Search for Author, Title, Keyword
Statistical distributions and reliability functions with type-2 fuzzy parameters
More details
Hide details
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.
Aisbett J, Rickard J T, Morgenthaler D. Multivariate modeling and type-2 fuzzy sets. Fuzzy Sets and Systems 2011; 163(1): 78–95,
Blewitt W, Coupland S, Zhou S M. A novel approach to type-2 fuzzy addition. In 'Proc. FUZZ-IEEE 2007', London, 2007; 1456 – 1461,
Hamrawi H. Type-2 fuzzy alpha-cuts, PhD. Thesis. De Montfort University 2011.
Kardan I, Akbarzadeh-T M R, Akbarzadeh K, Kalani H. Quasi type 2 fuzzy differential equations. Journal of Intelligent & Fuzzy Systems 2017; 32(1): 551–563,
Karnik N N, Mendel J M. Operations on type-2 fuzzy sets. Fuzzy Sets and Systems 2001; 122(2): 327–348,
Tao C W, Taur J S, Chang C W, Chang Y H. Simplified type-2 fuzzy sliding controller for wing rock system. Fuzzy Sets and Systems 2012; 207: 111–129,
Türkşen I B. Type-2 representation and reasoning for CWW. Fuzzy Sets and Systems 2002; 127(1): 17–36,
Wagenknecht M, Hartmann K. Application of fuzzy sets of type-2 to the solution of fuzzy equations systems. Fuzzy Sets and Systems 1988; 25(2): 183–190,
Wu D, Mendel J. Uncertainty measures for interval type-2 fuzzy sets. Information Sciences 2007a; 177(23): 5378–5393,
Wu D, Mendel J. Aggregation using the linguistic weighted average and interval type-2 fuzzy sets. IEEE Transactions on Fuzzy Systems 2007b; 15(6): 1145–1161,
Zadeh L A. The concept of a linguistic variable and its applications in approximate reasoning (I). Information Sciences 1975; 8(3): 199–249,
Cylinder liner wear as a function of selected physicochemical indicators of engine oil
Zbigniew Chmielewski
Combustion Engines
A new structural reliability analysis method in presence of mixed uncertainty variables
Lingfei YOU, Jianguo ZHANG, Xiaosong DU, Jie WU
Chinese Journal of Aeronautics
Computational Method and Simulation of Reliability for Series, Parallel, and k-Out-of-n Systems with Interval Parameters
Yongfeng Fang, Kong Tee, Zhengwei Cheng, Xu Yong, Chengwei Fei
Mathematical Problems in Engineering
On a type-2 fuzzy approach to solution of second-order initial value problem
Selami Bayeğ, Raziye Mert, Ömer Akın, Tahir Khaniyev
Soft Computing
A novel mixed uncertainty support vector machine method for structural reliability analysis
Ling-Fei You, Jian-Guo Zhang, Shuang Zhou, Jie Wu
Acta Mechanica
Multiple Criteria Decision Making with Fuzzy Sets
Mükerrem Başkır, Pelin Toktaş
Reliability assessment of wind turbine generators by fuzzy universal generating function
Tudi Huang, Tangfan Xiahou, Yan-Feng Li, Hua-Ming Qian, Yu Liu, Hong-Zhong Huang
Eksploatacja i Niezawodnosc - Maintenance and Reliability
Entropy Weight-Logarithmic Fuzzy Multiobjective Programming Method for Evaluating Emergency Evacuation in Crowded Places: A Case Study of a University Teaching Building
Zhian Huang, Wei Zhao, Zhenlu Shao, Yukun Gao, Yinghua Zhang, Ziyou Li, Jinyang Li, Qian Xixi
IEEE Access
A novel belief-based QFD-AHP model in interval type-2 fuzzy environment for lean after-sales service in automotive industry
Mukerrem Baskir
International Journal of Lean Six Sigma
The Concept of Reliability Measure of Recuperator in Spray Booth
Piotr Nikończuk, Włodzimierz Rosochacki
Eksploatacja i Niezawodność – Maintenance and Reliability