Abstract

     In parallel with the development of information and network technology, large amounts of data are being generated by the Internet, and data-driven methodologies are now often being used in decision-making. Recent studies have investigated personalized individual semantics (PIS) in various decision-making contexts to model a fact that words mean different things to different people. However, few studies have investigated PIS in the context of multi-attribute decision-making (MADM). In MADM, in addition to multi-attribute linguistic information, pre-existing classification of the alternatives is always present, which have not been considered in prior research. Most previous studies have simply demonstrated the feasibility of PIS methods with numerical examples using small-scale models, and not with realistic datasets. Therefore, in this study, we propose a data-driven learning model to analyze the PIS of decision makers to support a multi-attribute decision-making model that considers pre-existing classification of the alternatives. Specifically, we first propose a PIS multi-attribute learning function to define a general computation form for comprehensive evaluation of the value of alternatives. Then, considering this pre-existing classification of the alternatives, a PIS learning model is constructed by analyzing the relations between calculated values of alternatives and corresponding class assignments to obtain personalized numerical scales of linguistic terms for a decision maker. Finally, we present a case study based on two datasets and a comparison with other methods to justify the feasibility of the proposed model.

Introduction

     Multi-attribute decision-making (MADM) involves an individual or a group of decision makers selecting an option by evaluating a set of alternatives according to multiple attributes [1,2,3,4]. In realistic MADM problems, decision makers often prefer to use language and linguistic terms to express their preferences for evaluating the objects or alternatives, and such information is conventionally included in multi-attribute linguistic decision matrices to represent their preferences [5].

     This means there is a need for computing with words (CWW) [6,7] when dealing with linguistic preferences in decision making. Obviously, words mean different things to different people [8,9], and type-2 fuzzy sets [8] are commonly used to deal with this issue in CWW. The CWW model of type-2 fuzzy sets is a useful tool to deal with multiple meanings, but this model does not represent specific semantics for individuals. For example, if a family with three members wants to buy a car, perhaps the members of the family all think the car is “good”. However, the numerical decision-making meaning of the word “good” might be accurately represented as 0.9 for one member, and 0.7 for the other two members. This reflects PIS among the three members. Porro et al. [10] proposed the concept of perceptual maps to represent the differences between the decision makers’ semantics of linguistic terms in MADM. Recently, Li et al.

Conclusions

     In this study, considering the fact that words mean different things to different people, we propose a PIS learning method for DD-LMADM based on multi-attribute linguistic information and information on the classification of alternatives. The proposed model starts with a PIS multi-attribute learning function to provide a general computation form for evaluating the comprehensive values of alternatives in LMADM models; based on this function, we propose a data-driven PIS learning model that considers the distinct linguistic term sets and the unknown weights associated with the criteria to calculate the PNS of linguistic terms for decision makers.

     The practical examples with car evaluation datasets and house evaluation datasets illustrate the applicability of the proposed data-driven PIS learning approach. Furthermore, we compare our approach with the existing CWW methods based on a triangular membership function and a 2-tuple linguistic model in terms of the inconsistency between the calculated preference values of alternatives and their class assignment.