Solving multi-objective fuzzy probabilistic programming problem

Acharya, Srikumar; Ranarahu, Narmada; Dash, J. K.; Acharya, M.

doi:10.3233/ifs-130784

Cited by 11 publications

(4 citation statements)

References 18 publications

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“…[ 27 ] proposed a numerical approach for solving linear fractional programming problem in a fuzzy environment. [ 5 ] presented multi-objective probabilistic fractional programming problem involving two parameters Cauchy distribution. [ 28 ] Studied on probabilistic multi-objective linear fractional programming problems under fuzziness.…”

Section: Literature Surveymentioning

confidence: 99%

“…To get the optimal value of these programming model, it's deterministic equivalent is found by taking the data as continuous random variable [2,3]. Some other researchers [4][5][6][7] proposed a method for stochastic programming problems having multiple-objectives. But, getting the deterministic of probabilistic model is time wastage and even difficult.…”

Section: Literature Surveymentioning

confidence: 99%

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Genetic algorithmic based approach for multiple-objective probabilistic fractional programming problem involving discrete random variables

Belay

Gessesse

2022

PLoS ONE

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This manuscript presents a technique for solving a multiple-objective probabilistic fractional programming problem with discrete random variables. A multiple-objective probabilistic mathematical model is constructed with fractional objectives. In the model, some parameters of coefficients and right hand side parameters of restrictions are assumed as random variables having Pascal and Hyper geometric distributions. The feasibility of probabilistic constraints is checked by means of stochastic simulation. Genetic algorithm approach method is used to obtain the Pareto optimal solution of the proposed model without finding the deterministic model. Genetic algorithm parameters are fixed in all generation. The proposed method is coded by C++ programming language. To illustrate the method, a numerical example and practical example on the case of supply chain management are presented. The result shows that the values of the objective functions are conflicting each other.

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Section: Literature Surveymentioning

confidence: 99%

Section: Literature Surveymentioning

confidence: 99%

Genetic algorithmic based approach for multiple-objective probabilistic fractional programming problem involving discrete random variables

Belay

Gessesse

2022

PLoS ONE

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“…The concept of fuzzy set theory was first introduced by Zadeh [3]. Solution methodology of different types of multi-objective fuzzy probabilistic programming problems have developed by several researchers [4][5][6][7][8][9]. After this motivation, Mendel et al [10] discussed how type-2 fuzzy is different from type-1 fuzzy.…”

Section: Introductionmentioning

confidence: 99%

Type-2 Fuzzy Stochastic Transportation Problem with Gamma Distribution

Chaini

Ranarahu

2023

IJFIS

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The transportation problem in real-life is an uncertain problem. Particularly when goods are transported from the source to destinations with the best transportation setup that satisfies the decision maker's preferences by taking into account the competing objectives/criteria such as maintaining exact relationships between a few linear parameters, such as actual transportation fee/total transportation cost, delivery fee/desired path, total return/total investment, etc. Due to the uncertainty of nature, such a relationship is not deterministic. In this stochastic transportation problem supplies are considered as fuzzy random variables, which follow fuzzy gamma distribution, with shape parameter α and scale parameter β. Here β is a perfectly normal interval type-2 fuzzy random variable. This paper proposes a solution methodology for solving the fuzzy stochastic transportation problem, where fuzziness and randomness occur under one roof. Therefore, we converted it to an equivalent deterministic mathematical programming problem by applying the following two steps. In the first step of the solution procedure, fuzziness is removed by using alpha-cut technique to obtain stochastic transportation problem. In the second step, the stochastic transportation problem is converted to an equivalent crisp transportation problem using the chance constrained technique. This mathematical model is solved by existing methodology or software. In order to illustrate the methodology a case study is provided.

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“…The idea on the fuzz-ifying approach to multi-objective stochastic programming problem were developed by Mohan and Nguyen [20] . Recent developments in fuzzy stochastic problem can be found in (Acharya and Biswal [21] , Sakawa et al [22] , Wang and Watada [23] , Mousavi et al [24] , Sakawa and Matsui [25] , Aiche et al [26] , Acharya et al [27,28] , Li et al [29] ).…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Programming Approach to a Multi-Objective Fuzzy Stochastic Routing and Siting Hazardous Wastes

Dutta¹,

Acharya

Mishra

2020

Self Cite

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The aim of the research article is not only to propose a solution procedure to solve multi-objective fuzzy stochastic programming problem by using genetic-algorithm-based fuzzy programming method, but also to apply the computational techniques for transportation of the hazardous waste materials. In this article, routing and siting problems for nuclear hazardous waste material are studied and solved. The amount of waste materials generated in the nuclear reactors follows normal distribution. The two considered objective functions are about route selection which includes minimum travel time and minimum number of houses along the way, taking the safety measures into consideration. A multi-objective fuzzy stochastic mathematical model is formulated with the above mentioned objective functions and the route selection as the constraints. The proposed solution procedure is illustrated by a numerical example and a case study.

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Solving multi-objective fuzzy probabilistic programming problem

Cited by 11 publications

References 18 publications

Genetic algorithmic based approach for multiple-objective probabilistic fractional programming problem involving discrete random variables

Genetic algorithmic based approach for multiple-objective probabilistic fractional programming problem involving discrete random variables

Type-2 Fuzzy Stochastic Transportation Problem with Gamma Distribution

Fuzzy Programming Approach to a Multi-Objective Fuzzy Stochastic Routing and Siting Hazardous Wastes

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