Multi-granular Linguistic Contexts Research Articles

The 2-Rank Consensus Reaching Model in the Multigranular Linguistic Multiple-Attribute Group Decision-Making

In the multiple-attribute group decision-making (MAGDM), the decision objective is to obtain a complete ranking of the alternatives from best to worst. In the real world, however, obtaining such a complete ranking of alternatives is very time-consuming, and it is sometimes not necessary. There are many MAGDM problems that we need to assign two rank levels only, so as to create a ranking of one subset of alternatives above another subset. This type of MAGDM problem is called a 2-rank MAGDM problem. This paper investigates the 2-rank MAGDM problem under the multigranular linguistic context, and proposes a 2-rank consensus reaching framework with the minimum adjustments. In the consensus reaching framework, a 2-rank selection process is proposed to find the individual and collective 2-rank preference vectors, and a 2-rank consensus reaching process with the minimum adjustments is put forwarded to help decision makers achieve a consensus. To demonstrate the consensus efficiency of the 2-rank consensus reaching model, a comparison analysis between our proposal and the classical MAGDM models is presented. The main improvement of this paper is to provide a flexible framework to constitute a better approximate decision model to real-world MAGDM problems.

Tri-level multi-attribute group decision making based on regret theory in multi-granular linguistic contexts

Tri-level multi-attribute group decision making based on regret theory in multi-granular linguistic contexts

Method of Multiple Attribute Group Decision Making Based on 2-Dimension Interval Type-2 Fuzzy Aggregation Operators with Multi-granularity Linguistic Information

This paper proposes an approach to linguistic multiple attribute group decision-making (MAGDM) problems with 2-dimension multi-granularity linguistic information by adding a subjective imprecise estimation of reliability of the linguistic assessment information for expressing fuzzy information appropriately. To avoid the drawback of traditional transformation functions of multi-granularity linguistic information (MGLI) defined in the basic linguistic term set or 2-tuple linguistic information, in this paper, decision information is fully expressed by using 2-dimension interval type-2 trapezoidal fuzzy number (2DIT2TFN) representation model under multi-granular linguistic contexts. Firstly, the definition, operational laws, and ranking method of 2DIT2TFNs are proposed. Then 2-dimension interval type-2 trapezoidal fuzzy ordered weighted average (2DIT2TFOWA) operator and quasi-2-dimension interval type-2 trapezoidal fuzzy ordered weighted average (quasi-2DIT2TFOWA) operator are put forward. Moreover, we apply new operators to developing approach to MAGDM problem with linguistic term set of different odd cardinalities. Finally, a numerical example related to health management is provided to illustrate the utility and effectiveness of the developed method. We also make comparisons between the methods proposed in this paper and some existing ones to confirm its feasibility and rationality. The main contribution of this paper possesses three points: (1) proposing the 2DIT2TFNs, which can reflect the evaluation on objects more reasonably; (2) developing some new aggregation operators under 2-dimension interval type-2 trapezoidal fuzzy environment; and (3) applying new operators to developing approach to MAGDM problem with MGLI.

A model based on subjective linguistic preference relations for group decision making problems

In a group decision making problem, experts often express their opinions through the so-called preference relations. In recent years, several different definitions of preference relations depending on the framework and the nature of the problem have been introduced. These approaches vary from interval-valued fuzzy preference relations to incomplete fuzzy linguistic preference relations. In this paper, a novel definition of preference relation, the so-called subjective linguistic preference relation, is proposed. These preference relations are based on the concept of subjective evaluations, introduced in the linguistic computational model based on discrete fuzzy numbers. In this framework, the experts have more flexibility to express their opinions and the solid mathematical background of this model is a guarantee of no loss of information. Finally, an example of a multi-expert decision making problem with a hierarchical multi-granular linguistic context is analyzed to illustrate the potential of the proposed method and its advantages with respect to other methods.

Type-1 OWA methodology to consensus reaching processes in multi-granular linguistic contexts

A crucial step in group decision making (GDM) processes is the aggregation of individual opinions with the aim of achieving a “fair” representation of each individual within the group. In multi-granular linguistic contexts where linguistic term sets with common domain but different granularity and/or semantic are used, the methodology widely applied until now requires, prior to the aggregation step, the application of a unification process. The reason for this unification process is the lack of appropriate aggregation operators for directly aggregating uncertain information represented by means of fuzzy sets. With the recent development of the Type-1 Ordered Weighted Averaging (T1OWA) operator, which is able to aggregate fuzzy sets, alternative approaches to multi-granular linguistic GDM problems are possible. Unlike consensus models based on unification processes, this paper presents a new T1OWA based consensus methodology that can directly manage linguistic term sets with different cardinality and/or semantic without the need to perform any transformation to unify the information. Furthermore, the linguistic information could be assumed to be balanced or unbalanced in its mathematical representation, and therefore the new T1OWA approach to consensus is more general in its application than previous consensus reaching processes with muti-granular linguistic information. To test the goodness of the new consensus reaching approach, a comparative study between the T1OWA based consensus model and the unification based consensus model is carried out using six randomly generated GDM problems with balanced multi-granular information. When distance between fuzzy sets used in the T1OWA based approach is defined as the corresponding distance between their centroids, a higher final level of consensus is achieved in four out of the six cases although no significant differences were found between both consensus approaches.

A new linguistic computational model based on discrete fuzzy numbers for computing with words

In recent years, several different linguistic computational models for dealing with linguistic information in processes of computing with words have been proposed. However, until now all of them rely on the special semantics of the linguistic terms, usually fuzzy numbers in the unit interval, and the linguistic aggregation operators are based on aggregation operators in [0,1]. In this paper, a linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is presented ensuring the accuracy and consistency of the model. In this framework, no underlying membership functions are needed and several aggregation operators defined on the set of all discrete fuzzy numbers are presented. These aggregation operators are constructed from aggregation operators defined on a finite chain in accordance with the granularity of the linguistic term set. Finally, an example of a multi-expert decision-making problem in a hierarchical multi-granular linguistic context is given to illustrate the applicability of the proposed method and its advantages.

Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making

This paper deals with multiattribute group decision making (MAGDM) problems with interval-valued 2-tuple linguistic information. First, we introduce some new aggregation operators, such as the interval-valued 2-tuple weighted geometric (IVTWG) operator, the interval-valued 2-tuple ordered weighted geometric (IVTOWG) operator, the generalized interval-valued 2-tuple weighted average (GIVTWA) operator and the generalized interval-valued 2-tuple ordered weighted average (GIVTOWA). Then, we discuss their desired properties and relationships among them. Furthermore, we put forward a new method to determine the weight vector of interval-valued 2-tuple aggregation operator based on the concept of degree of precision. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in dealing with interval-valued 2-tuple linguistic information under multi-granular linguistic contexts.

An Adaptive Consensus Support Model for Group Decision-Making Problems in a Multigranular Fuzzy Linguistic Context

Different consensus models for group decision-making (GDM) problems have been proposed in the literature. However, all of them consider the consensus reaching process a rigid or inflexible one because its behavior remains fixed in all rounds of the consensus process. The aim of this paper is to improve the consensus reaching process in GDM problems defined in multigranular linguistic contexts, i.e., by using linguistic term sets with different cardinality to represent experts' preferences. To do that, we propose an adaptive consensus support system model for this type of decision-making problem, i.e., a process that adapts its behavior to the agreement achieved in each round. This adaptive model increases the convergence toward the consensus and, therefore, reduces the number of rounds to reach it.

A multigranular linguistic content-based recommendation model

Recommendation systems are a clear example of an e-service that helps the users to find the most suitable products they are looking for, according to their preferences, among a vast quantity of information. These preferences are usually related to human perceptions because the customers express their needs, taste, and so forth to find a suitable product. The perceptions are better modeled by means of linguistic information due to the uncertainty involved in this type of information. In this article, we propose a content-based recommendation model that will offer a more flexible context to improve the final recommendations where the preferences provided by the sources will be modeled by means of linguistic variables assessed in different linguistic term sets. The proposal consists of offering a multigranular linguistic context for expressing the preferences instead of forcing users to use a unique scale. Then the content-based recommendation model will look for the most suitable product(s), comparing them with the customer(s) information according to its resemblance. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 419–434, 2007.

A Satisfactory-Oriented Approach to Multiexpert Decision-Making With Linguistic Assessments

This paper proposes a multiexpert decision-making (MEDM) method with linguistic assessments, making use of the notion of random preferences and a so-called satisfactory principle. It is well known that decision-making problems that manage preferences from different experts follow a common resolution scheme composed of two phases: an aggregation phase that combines the individual preferences to obtain a collective preference value for each alternative; and an exploitation phase that orders the collective preferences according to a given criterion, to select the best alternative/s. For our method, instead of using an aggregation operator to obtain a collective preference value, a random preference is defined for each alternative in the aggregation phase. Then, based on a satisfactory principle defined in this paper, that says that it is perfectly satisfactory to select an alternative as the best if its performance is as at least "good" as all the others under the same evaluation scheme, we propose a linguistic choice function to establish a rank ordering among the alternatives. Moreover, we also discuss how this linguistic decision rule can be applied to the MEDM problem in multigranular linguistic contexts. Two application examples taken from the literature are used to illuminate the proposed techniques.

A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making

In those problems that deal with multiple sources of linguistic information we can find problems defined in contexts where the linguistic assessments are assessed in linguistic term sets with different granularity of uncertainty and/or semantics (multigranular linguistic contexts). Different approaches have been developed to manage this type of contexts, that unify the multigranular linguistic information in an unique linguistic term set for an easy management of the information. This normalization process can produce a loss of information and hence a lack of precision in the final results. In this paper, we shall present a type of multigranular linguistic contexts we shall call linguistic hierarchies term sets, such that, when we deal with multigranular linguistic information assessed in these structures we can unify the information assessed in them without loss of information. To do so, we shall use the 2-tuple linguistic representation model. Afterwards we shall develop a linguistic decision model dealing with multigranular linguistic contexts and apply it to a multi-expert decision-making problem.