RESEARCH PAPER
Statistical distributions and reliability functions with type-2 fuzzy parameters
| 1 | Department of Industrial Engineering TOBB University of Economics and Technology Sogutozu str., 06560 Ankara, Turkey |
| 2 | Department of Statistics Bartin University Kutlubey-Yazicilar campus, 74100 Bartin, Turkey |
| 3 | Department of Statistics Gazi University Teknikokullar str., 06500 Ankara, Turkey |
| 4 | 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
KEYWORDS
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.
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