On Complex Extensions and Information Measures of Neutrosophic Hesitant and Picture Fuzzy Sets in Decision Making

Abstract

The objective of this thesis entitled, \On Complex Extensions and Information Measures of Neutrosophic, Hesitant and Picture Fuzzy Sets in Decision Makingquot is tostudy the concept of fuzzy extensions on real and complex planes along with variousapplications in detail. The work presented in this thesis has been carried out inorder to fulfill the objective to propose the notion of cohesive fuzzy set, complexneutrosophic matrix, energy of picture fuzzy graphs with their various importantoperations and applications in the field of decision-making. newline newlineIn literature, the notion of fuzzy sets and its generalized extensions have madea large amount of contribution in the progress of scientific and engineering researcharea. It has large number of applications in the areas (theoretical as well as practical) related to engineering, arts,humanities, computer science, health sciences,life sciences, physical sciences etc due to its ability of dealing with the uncertaintyfactor. In the current work, these concepts have been explained in detail and briefstructure of the format of the presented work is presented below: newline newlineWe have presented the fundamental background of hesitant, neutrosophic, pictureand complex fuzzy sets with their mathematical form, definitions, operations andliterature survey in Chapter 1. newline newlineIn Chapter 2, a novel concept of Cohesive fuzzy set (CHFS) has been proposed as asynchronized generalization from innovative notions of complex fuzzy set and hesitant fuzzy set. We have also studied the relationship and connections between theCohesive Fuzzy Set and Complex Intuitionistic Fuzzy Set along with the validationof the obtained results. Based on the proposed notion, various properties, operationsand identities have been established with their necessary proof. The applications ofCHFS in the process of filtering the signals for getting the reference signal using the necessary Fourier cosine transform (FCT)/inverse FCT and identifying maximum newlinenumber of sunspots in a particular interval under a solar activity have been suitably