New approaches for optimizing standby redundant systems with fuzzy lifetimes

Zhou, Jian; Han, Yulin; Liu, Jing; Pantelous, Athanasios A.

doi:10.1016/j.cie.2018.06.028

Cited by 10 publications

(2 citation statements)

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“…One of the representative form of regular fuzzy interval is the commonly used trapezoidal fuzzy number. Scholars have continued interests in updating the fuzzy simulation of the expected value of functions that contain trapezoidal fuzzy numbers (from [6] to [7]). In this section, to calculate the expected value of a strictly monotone function f of regular fuzzy intervals ξ 1 , ξ 2 , • • • , ξ n , the αoptimistic value ξ sup (α) and α-pessimistic value ξ inf (α) of regular fuzzy intervals are deduced.…”

Section: Extensions To Regular Fuzzy Intervalsmentioning

confidence: 99%

“…In real-life projects, it seems reasonable that measuring the expected values for different functions that contain fuzzy parameters to obtain a general evaluation, like the expected value of the wind speed in [5] or the expected value of the lifetime of a certain product in [6], [7]. For a single fuzzy variable, based on the credibility measure, Xue et al [8] derived a direct formula for calculating the exact expected value of a monotone function of a fuzzy variable with a continuous membership function.…”

Section: Introductionmentioning

confidence: 99%

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On Fuzzy Simulations for Expected Values of Functions of Fuzzy Numbers and Intervals

Liu

Miao

Pantelous

et al. 2021

IEEE Trans. Fuzzy Syst.

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Based on existing fuzzy simulation algorithms, this paper presents two innovative techniques for approximating the expected values of fuzzy numbers' monotone functions, which is of utmost importance in fuzzy optimization literature. In this regard, the stochastic discretization algorithm of is enhanced by updating the discretization procedure for the simulation of the membership function and the calculation formula for the expected values. This is achieved through initiating a novel uniform sampling process and employing a formula for discrete fuzzy numbers, respectively, as the generated membership function in the stochastic discretization algorithm would adversely affect its accuracy to some extent. What is more, considering that the bisection procedure involved in the numerical integration algorithm of Li ( 2015) is time-consuming and also not necessary for the specified types of fuzzy numbers, a special numerical integration algorithm is proposed, which can simplify the simulation procedure by adopting the analytical expressions of α-optimistic values. Subsequently, concerning the extensive applications of regular fuzzy intervals, several theorems are introduced and proved as an extended effort to apply the improved stochastic discretization algorithm and the special numerical integration algorithm to the issues of fuzzy intervals. Throughout the article, a series of numerical experiments are conducted from which the superiority of both the two novel techniques over others are conspicuously displayed in aspects of accuracy, stability, and efficiency.

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Section: Extensions To Regular Fuzzy Intervalsmentioning

confidence: 99%