Information and Similarity Measures of Intuitionistic Fuzzy and Soft Sets

Abstract

Fuzzy sets introduced by LA Zadeh 1965 provide a flexible framework for handling the uncertain situations containing ambiguity and vagueness Fuzzy sets find applications in several fields such as reliability marketing image processing pattern recognition artificial intelligence etc However fuzzy sets do not handle the situation where the vague incomplete uncertain information involves some degree of hesitation Atanassov 1986 introduced the concept of Intuitionistic Fuzzy Set IFS as a generalization of fuzzy set which is found to be more useful in capturing the vague incomplete or uncertain information that involves some degree of hesitation and applicable in various fields of research newline newlineThe objective of this thesis entitled Information and Similarity Measures of Intuitionistic Fuzzy and Soft Sets is to study new intuitionistic fuzzy information measures similarity measures fuzzy linear regression model intuitionistic fuzzy reliability and complex intuitionistic fuzzy soft sets with their entropies A new R norm Intuitionistic fuzzy entropy and R norm Intuitionistic fuzzy directed divergence measure have been proposed with their proof of validity Computational applications of these information measures in the field of pattern recognition and image thresholding has been proposed with discussion The estimators of regression coefficients have been obtained with the help of fuzzy entropy for the restricted unrestricted fuzzy linear regression model by assigning some weights in the distance function in order to compare the performance of unrestricted estimator and restricted estimator a simulation study has been conducted by using two fundamental criteria of dominancemean squared error matrix and absolute bias new similarity measures for Intuitionistic fuzzy sets and intervalvalued intuitionistic fuzzy sets based on NTV metric along with their weighted form new algorithm for multicriteria group decision making has been provided using the proposed weighted similarity measure in which the weights have been calculated usi