Test of Hypotheses on Fuzzy Observations under Fuzzy Ranking and Alpha Cuts

Abstract

This research work examines numerous fuzzy numbers to manage and overcome the uncertainty in statistical data in order to get a reliable conclusion. To achieve these outcomes, fuzzy numbers such as trapezoidal, pentagonal, intuitionistic and hexagonal have been utilised. In different scenarios, interval data, ranks and and#945;-cuts of various fuzzy number types have been utilised. In the first chapter, a concise introduction to fuzzy theory, fuzzy logic, fuzzy sets, random variables, and statistics is provided. In the second chapter, the hypothesis test under the two-sample t-test has been analysed using trapezoidal fuzzy numbers (TrFNs). In the third chapter, the membership function of a pentagonal fuzzy numbers (PFNs) has been explained briefly. In addition to this, the pentagonal fuzzy numbers have been analysed utilising their and#945;-cut intervals through a distinct ranking approach. The fourth chapter is a continuum of the previous chapter, in this chapter, intuitionistic pentagonal fuzzy numbers (IPFNs) have been examined and their and#945;-cuts are utilised to test the hypothesis; furthermore, the rankings of these IPFNs are used to provide some more precise decision. The fifth chapter is a continuum of chapter four where statistical analysis has been used for hexagonal fuzzy numbers (HFNs). Chapter six is connected with rainfall data in which the hypothesis test through all four types of fuzzy numbers has been analysed for a concrete comparative study. newlineKEYWORDS: Test of Hypothesis, TrFNs, PFNs, IPFNs, HFNs, Pivotal Spot, Rank, Euler Line, Samples, Alpha Cut. newline newline