Comparative State-of-the-Art Survey of Classical Fuzzy Set and Intuitionistic Fuzzy Sets in Multi-Criteria Decision Making

Abstract

Fuzzy sets extend deterministic multi-criteria decision-making (MCDM) methods to deal with uncertainty and imprecision in decision making. Over the years, many generalizations have been proposed to the classical Fuzzy sets to deal with different kinds of imprecise and subjective data. One such generalization is Atanassov’s Intuitionistic Fuzzy Set (IFS) which is becoming increasingly popular in MCDM research. Together, the two notions of uncertainty modeling: ‘classical fuzzy set’ (Zadeh) and intuitionistic fuzzy set (Atanassov) have been utilized in many real-world MCDM applications spanning diverse disciplines. As IFS grows in popularity by the day, this paper conducts a literature survey to (1) compare the trend of publications of ‘classical fuzzy’ set theory and its generalized form, the intuitionistic fuzzy set (IFS) as used in MCDM methods from 2000 to 2015; (2) classify their contributions into three novel tracks of applications, hybrid, and extended approaches; (3) determine which MCDM method is the most used together with the two forms of fuzzy modeling; and (4) report on other measures such as leading authors and their country affiliations, yearly scholarly contributions, and the subject areas where most of the two fuzzy notions in MCDM approaches are applied. Finally, the study presents trends and directions as far as the applications of classical fuzzy set and intuitionistic fuzzy sets in MCDM are concerned.