Statistical distributions and reliability functions with type-2 fuzzy parameters
Tahir Khanıyev, Mükerrem Bahar Başkır, Fikri Gökpınar, Farhad Mirzayev · Eksploatacja i Niezawodnosc - Maintenance and Reliability · 2019
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.