96 > > > > > s9 > > : 79 s8

Noneð0; 0; :12Þ AlmostNoneð0; :12; :25Þ VeryLowð:12; :25; :37Þ Lowð:25; :37; :5Þ Mediumð:37; :5; :62Þ Highð:5; :62; :75Þ SightlyHighð:62; :75; :87Þ VeryHighð:75; :87; 1Þ Perfectð:87; :1; 1Þ

5.1.2. Information gathering Once the evaluation framework has been fixed, the experts provide their opinions about the alternatives (see Table 2).

e1 ! Management Director ! S5 e2 ! Technical Area Superv isor ! S5 e3 ! Administrativ e Department Superv isor ! S5 e4 ! Employee of ICT Department ! S7 e5 ! Employee of ICT Department ! S7 e6 ! Director of ICT Department ! S9 e7 ! Co  Director of ICT Department ! S9 where S5, S7, S9 are linguistic term sets with five, seven and nine linguistic terms.

  S5 ¼ s50 ; s51 ; s52 ; s53 ; s54   S7 ¼ s70 ; s71 ; s72 ; s73 ; s74 ; s75 ; s76   S9 ¼ s90 ; s91 ; s92 ; s93 ; s94 ; s95 ; s96 ; s97 ; s98

Fig. 8. ELH of 5, 7, 9 and 25 terms.

S. Gramajo, L. Martı´nez / Knowledge-Based Systems 32 (2012) 65–75

5.1.3. Computing QoS assessments According to the computational model of the ELH, the information provided by experts is conducted in the t⁄ level of the ELH, in our case t⁄ = 4, see Table 3. Once the information has been unified, the assessments provided by experts are aggregated by using the OWA operator whose weighting vector, w, for the linguistic quantifier most used in this case (see Table 4), is applied. The QoS assessments obtained are shown in Table 5.

Table 4 Weighting vector. ‘‘most’’ (0, 0, 0.26, 0.29, 0.29, 0.17, 0)

Table 5 QoS assessments.

5.2. Priorities assignment for network services Let us suppose that the network technology used in the company can deal with seven that we model linguistically as follows:

8 o p > > > 0o > > p > > > 1o > > >p  o o o o o o o  < 2o Po ¼ p0 ; p1 ; p2 ; p3 ; p4 ; p5 ; p6 ¼ p3 > > > > po4 > > > > > po5 > > : o p6

73

Noneð0; 0; :17Þ VeryLowð0; :17; :33Þ Lowð:17; :33; :5Þ Mediumð:33; :5; :67Þ

QoS assessments

‘‘most’’ quantifier

v(x1) v(x2) v(x3) v(x4) v(x5) v(x6) v(x7) v(x8) v(x9) v(x10)

(s20, 0.46) (s20, 0.12) (s12, 0.49) (s14, 0.03) (s13, 0.1) (s15, 0.16) (s10, 0.23) (s12, 0.49) (s13, 0.1) (s18, 0.33)

Highð:5; :67; :83Þ AlmostTotalð:67; :83; :1Þ Totalð:83; 1; 1Þ

Table 6 Results in its original linguistic term set.

The QoS assessments, v(xj) (see Table 5) might be transformed to any level of original linguistic term set, l(tC, n(tC)), in oo S nn nðtX Þ nðtX Þ ELH ¼ t¼m . S1 ; . . . ; Sm t¼1



S7 2 ELH



ðs5 ; 0:11Þ ðs5 ; 0:03Þ

TF t7 ðv ðxj ÞÞ TF t7 ðv ðx1 ÞÞ 

TF t7 ðv ðx2 ÞÞ

To facilitate the distance computations process they are transformed to S7 2 ELH (see Table 6). Therefore, by using the priority assignment Algorithm a priority is assigned to each alternative, see Table 7. Consequently, by using the previous priorities a prioritized order is established to planning the network traffic. The priorities assigned to the alternatives will be then implemented in the QoS system of the company with traffic shaping that consists in the identification of network traffic by filters such a priority and assign different types of network traffic to a class. In the illustrative example we have used a smaller set of alternatives than in real world problems to make it more understandable. However in such real problems with more alternatives their



TF t7 ðv ðx3 ÞÞ

ðs3 ; 0:1Þ ðs4 ; 0:49Þ

 TF t7 ð  TF t7 ð t TF 7 ð  TF t7 ð t TF 7 ð  TF t7 ð t TF 7 ð

v ðx4 ÞÞ v ðx5 ÞÞ v ðx6 ÞÞ v ðx7 ÞÞ v ðx8 ÞÞ v ðx9 ÞÞ v ðx10 ÞÞ

ðs3 ; 0:23Þ ðs4 ; 0:29Þ ðs3 ; 0:44Þ ðs3 ; 0:1Þ ðs3 ; 0:23Þ ðs4 ; 0:42Þ

classification tends to be more distributed in different priorities and if necessary a finer discrimination may be carried out by using

Table 2 Assessments for each alternative.

v 1k 2 S51 v 2k 2 S51 v 3k 2 S51 v 4k 2 S72 v 5k 2 S72 v 6k 2 S93 v 7k 2 S93

x1

x2

x3

x4

x5

x6

x7

x8

x9

x10

v 11 ¼ s54 v 21 ¼ s54 v 31 ¼ s53 v 41 ¼ s74 v 51 ¼ s75 v 61 ¼ s96 v 71 ¼ s97

v 12 ¼ s53 v 22 ¼ s54 v 32 ¼ s53 v 42 ¼ s75 v 52 ¼ s75 v 62 ¼ s97 v 72 ¼ s98

v 13 ¼ s52 v 23 ¼ s53 v 33 ¼ s52 v 43 ¼ s72 v 53 ¼ s73 v 63 ¼ s93 v 73 ¼ s94

v 14 ¼ s53 v 24 ¼ s52 v 34 ¼ s51 v 44 ¼ s73 v 54 ¼ s74 v 64 ¼ s96 v 74 ¼ s95

v 15 ¼ s52 v 25 ¼ s53 v 35 ¼ s52 v 45 ¼ s73 v 55 ¼ s74 v 65 ¼ s95 v 75 ¼ s94

v 16 ¼ s54 v 26 ¼ s52 v 36 ¼ s53 v 46 ¼ s74 v 56 ¼ s73 v 66 ¼ s96 v 76 ¼ s94

v 17 ¼ s51 v 27 ¼ s51 v 37 ¼ s52 v 47 ¼ s74 v 57 ¼ s73 v 67 ¼ s93 v 77 ¼ s94

v 18 ¼ s52 v 28 ¼ s52 v 38 ¼ s52 v 48 ¼ s73 v 58 ¼ s72 v 68 ¼ s94 v 78 ¼ s93

v 19 ¼ s51 v 29 ¼ s52 v 39 ¼ s52 v 49 ¼ s74 v 59 ¼ s73 v 69 ¼ s95 v 79 ¼ s96

v 110 ¼ s53 v 210 ¼ s54 v 310 ¼ s53 v 410 ¼ s75 v 510 ¼ s73 v 610 ¼ s95 v 710 ¼ s96

Table 3 Assessments conducted in t⁄.

v v v v v v v

 1k  2k  3k  4k  5k  6k  7k

x1

x2

x3

x4

x5

x6

x7

x8

x9

nðtÞ

2S

(s24, 0)

(s18, 0)

(s12, 0)

(s18, 0)

(s12, 0)

(s24, 0)

(s6, 0)

(s12, 0)

(s6, 0)

x10 (s18, 0)

2 SnðtÞ

(s24, 0)

(s24, 0)

(s18, 0)

(s12, 0)

(s18, 0)

(s12, 0)

(s6, 0)

(s12, 0)

(s12, 0)

(s24, 0)

2 SnðtÞ

(s18, 0)

(s18, 0)

(s12, 0)

(s6, 0)

(s12, 0)

(s18, 0)

(s12, 0)

(s12, 0)

(s12, 0)

(s18, 0)

2 SnðtÞ

(s16, 0)

(s20, 0)

(s8, 0)

(s12, 0)

(s12, 0)

(s16, 0)

(s16, 0)

(s12, 0)

(s16, 0)

(s20, 0)

2 SnðtÞ

(s20, 0)

(s20, 0)

(s12, 0)

(s16, 0)

(s16, 0)

(s12, 0)

(s12, 0)

(s8, 0)

(s12, 0)

(s12, 0)

2 SnðtÞ

(s18, 0)

(s21, 0)

(s9, 0)

(s18, 0)

(s15, 0)

(s18, 0)

(s9, 0)

(s12, 0)

(s15, 0)

(s15, 0)

2 SnðtÞ

(s21, 0)

(s24, 0)

(s12, 0)

(s15, 0)

(s12, 0)

(s12, 0)

(s12, 0)

(s9, 0)

(s18, 0)

(s18, 0)

S. Gramajo, L. Martı´nez / Knowledge-Based Systems 32 (2012) 65–75

74 Table 7 Allocation table for organization ‘‘O’’. po0

po1

po2

po3

po4

po5

x3x5x7 x8x9

x4x6 x10

x1x2

po6

[19] [20]

[21]

the symbolic translation of the values obtained in Table 6 to differentiate the alternatives and avoid large groups of alternatives in each priority.

[22]

[23]

6. Conclusions The QoS for networking is key problem in organizations due to the imbalance demand of resources of the different network services. In this paper a decision support model for QoS in networking that helps to classify and prioritize the network traffic has been proposed. Such a decision support model is based on the opinions of network users that work across the organization and know the necessities of the organization and of the end users. The information used by this model is based on users’ perceptions that involve uncertain and vague information. Therefore, to model and manage this type of information it has been used linguistic information modeled by extended linguistic hierarchies that allow a flexible and accurate way of dealing with linguistic information assessed in multiple linguistic scales. The decision support model computes QoS for each network service that will be used to assign it a priority utilized in a traffic shaper to improve the QoS of the different network services in the organizations.

[24] [25]

[26] [27]

[28]

[29]

[30] [31] [32] [33]

References [1] A. Campbell, C. Aurrecoechea, L. Hauw, A review of QoS architectures, ACM Multimedia Systems Journal 6 (1996) 138–151. [2] T. Szigeti, C. Hattingh, End-to-End QoS Network Design: Quality of Service in LANs, WANs, and VPNs, Cisco Press, Indianapolis, 2004. [3] S. Vegesna, IP Quality of Service, Cisco Press, Indianapolis, 2001. [4] E. Crawley, R. Nair, B. Rajagopalan, H. Sandick, A framework for QoS-based routing in the internet, Request for comments, RFC 2386, 1998. [5] S. Floyd, V. Jacobson, Link-sharing and resource management models for packet networks, IEEE/ACM Transactions on Networking 3 (1995) 365–386. [6] L. Georgiadis, R. Guérin, V. Peris, K. Sivarajan, Efficient network QoS provisioning based on per node traffic shaping, IEEE/ACM Transactions on Networking 4 (4) (1996) 482–501. [7] M.F. Alam, M. Atiquzzaman, M.A. Karim, Traffic shaping next term for MPEG video transmission over the next generation internet, Computer Communications 23 (14-15) (2000) 1336–1348. [8] Y. Wang, J. Wang, F. Tsai, Space priority queue with fuzzy set threshold, Computer Communications 30 (10) (2007) 2301–2310. [9] D. Grossman, New Terminology and Clarifications for Diffserv, Request for comments, RFC 3260, 2002. [10] R.H. Sprague, E.D. Carlson, Building Effective Decision Support Systems, Prentice-Hall, N.J., 1982. [11] N.F. Matsatsinis, Y. Siskos, Intelligent Support Systems for Marketing Decisions, Kluwer Academic Publishers., 2002. [12] E.J. Castellano, L. Martínez, A web-decision support system based on collaborative filtering for academic orientation. Case study of the spanish secondary school, Journal of Universal Computer Science 15 (14) (2009) 2786– 2807. [13] J. Lu, G. Zhang, F. Wu, Team situation awareness using web-based fuzzy group decision support systems, International Journal of Computational Intelligence Systems 1 (1) (2008) 51–60. [14] Y.H. Sun, J. Ma, Z.P. Fan, J. Wang, A group decision support approach to evaluate experts for R&D project selection, IEEE Transactions on Engineering Management 55 (1) (2008) 158–170. [15] P.J. Sánchez, L. Martı´nez, C. Garcı´a, F. Herrera, E. Herrera-Viedma, A fuzzy model to evaluate the suitability of installing an ERP system, Information Sciences 179 (14) (2009) 2333–2341. [16] L. Martínez, D. Ruan, F. Herrera, Computing with words in decision support systems: an overview on models and applications, International Journal of Computational Intelligence Systems (IJCIS) 3 (4) (2010) 382– 395. [17] M. Espinilla, J. Liu, L. Martínez, An extended hierarchical linguistic model for decision-making problems, Computational Intelligence 27 (3) (2011). [18] F. Herrera, L. Martı´nez, A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-

[34]

[35]

[36]

[37]

[38]

[39]

[40] [41]

[42]

[43] [44]

[45]

[46]

[47]

[48]

making, IEEE Transactions on Systems, Man and Cybernetics – Part B: Cybernetics 31 (2) (2001) 227–234. L. Martínez, Sensory evaluation based on linguistic decision analysis, International Journal of Approximated Reasoning 44 (2) (2007) 148–164. L. Martı´nez, M. Espinilla, L.G. Pérez, A linguistic multi-granular sensory evaluation model for olive oil, International Journal of Computer Intelligence Systems 1 (2008) 148–158. R.d. Andrés, M. Espinilla, L. Martı´nez, An extended hierarchical linguistic model for managing integral evaluation, International Journal of Computational Intelligence Systems 3 (4) (2010) 486–500. R.d. Andrés, J.L. García-Lapresta, A multi-granular linguistic model for management decision-making in performance appraisal, Soft Computing 14 (1) (2010) 21–34. R. Braden, E. Zhang, S. Berson, S. Herzog, S. Jamin, Resource ReSerVation Protocol (RSVP), Request for comments, RFC 2205, 1997. E. Rosen, A. Viswanathan, R. Callon, Multiprotocol label switching architecture, Request for comments, RFC 3031, 2001. R. Yavatkar, D. Hoffman, Y. Bernet, F. Baker, F. Speer, SBM (Subnet Bandwidth Manager): a protocol for RSVP-based admission control over IEEE 802-style Networks, Request for comments, RFC 2814, 2000. I.S. 802.1D, IEEE Standard for Local and Metropolitan Area Networks: Media Access Control (MAC) Bridges, IEEE Computer Society and ANSI, 2004. Z. Mammeri, Framework for parameter mapping to provide end-to-end QoS guarantees in IntServ/DiffServ architectures, Computer Communications 28 (9) (2005) 1074–1092. E. Vayias, J. Soldatos, G. Kormentzas, Traffic shaping based on an exponential token bucket for quantitative QoS: implementation and experiments on DiffServ routers, Computer Communications. End-to-End QoS Provisioning Advances 29 (6) (2006) 781–797. B. Gaujal, N. Navet, Traffic shaping in real-time distributed systems: a lowcomplexity approach, Computer Communications 22 (17) (1999) 1562– 1573. L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning. Part I, Information Sciences 8 (3) (1975) 199–249. L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning. part II, Information Sciences 8 (4) (1975) 301–357. L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning. part III, Information Sciences 9 (1) (1975) 43–80. F. Herrera, E. Herrera-Viedma, Linguistic decision analysis: steps for solving decision problems under linguistic information, Fuzzy Sets and Systems 115 (2000) 67–82. G. Bordogna, M. Fedrizzi, G. Pasi, A linguistic modeling of consensus in group decision making based on OWA operators, IEEE Transactions on Systems Man and Cybernetics 27 (1997) 126–132. F. Herrera, E. Herrera-Viedma, L. Martı´nez, A fusion approach for managing multi-granularity linguistic term sets in decision making, Fuzzy Sets and Systems, Fuzzy Sets and Systems 114 (2000) 43–58. C. Porcel, E. Herrera-Viedma, Dealing with incomplete information in a fuzzy linguistic recommender system to disseminate information in university digital libraries, Knowledge-Based Systems 23 (1) (2010) 32–39. P. Liu, F. Jin, X. Zhang, Y. Su, M. Wang, Research on the multi-attribute decision-making under risk with interval probability based on prospect theory and the uncertain linguistic variables, Knowledge-Based Systems 24 (4) (2011) 554–561. L. Martı´nez, L.G. Pérez, M.J. Barranco, A multi-granular linguistic basedcontent recommendation model, International Journal of Intelligent Systems 22 (5) (2007) 419–434. S.L. Chang, R.C. Wang, S.Y. Wang, Applying a direct multi-granularity linguistic and strategy-oriented aggregation approach on the assessment of supply performance, European Journal of Operational Research 177 (2) (2007) 1013– 1025. P.P. Bonissone, K.S. Decker, Uncertainty in Artificial Intelligence, NorthHolland, 1986. P.P. Bonissone, K.S. Decker, Selecting uncertainty calculi and granularity: an experiment in trading-off precision and complexity, Uncertainty in Artificial Intelligence, North-Holland, Amsterdam, 1997. R. Degani, G. Bortolan, The problem of linguistic approximation in clinical decision making, International Journal of Approximate Reasoning 2 (1988) 143–162. M. Delgado, J.L. Verdegay, M.A. Vila, Aggregation operations of linguistic labels, International Journal of Intelligent Systems 2 (1993) 351–370. F. Herrera, L. Martı´nez, A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems 8 (6) (2000) 746– 752. F. Herrera, L. Martı´nez, The 2-tuple linguistic computational model, advantages of its linguistic description, accuracy and consistency, International Journal of Uncertainly, Fuzziness and Knowledge-Based Systems 9 (2001) 33–48. R.R. Yager, P.F. Dimitar, Induced ordered weighted averaging operators, IEEE Transaction on Systems, Man, and Cybernetics – Part. B: Cybernetics 29 (2) (1999) 141–150. R.R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transaction on Systems, Man, and Cybernetics 18 (1998) 183–190. R.R. Yager, J. Kacprzyk, The Ordered Weighted Averaging Operators: Theory and Applications, Kluwer Academic Publishers., Boston, 1997.

S. Gramajo, L. Martı´nez / Knowledge-Based Systems 32 (2012) 65–75 [49] R.R. Yager, Quantifier guided aggregation using OWA operators, International Journal of Intelligent Systems 11 (1) (1996) 49–73. [50] B. Hubert and e. al., Linux Advanced Routing and Traffic Control How-to, 2003. .

75

[51] T.M. Mitchel, Machine Learning, New York, 1997. [52] P.J.F. Groenen, K. Jajuga, Fuzzy clustering with squared Minkowski distances, Fuzzy Sets and Systems 120 (2001) 227–237.