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Statistical distributions and reliability functions with type-2 fuzzy parameters
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Department of Industrial Engineering TOBB University of Economics and Technology Sogutozu str., 06560 Ankara, Turkey
Department of Statistics Bartin University Kutlubey-Yazicilar campus, 74100 Bartin, Turkey
Department of Statistics Gazi University Teknikokullar str., 06500 Ankara, Turkey
Department of Economic Cybernetics Baku State University Khalilov str. 23, AZ 1148 Baku, Azerbaijan
Publication date: 2019-06-30
Eksploatacja i Niezawodność – Maintenance and Reliability 2019;21(2):268-274
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.
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