Statistical distributions and reliability functions with type-2 fuzzy parameters Rozkłady statystyczne i funkcje niezawodności o parametrach rozmytych typu-2

Xanıyev T., Baskir M. B., GÖKPINAR F., Mirzayev F.

Eksploatacja i Niezawodnosc, vol.21, no.2, pp.268-274, 2019 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.17531/ein.2019.2.11
  • Journal Name: Eksploatacja i Niezawodnosc
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.268-274
  • Keywords: (α,β)-cuts, Fuzzy probability distribution, Fuzzy reliability function, Type-2 fuzzy number, Type-2 fuzzy parameters
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

Type-2 fuzzy sets were initially given by Zadeh as an extension of type-1 fuzzy sets. There is a growing interest in type-2 fuzzy set and its memberships (named secondary memberships) to handle the uncertainty in type-1 fuzzy set and its primary membership values. However, arithmetical operators on type-2 fuzzy sets have computational complexity due to third dimension of these sets. In this study, we present some mathematical operators which can be easily applied to type-2 fuzzy sets and numbers. Also, mathematical functions of type-2 fuzzy numbers are given according to their monotonicity. These functions are adapted to reliability and distribution functions of the random variables with the type-2 fuzzy parameters. These functions are applied to Exponential, Chi-square, Weibull distributions with respect to monotonicity of the parameters of these distributions.