Induced OWA Operator for Group Decision Making Dealing with Extended Comparative Linguistic Expressions with Symbolic Translation

Wen He,Ahmad A Alzahrani,Bapi Dutta,Luis Martínez,Rosa M Rodríguez

doi:10.3390/math9010020

Wen He, Ahmad A Alzahrani + Show 3 more

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https://doi.org/10.3390/math9010020

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Abstract

Nowadays, decision making problems have increased their complexity and a single decision maker cannot handle these problems, with a more diverse and comprehensive view of them being necessary, which results in group decision making (GDM) schemes. The complexity of GDM problems is often due to their inherent uncertainty that is not solved just by using a group. Consequently, different methodologies has been proposed to handle it, in which, the use of the fuzzy linguistic approach stands out. Among the multiple fuzzy linguistic modeling approaches, Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) information has been recently introduced, which enhances classical linguistic modeling that is based on single terms by providing linguistic expressions in a continuous linguistic domain. Its application to decision making is quite promising, but it is necessary to develop enough operators to accomplish aggregation processes in the decision solving scheme. So far, just a small number of aggregation operators have been defined for ELICIT information. Hence, this paper aims at providing new aggregation operators for ELICIT information by developing novel OWA based operators, such as the Induced OWA (IOWA) operator in order to avoid the OWA operator needs of reordering its arguments, because ELICIT information does not have an inherent order due to its fuzzy representation. Our proposal not only consists of extending the definition of an IOWA operator for ELICIT information with crisp weights, but it is also proposed a type-1 IOWA operator for ELICIT information in which both weights and arguments are fuzzy as well as the use of ELICIT information constructing the order inducing variable to reorder the arguments. Additionally, the use of ELICIT information in GDM demands the ability to manage majority based decisions that are better represented in the IOWA operator by linguistic quantifiers. Hence, a majority-driven GDM process for ELICIT information is proposed, which it is the first proposal for fulfilling the majority solving process for GDM while using ELICIT information. Eventually, an illustrative example and a brief comparative analysis are presented in order to show the performance of the proposal and its feasibility.

Highlights

Decision making is an everyday life activity for human beings that range from simple to very complex problems
The fuzzy arithmetic mean operator is a special case of the induced ordered weighted averaging (OWA) (IOWA) operator, we will replace the ELICIT-t1-IOWA operator with the fuzzy arithmetic mean in the current proposal, the ELICIT-I-IOWA operator used will be guided by the previous linguistic quantifiers that were used in previous sections
In this article, when considering that the fuzzy representation of F has no inherent order, where F is the set of all possible ELICIT expressions, we developed the induced OWA (IOWA) operator for ELICIT information

Summary

Introduction

Decision making is an everyday life activity for human beings that range from simple to very complex problems. The increasing complexity of decision making problems that face companies, organizations, and decision makers has made necessary the development of comprehensive frameworks in which multiple views and knowledge about the problem are included [1] Such a type of problems conform the group decision making (GDM) scheme [2], in which collective solutions are chased to make the decision and they are usually defined under high uncertain contexts [3]. To handle such an uncertainty, multiple proposals have been developed in the specialized literature for modeling decision makers’ preferences uncertainties [3,4,5,6,7], in which fuzzy sets theory and the fuzzy linguistic approach have provided successful results in multiple applications to decision making under uncertainty [8,9,10]. The linguistic preference modeling implied the need of operating with linguistic values that have been accomplished by the Computing with Words (CW) methodology [18,19]

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