Fuzzy Stochastic Linear Fractional Programming based on Fuzzy Mathematical Programming

Nasseri, Seyed Hadi; Bavandi, Salim

doi:10.1080/16168658.2019.1612605

Cited by 15 publications

(9 citation statements)

References 19 publications

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“…Let f(x)=(f 1 (x), f 2 (x), …, f m (x) is the vector of partial control criteria that evaluates the operating modes, i.e., the CES operation quality. Values of these criteria depend on x=(x 1 , x 2 , …, x n ), i.e., the vector of operating parameters [13,[32][33][34][35][36]. Assume that this dependence is described by mathematical models developed on the basis of the above method.…”

Section: 3 Statement Of the Optimization Problem For The Control Of Operating Modes Of A Chemical Engineering System In A Fuzzy Environmementioning

confidence: 99%

Methods of constructing models and optimizing the operating modes of a chemical engineering system for the production of benzene in a fuzzy environment

Orazbayev

Orazbayeva

Мakhatova

et al. 2021

EEJET

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The study object: the chemical engineering system for production of benzene and optimization of the system operation modes based on modeling. An approach to the effective solution of problems of optimization of operating modes of real chemical engineering systems was proposed. Since such systems are usually multicriterial and characterized by the fuzziness of initial information, an approach to the development of their models and optimization of their operating modes in a fuzzy environment was proposed. The essence of this approach lies in the construction of mathematical models and optimization of system operation modes based on the system analysis methodology using available information of deterministic, statistical, and fuzzy nature. Statements of the problems of optimization by means of chemical engineering systems in a fuzzy environment have been obtained by modifying various principles of optimality for working in a fuzzy environment. Based on a modification of the principles of maximin and Pareto optimality, a heuristic algorithm for solving the formulated optimization problem was proposed based on the use of knowledge and experience of decision-makers. The proposed method of model construction and an optimization algorithm were implemented in practice when constructing models of benzene and rectification columns of a chemical engineering system of production of benzene when formulating and solving the problem of optimizing their operation modes in a fuzzy environment. Analysis and comparison of optimization results allow us to conclude about the effectiveness of the proposed fuzzy approach to solving optimization problems in a fuzzy environment. As a result of optimization of the benzene production process, the benzene yield increased by 1.45 thousand t or by 1.1 %, the raffinate output volume increased by 0.4 thousand t in conditions of upholding constraints on benzene quality. The proposed approach makes it possible to assess the degree of upholding of fuzzy constraints

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Section: 3 Statement Of the Optimization Problem For The Control Of Operating Modes Of A Chemical Engineering System In A Fuzzy Environmementioning

confidence: 99%

Methods of constructing models and optimizing the operating modes of a chemical engineering system for the production of benzene in a fuzzy environment

Orazbayev

Orazbayeva

Мakhatova

et al. 2021

EEJET

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“…Fuzzy stochastic linear fractional programming based on fuzzy mathematical programming is suggested in the paper [19]. This method provides the solution for the stochastic linear programming with fuzzy coefficients, but different approaches need to be used for reducing the model into single-objective linear programming (LP) problem.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

A novel approach for solving decision-making problems with stochastic linear-fractional models

Laith

Al-Salih

Habeeb

2021

EEJET

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Stochastic chance-constrained optimization has a wide range of real-world applications. In some real-world applications, the decision-maker has to formulate the problem as a fractional model where some or all of the coefficients are random variables with joint probability distribution. Therefore, these types of problems can deal with bi-objective problems and reflect system efficiency. In this paper, we present a novel approach to formulate and solve stochastic chance-constrained linear fractional programming models. This approach is an extension of the deterministic fractional model. The proposed approach, for solving these types of stochastic decision-making problems with the fractional objective function, is constructed using the following two-step procedure. In the first stage, we transform the stochastic linear fractional model into two stochastic linear models using the goal programming approach, where the first goal represents the numerator and the second goal represents the denominator for the stochastic fractional model. The resulting stochastic goal programming problem is formulated. The second stage implies solving stochastic goal programming problem, by replacing the stochastic parameters of the model with their expectations. The resulting deterministic goal programming problem is built and solved using Win QSB solver. Then, using the optimal value for the first and second goals, the optimal solution for the fractional model is obtained. An example is presented to illustrate our approach, where we assume the stochastic parameters have a uniform distribution. Hence, the proposed approach for solving the stochastic linear fractional model is efficient and easy to implement. The advantage of the proposed approach is the ability to use it for formulating and solving any decision-making problems with the stochastic linear fractional model based on transforming the stochastic linear model to a deterministic linear model, by replacing the stochastic parameters with their corresponding expectations and transforming the deterministic linear fractional model to a deterministic linear model using the goal programming approach

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“…Definition 2.6: Let X and Y be fuzzy random variables. Then the relations '=' and '≤' are defined respectively as follows [21]:…”

Section: Lemma 22mentioning

confidence: 99%

“…Hence, the necessity of dealing with fuzzy random compound environments is created. There has been a good deal of research done in this regard [21]. In this paper, we consider an MCP problem in which the alternatives choices are fuzzy random variables.…”

Section: Introductionmentioning

confidence: 99%

Multi-choice Linear Programming in Fuzzy Random Hybrid Uncertainty Environment and Their Application in Multi-commodity Transportation Problem

Nasseri

Bavandi

2020

Fuzzy Information and Engineering

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In this paper, due to increasing competition in the business world, which makes decision makers dealing with multiple options/ information for optimal decisions on a single task, we will look at multi-choice programming in hybrid fuzzy random environment. Alternative choices multi-choice parameters are considered as fuzzy random variables. By using polynomials interpolation for each multichoice parameter, the model is transformed into a fuzzy random programming problem. Then, to convert this model to its deterministic form, we use the concept of the mean value of fuzzy random variables. Finally, to validate the proposed mathematical operations, we solve a multi-commodity transportation problem with fuzzy random multi-choice parameters.

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Fuzzy Stochastic Linear Fractional Programming based on Fuzzy Mathematical Programming

Cited by 15 publications

References 19 publications

Methods of constructing models and optimizing the operating modes of a chemical engineering system for the production of benzene in a fuzzy environment

Methods of constructing models and optimizing the operating modes of a chemical engineering system for the production of benzene in a fuzzy environment

A novel approach for solving decision-making problems with stochastic linear-fractional models

Multi-choice Linear Programming in Fuzzy Random Hybrid Uncertainty Environment and Their Application in Multi-commodity Transportation Problem

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