STATISTICAL DISTRIBUTIONS AND RELIABILITY FUNCTIONS WITH TYPE-2 FUZZY PARAMETERS

Khaniyev T., BAŞKIR M. B., GÖKPINAR F., Mirzayev F.

EKSPLOATACJA I NIEZAWODNOSC-MAINTENANCE AND RELIABILITY, cilt.21, sa.2, ss.268-274, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.17531/ein.2019.2.11
  • Dergi Adı: EKSPLOATACJA I NIEZAWODNOSC-MAINTENANCE AND RELIABILITY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.268-274
  • Anahtar Kelimeler: type-2 fuzzy number, type-2 fuzzy parameters, (a,beta)-cuts, fuzzy probability distribution, fuzzy reliability function
  • Gazi Üniversitesi Adresli: Evet

Özet

Type-2 fuzzy sets were initially given by Zadeh as an extension of type-1 fuzzy sets. There is a gnawing 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.