Information measures and aggregation operators on fuzzy/ intuitionistic fuzzy sets with applications in decision making

Abstract

The work reported in this thesis is a unified attempt in two important research areas, namely, information theoretic measures and aggregation operators under fuzzy and intuitionistic fuzzy set theory. Fuzzy set theory and intuitionistic fuzzy set theory are used for effectively representing / handling vagueness or incomplete information that widely arises in real world problems. In the last few decades, a number of attempts have been made by researchers and practitioners for defining measures associated with vagueness. In chapter 1 of the thesis, a good literature survey of basic and latest relevant work and background material of investigations reported in later chapters is attempted. In chapters 2 to 7, we have introduced new measures associated with vagueness in terms of Entropy, Divergence and Inaccuracy under fuzzy and intuitionistic fuzzy set theory. These measures have been studied in quite some details. Fuzzy sets and intuitionistic fuzzy sets are rich in their properties because of a good number of operations that are defined on them. This has lead to a number of results on these measures and their applications in multiple criteria decision making in the presence of vagueness. Aggregation has come to be recognized as a very general process of combining / fusing several numerical values in one representative value, and aggregation operators performs this operation. In the literature, many aggregation operators have been developed to aggregate numerical (crisp) data. However, in many real world problems, the available data is vague or imprecise and can not be represented in terms of numerical (crisp) values. In general, fuzzy numbers and intuitionistic fuzzy numbers are used for representing such types of data and several aggregation operators have been developed by researchers for combining / fusing these numbers. In chapters 8 and 9 of the thesis, we have developed some new aggregation operators with fuzzy and intuitionistic fuzzy numbers. A characteristic of these operators studied by us is that they take into account prioritization among the aggregated arguments. Based on these operators, we have also developed some decision making algorithms for solving real world decision making problems.