Applications of Generalized Fuzzy Measures in Various Disciplines and their Hybridization

Abstract

These days, Fuzzy theory and its generalization has become a most popular area of Research. A lot of research has been done from the last three or four decades. This theory and techniques are applicable in those situations, where the exact and clear picture of any decision-making situation is not possible. Fuzzy theory is related with the qualitative aspect of the problem. In almost every branch of sciences, the application of intuitionistic fuzzy set theory is possible. In this thesis, the work has found those situations of daily life activities, where the system can apply the applications of Fuzzy theories. The work done in this thesis is mainly divided into eight parts. newlineChapter 1 is of introduction. Here, the detailed discussion is given about information theory, directed-divergence measure, generalized fuzzy information theory, some decision-making techniques and importance of hybridization along with research objectives. newlineChapter 2 deals with the literature review on some generalizations and developed new measures in intuitionistic fuzzy environment. newlineChapter 3 referred the discussion about, the concept of the directed-divergence and the concept of weightage for measuring the directed-divergence. Then model constructed a new intuitionistic fuzzy directed-divergence measure and have verified its reliability and validity. Therefore the application of this newly developed measure has been done in share market from investment point of view. newlineChapter 4 and 5 deals with the concept of hybridization. In these chapters, some new intuitionistic fuzzy measures have been developed. The comparison between the results of these two measures in different decision-making situations which has been taken from real life situations is also discussed. The result is same in pattern even after applying different intuitionistic fuzzy measures. The application of these newly constructed measures also represents the concept of hybridization. newlineChapter 6 is related to fuzzy rough set theory which is also an important generalization of fuzzy set theory. Rough set theory works on lower bound and upper bound rather than the intuitionistic fuzzy values that range between 0 and 1. In this chapter two similarity measures are applied in newlinecorporate sector especially for the selection of mutual fund. When there is similarity between two functions then people make the use of similarity measure. newlineChapter 7 represent the uncertainity of life during Covid-19 and numerically analyzed that maximum people benefitted through insurance sector. A digitalization growth in insurance sector was recorded during Covid-19. Sanchez s Criteria is used to analyze the system. newlineChapter 8, the last chapter is of conclusion and future scope. The generalization of any measure or function provide some more fruitful results. Some new measures in various generalizations of fuzzy set theory can be constructed. The application of these measures can be done in various disciplines. This work might helpful for the upcoming researchers and scientists and will give newline