Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Genetic algorithms + data structures = evolution programs (2nd, extended ed.)
Genetic algorithms + data structures = evolution programs (2nd, extended ed.)
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Simulation and the Monte Carlo Method
Simulation and the Monte Carlo Method
Theory and Practice of Uncertain Programming
Theory and Practice of Uncertain Programming
Multi-item stochastic and fuzzy-stochastic inventory models under two restrictions
Computers and Operations Research
On minimum-risk problems in fuzzy random decision systems
Computers and Operations Research
Toward a generalized theory of uncertainty (GTU): an outline
Information Sciences—Informatics and Computer Science: An International Journal
Standby redundancy optimization problems with fuzzy lifetimes
Computers and Industrial Engineering
A new perspective for optimal portfolio selection with random fuzzy returns
Information Sciences: an International Journal
Information Sciences: an International Journal
Computers and Industrial Engineering
Fuzzy random renewal process with queueing applications
Computers & Mathematics with Applications
Uncertainty Theory
Fuzzy Systems Engineering: Toward Human-Centric Computing
Fuzzy Systems Engineering: Toward Human-Centric Computing
Generalized theory of uncertainty (GTU)-principal concepts and ideas
Computational Statistics & Data Analysis
Recent Advances in Optimal Reliability Allocation
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Expected value of fuzzy variable and fuzzy expected value models
IEEE Transactions on Fuzzy Systems
Some properties of fuzzy random renewal processes
IEEE Transactions on Fuzzy Systems
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Due to subjective judgment, imprecise human knowledge and perception in capturing statistical data, the real data of lifetimes in many systems are both random and fuzzy in nature. Based on the fuzzy random variables that are used to characterize the lifetimes, this paper studies the redundancy allocation problems to a fuzzy random parallel-series system. Two fuzzy random redundancy allocation models (FR-RAM) are developed through reliability maximization and cost minimization, respectively. Some properties of the FR-RAM are obtained, in which an analytical formula of reliability with convex lifetimes is derived and the sensitivity of the reliability is discussed. To solve the FR-RAMs, we first address the computation of reliability. A random simulation method based on the derived analytical formula is proposed to compute the reliability with convex lifetimes. As for the reliability with nonconvex lifetimes, the technique of fuzzy random simulation together with the discretization method of fuzzy random variable is employed to compute the reliability, and a convergence theorem of the fuzzy random simulation is proved. Subsequently, we integrate the computation approaches of the reliability and genetic algorithm (GA) to search for the approximately optimal redundancy allocation of the models. Finally, some numerical examples are provided to illustrate the feasibility of the solution algorithm and quantify its effectiveness.