Probabilistic linguistic fuzzy rough Sets rough matrices and their Applications

Abstract

The objective of this thesis is to propose a novel notion of sigmoid valued probabilistic linguistic hesitant fuzzy rough sets (SVPLHFRS) in a robabilistic linguistic fuzzy rough information system. We establish a new hesitant fuzzy rough set method for solving the multi-attribute group decision making (MAGDM) problem. This thesis also aims to integrate rough set theory with an information system, an assignment model and a wireless sensor network WSN). We envision rough sets as information systems in the game of cricket, using MCDM, rough matrices and assignment model. We induce an idea to select the Best 11 in all three formats (test, odi, and t20i) from two national teams in the game of cricket. We unveil a new connected adjacent dominating set (CADS) algorithm using rough set s reduct technique for minimizing the cardinality of the virtual backbone (VB) and solve the NP-hard problem for semi-graphs . The first chapter is devoted to review the literature on fuzzy sets, rough sets, information systems, semi-graphs and other terms relevant to the newlinedevelopment of the thesis. In chapter 2, we propose a new concept of sigmoid valued probabilistic linguistic hesitant fuzzy rough set (SVPLHFRS) and create a new hesitant fuzzy rough set technique. The main objective of chapter 3 is to create a novel algorithm to newlinetackle the MAGDM problem based on PLTSs and fuzzy rough set approach. Multi - attribute group decision making (MAGDM) algorithm for a comparative iv analysis of our work with the three existing methods are performed to reveal the novelty of SVPLHFRS. newline newline