Multi-Objective Probabilistic Fractional Programming Problem Involving Two Parameters Cauchy Distribution

Acharya, Srikumar; Belay, Berhanu; Mishra, Rajashree

doi:10.3846/mma.2019.024

Cited by 8 publications

(5 citation statements)

References 24 publications

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“…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. The paper [20] presented the solution of a probabilistic fractional programming problem, where the parameters of the righthand side constraints follow the Cauchy distribution. Using this method, the stochastic model can be transformed into a deterministic model.…”

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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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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“…However, such type of problems are more complex when the parameters are uncertain. Recently Acharya et al [1] solved multi-objective chance constraint fractional programming problems involving two parameters independent Cauchy random variables.…”

Section: Introductionmentioning

confidence: 99%

Optimizing Chance Constraint Multiple-Objective Fractional Mathematical Programming Problem Involving Dependent Random Variable

BELAY,

ACHARYA

2024

KgJMat

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This manuscript suggests a methodology to solve chance constraint multiple-objective linear fractional mathematical programming problem in which the parameters are dependent random variables to each other. The proposed problem is formulated by taking few of the parameters as continuous dependent random variables. The proposed model cannot be solved directly by using existing methodology. Thus in order to solve the proposed model, an equivalent deterministic model is derived. The procedure to solve the proposed model is accomplished in two main steps. Initially, the proposed multiple-objective chance constraint linear fractional mathematical problem is transformed to deterministic equivalent multiple-objective linear fractional mathematical programming by the help of chance constrained method. In the second step, multiple-objective functions, which consist of fractional functions is solved by using lexicographic programming approach. Finally, an example is mentioned to illustrate the methodology.

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“…In subjective methods, attribute weights are derived from value judgments about attributes given by decision makers (DMs), including eigenvectorbased method [3][4][5][6], weighted averaging or least square method [7][8][9][10], AHP or ANP-based method [11,12], and D-TOPSIS method [13]. And the objective methods determine attribute weights according to objective information (e.g., the information in the decision matrix), such as principal component analysis method [14], entropy method [15,16], and multi-objective programming model-based method [17,18]. Either way, the process of determining attribute weights is not easy.…”

Section: Introductionmentioning

confidence: 99%

A Rule-Based Decision Support Method Combining Variable Precision Rough Set and Stochastic Multi-Objective Acceptability Analysis for Multi-Attribute Decision-Making

Zhu

Liu

Zhang

et al. 2022

Mathematical Problems in Engineering

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In an open environment, the demands of users are diverse and dynamic because users can participate in product design from beginning to end. Owing to this, the disorderly and unplanned participation of users will greatly increase the complexity of multi-attribute decision-making (MADM) in the product design process. In order to ensure the smooth development of the open design process, the decision support model and method need to repeatedly provide decision makers (DMs) with necessary decision support information in a relatively short period of time, which can realize the evaluation of the scheme and improve the utilization efficiency of community resources. However, the process of eliciting preference information is complex, exhausting, inefficient, and time-consuming in existing methods, which will result in a poor decision-making. With the purpose of optimizing the eliciting process in MADM, a rule-based decision support method is proposed in this paper, where the process of eliciting preference information and decision-making are synchronized and guided by pre-extracted decision rules. The rules are deduced from comparison relations on attributes and their outcomes through the combination of variable precision rough set approach (VPRS) and stochastic multi-objective acceptability analysis (SMAA). With the concept of attribute reduction and approximation accuracy in rough set theory, the extracted rules could eliminate redundant attributes and assign the relative priority of preference information. Based on the extracted rules, the multi-attribute decision-making process could be carried out step by step in an orderly manner. In each step, DMs only need to provide partial preference information by non-quantitative statements according to extracted rules. Once the decision result is reliable enough, the eliciting and decision-making process can be terminated promptly. In order to validate the proposed approach, experiments of decision rule extraction are implemented, and the results show that the proposed approach is effective both in the weak rule extraction and the strong rule extraction.

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Multi-Objective Probabilistic Fractional Programming Problem Involving Two Parameters Cauchy Distribution

Cited by 8 publications

References 24 publications

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

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

Optimizing Chance Constraint Multiple-Objective Fractional Mathematical Programming Problem Involving Dependent Random Variable

A Rule-Based Decision Support Method Combining Variable Precision Rough Set and Stochastic Multi-Objective Acceptability Analysis for Multi-Attribute Decision-Making

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