Generalized fuzzy and rough sets based models of automata and decision making techniques

Abstract

In recent eras, fuzzy and rough set theories have become very important for handling newlinecomplex real-world systems with uncertainties and insufficient information. Since their newlineinception, several generalizations of these theories have been reported in the literature. newlineThese developments have made fuzzy sets and rough sets more useful and applicable from newlineboth theoretical and practical perspectives and have shown to be useful in mathematics, newlinecomputer science, medical science, decision-making, social sciences, engineering, and newlinetechnology. On the other hand, these two theories have been used together to introduce newlinenotions of fuzzy RSs (FRSs) and rough FSs (RFSs) [71], and even more generalized newlineversions such as hesitant FRSs (HFRSs) [212], and weighted HFRSs (WHRSs) to handle newlineuncertainty and insufficient information of real-world complex systems more effectively newlineand efficiently. newlineThis thesis aims to introduce and study the computing models automata and languages newlinebased on generalized versions of fuzzy and rough sets mentioned above and to develop newlinean algorithm for the use of introduced WHFRSs in decision making. We have shown newlinehow these generalized concepts of FSs and RSs can be applied to the theory of automata newlineand languages, enhancing our understanding of computational processes in uncertain and newlineimprecise environments. newlineThis thesis can be separated into two parts. In the first part, generalized versions of fuzzy newlinesets play key roles and include introductions and study of automata and languages based on newline(i) intuitionistic L-fuzzy sets (ILF-sets) over residuated lattice and use categorical methods newlineto analyze intuitionistic L-fuzzy automata; (ii) typical hesitant fuzzy sets (THFSs) in the newlinecontext of multisets, where we introduce the concept of typical hesitant fuzzy multiset finite newlineautomata (THFMFA) that accepts multiset languages and discuss its minimization process. newline(iii) THFSs in multiset context, here in contrast to case (ii) instead of multiset language we newlineconsidered typical hesitant fuzzy multiset languages (THFMLs)