A Fuzzifying Approach to Stochastic Programming

Mohan, Chilukuri K.; Nguyen, Hoang-Phu

doi:10.1007/bf03398512

Cited by 19 publications

(6 citation statements)

References 7 publications

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“…The above-mentioned developments were followed by systematic comparisons between Stochastic Programming and Fuzzy Optimisation [17,38,47]. These comparative studies displayed many similarities and di erences which have been put in good use to deal with some hard stochastic programs through simple and relevant fuzzy optimisation techniques [31,39]. Along the same line, a method for incorporating random variables with exible distribution in a mathematical program was obtained [44].…”

Section: Fuzzy Stochastic Optimisationmentioning

confidence: 99%

“…The transformations given in Table 1, that respectively convert a possibilistic constraintâx6b and a probabilistic constraint Ä ax6 Ä b into deterministic terms are needed in the sequel. Moreover f prob i (i = 3; 4) are procedures that yield a solution of probabilistic program through the two stages method [16] and the random simplex method [31,33], respectively. f prob 5 ÿnds the distribution and the expectation of the optimum of a probabilistic program.…”

Section: Other Special Cases Of the General Constructmentioning

confidence: 99%

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Optimisation under hybrid uncertainty

Luhandjula

2004

Fuzzy Sets and Systems

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Section: Fuzzy Stochastic Optimisationmentioning

confidence: 99%

Section: Other Special Cases Of the General Constructmentioning

confidence: 99%

Optimisation under hybrid uncertainty

Luhandjula

2004

Fuzzy Sets and Systems

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“…We shall focus on three hybrid problems mentioned in the Introduction. For a state of the art in Fuzzy Stochastic Optimisation, the reader is referred to Mohan and Nguyen (1997) and Luhandjula (2004Luhandjula ( , 2006.…”

Section: Problem Formulationmentioning

confidence: 99%

On some optimisation models in a fuzzy-stochastic environment

Luhandjula

Joubert

2010

European Journal of Operational Research

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This paper is on Fuzzy Stochastic Optimisation, an area that is quickly coming to the forefront of mathematical programming under uncertainty. An even stronger motivating factor for the growing interest in this area can be found in the ubiquitous nature of decision problems involving hybrid undeterminacy. More precisely, we consider a range of situations in which random factors and fuzzy information co-occur in an optimisation setting. Related hybrid optimisation models are discussed and converted into deterministic terms through appropriate tools like probabilistic set, uncertain probability, and fuzzy random variable, making good use of uncertainty principles. We also discuss ways to deal with the resulting problems. Numerical examples carried out using class optimisation software demonstrate the efficiency of the proposed approaches. We shall end this article by pointing out some of the challenges that currently occupy researchers in this emerging field.

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“…Extensive discussion on the convex properties of stochastic problems can be found in [16]. Meanwhile, a fuzzy approach to stochastic programming has been presented by Mohan and Nguyen [17]. An interactive fuzzy satisfying method was also developed by Sakawa et al [18].…”

Section: Introductionmentioning

confidence: 99%

A New Methodology for Solving Multiobjective Chance-Constrained Problems: An Application on IoT Systems

Atalay

Pekin

Apaydin

2021

Mathematical Problems in Engineering

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This study presents a newly developed methodology to transform the chance-constrained problem into a deterministic problem and then solving this multiobjective deterministic problem with the proposed method. Chance-constrained problem contains independent gamma random variables that are denoted as a i j . Two methods are proposed to obtain the deterministic equivalent of chance-constrained problem. The first of the methods is directly based on using the distribution, and the second consists of normalizing probabilistic constraints using Lyapunov’s central limit theorem. An algorithm which uses the Global Criterion Method is developed to solve the multiobjective deterministic equivalent of chance-constrained problem. The methodology is applied to a real-life engineering problem that consists of an IoT device and its data sending process. Using Lyapunov’s central limit theorem for large numbers of random variables is found to be more appropriate.

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A Fuzzifying Approach to Stochastic Programming

Cited by 19 publications

References 7 publications

Optimisation under hybrid uncertainty

Optimisation under hybrid uncertainty

On some optimisation models in a fuzzy-stochastic environment

A New Methodology for Solving Multiobjective Chance-Constrained Problems: An Application on IoT Systems

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