Measures & Aggregation Operators on Fuzzy/Intuitionistic Fuzzy Soft Sets with Applications to Decision-Making

Abstract

Multiple-criteria or multiattribute decision-making problems are the imperative part of modern decision theory where a set of alternatives has to be assessed against the multiple influential attributes before the best alternative is selected. In a decision-making(DM) process, an important problem is how to express the preference value. Due to the increasing complexity of the socioeconomic environment and the lack of knowledge or the data about the DM problems, it is difficult for the decision maker to give the exact decision as there is always an imprecise, vague or uncertain information. To deal with this, the theory of the fuzzy sets or its extensions such as intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, soft sets, vague sets, type-2 fuzzy sets, etc., are widely used by the researchers so as to minimize the uncertainty level. During the last decades, the researchers are paying more attention to these theories and have successfully applied it to the various situations in the DM process. Among these, an aggregation operator is an important part of the DM which usually takes the form of mathematical function to aggregate all the input individual data into a single one. However, an information measure such as the distance and similarity measures, complementary to each other, are defined to differentiate between the two or more objects. These two measures can be considered as two diverse perspectives of discrimination. The similarity measure utilized to show the proximity whereas the distance measure is utilized to show the contrast between the objects. In the existing theories and their corresponding work, there occur some limitations such as how to set the membership function in each particular object, insufficiency to consider the parameterizations tool, etc., and hence their corresponding analysis does not give the correct decision to the decision-maker. To overcome these limitations, Molodtsov in 1999, took the soft set (SS) theory where the preferences for each alternative is given on different parameters. The advantage of this extended theory is that they are capable of facilitating the descriptions of the real-world situation with the help of their parameterized property. Thus in order to handle the information in a more accurate and certain manner, there is a need to plan/adopt suitable methodologies to solve the DM problems.

The objective of this research work is to develop some new methodologies under the intuitionistic fuzzy soft set (IFSS) environment by utilizing available information and uncertain data. For analyzing this, some aggregation operators and information measures are proposed for solving the problems under the intuitionistic and/or interval-valued IFSS information. The various desirable relations between the proposed measures and operators are studied. Later, based on the proposed measures, an efficient method is developed to solve the multicriteria DM (MCDM) problems in which information related to each alternative is assessed under the consideration of the experts as well as parameters features. The presented approaches are the extensions of the existing studies under the intuitionistic fuzzy set environment. Several real-life practical examples are taken to demonstrate the approach and compared their performance with some of the existing studies.

The present thesis is organized into eleven chapters.