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Determination of multi-objective linear programming problem in Interval-Valued Intuitionistic Fuzzy Environment by Considering the Concept of Conflict

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2025年 1-13页

作者： Bharti, Apurwa Mishra, Babita Mahatma Gandhi Cent Univ Dept Math Motihari 845401 Bihar India

In real-life decision-making problems, the decision-maker faces lots of challenges while dealing with objectives that are conflicting in nature. Also, most often the parameters involved in such problems are uncertain and imprecise in nature. Here, through this research we are trying to give a new computational approach to solve an interval-valued intuitionistic fuzzy multi-objective linear programming problem (IV-IF-MOLPP). In this paper, we have considered a multi-objective linear programming problem with conflicting objectives and tried to solve these objectives simultaneously, using the concept of the conflict and non-conflict nature of IV-IF objectives. This concept refers to the relationship between the multiple objectives being optimized simultaneously. This work aims to give a new and effective computational procedure for solving MOLPP in an IV-IF environment. We demonstrate the effectiveness of the proposed method by applying it to a numerical example taken from the paper of "Yucel and Guneri" and show that this methodology performs equally well in terms of results, computational efficiency, and accuracy and also compare the results with the existing method. We have also added comparisons with the recent existing methodologies to showcase the potential of our proposed methodology. The findings of this research can be useful in decision-making processes for complex problems where multiple objectives need to be optimized under uncertainty.

关键词： Interval-valued intuitionistic fuzzy sets Conflict and non-conflict Aspiration level Weighted goal programming multi-objective linear programming problem

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Intuitionistic fuzzy multi-objective linear programming problem with various membership functions

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ANNALS OF OPERATIONS RESEARCH 2018年第1-2期269卷 693-707页

作者： Singh, Sujeet Kumar Yadav, Shiv Prasad Natl Univ Singapore Logist Inst Asia Pacific Singapore 119613 Singapore Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India

This study addresses intuitionistic fuzzy multi-objective linear programming problems using triangular intuitionistic fuzzy numbers with mixed constraints. We convert the problem into single objective fuzzy programming problem. Then using different types of membership functions (linear and nonlinear), we transform the problem into crisp linear/non-linear programming problem, which is solved by suitable crisp programming approaches. The methodology is demonstrated with the help of a numerical example and the usefulness of various membership functions is discussed.

关键词： Intuitionistic fuzzy number Membership function multi-objective linear programming problem

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Fuzzy multi-objective linear programming problem Using DM's Perspective

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INTERNATIONAL JOURNAL OF DECISION SUPPORT SYSTEM TECHNOLOGY 2022年第1期14卷 1-17页

作者： Singh, Vishnu Pratap Deshmukh, Madhura Sharma, Kirti Visvesvaraya Natl Inst Technol Dept Math Nagpur Maharashtra India

In this paper, a two-stage method has been proposed for solving fuzzy multi-objective linear programming problem (FMOLPP) with interval type-2 triangular fuzzy numbers (IT2TFNs) as its coefficients. In the first stage of problem solving, the imprecise nature of the problem has been handled. All technological coefficients given by IT2TFNs are first converted to a closed interval and then the objectives are made crisp by reducing a closed interval into a crisp number, and constraints are made crisp by using the concept of acceptability index. The amount by which a specific constraint can be relaxed is decided by the decision maker, and thus, the problem reduces to a crisp multi-objective linear programming problem (MOLPP). In the second stage of problem solving, the multi-objective nature of the problem is handled by using fuzzy mathematical programming approach. In order to explain the methodology, two numerical examples of the proposed methodology in production planning and diet planning problems have also been worked out in this paper.

关键词： Acceptability Index Fuzzy programming Approach Interval linear programming Interval Type-2 Triangular Fuzzy Numbers multi-objective linear programming problem

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Solving multi-objective linear programming problem by Statistical Averaging Method with the Help of Fuzzy programming Method

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American Journal of Operations Research 2023年第2期13卷 19-32页

作者： Samsun Nahar Marin Akter Md. Abdul Alim Department of Basic Sciences and Humanities University of Asia Pacific Dhaka Bangladesh General Education Department City University Dhaka Bangladesh Department of Mathematics Bangladesh University of Engineering and Technology Dhaka Bangladesh

A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

关键词： Fuzzy programming Method Fuzzy linear programming problem multi-objective linear programming problem Statistical Averaging Method New Statistical Averaging Method

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Solving multi-objective linear Fractional programming problem-First Order Taylor's Series Approximation Approach

Solving Multi-Objective Linear Fractional Programming Proble...

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International Conference on Computational Intelligence, Cyber Security, and Computational Models (ICC3)

作者： Veeramani, C. Sumathi, M. PSG Coll Technol Dept Appl Math & Computat Sci Coimbatore 641004 Tamil Nadu India

ISBN: (纸本)9788132216803;9788132216797

In this paper, a method is proposed for solving multi-objective linear fractional programming (MOLFP) problem. Here, the MOLFP problem is transformed into an equivalent multi-objective linear programming (MOLP) problem. Using the first-order Taylor's series approximation, the MOLFP problem is reduced to single-objective linear programming (LP) problem. Finally, the solution of MOLFP problem is obtained by solving the resultant LP problem. The proposed procedure is verified with the existing methods through the numerical examples.

关键词： linear programming problem multi-objective linear programming problem Taylor's series

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Fuzzy programming Approach for Solving Intuitionistic Fuzzy linear Fractional programming problem

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2016年第2期18卷 263-269页

作者： Singh, Sujeet Kumar Yadav, Shiv Prasad Indian Inst Technol Dept Math Roorkee 247667 Uttar Pradesh India

This paper develops an approach for solving intuitionistic fuzzy linear fractional programming problem (IFLFPP). The cost of the objective function, the resources, and the technological coefficients are taken to be triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming problem (MOLFPP). By using fuzzy mathematical programming approach, the transformed MOLFPP is reduced into a single objective linear programming problem (LPP) which can be solved easily by suitable LPP algorithm. The proposed procedure is illustrated by a numerical example.

关键词： Triangular intuitionistic fuzzy number linear programming problem multi-objective linear programming problem Fuzzy Mathematical programming Membership function

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A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem

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APPLIED MATHEMATICAL MODELLING 2015年第12期39卷 3183-3193页

作者： Ezzati, R. Khorram, E. Enayati, R. Islamic Azad Univ Karaj Branch Dept Math Karaj Iran Amirkabir Univ Technol Fac Math & Comp Sci Tehran Iran

Recently, two new algorithms have been proposed to solve a fully fuzzy linear programming (FFLP) problem by Lotfi et al. [F.H. Lotfi, T. Allahviranloo, M.A. Jondabeha, L. Alizadeh, Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Model. 33 (2009) 3151-31561 and Kumar et al. [A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. Model. 33 (2011) 817-824 In this paper, based on a new lexicographic ordering on triangular fuzzy numbers, a novel algorithm is proposed to solve the FFLP problem by converting it to its equivalent a multi-objective linear programming (MOLP) problem and then it is solved by the lexicographic method. By a theorem, it is shown that the lexicographic optimal solution of MOLP problem can be considered as an optimal solution of the FFLP problem. Then, a simple example and two real problems, as two case studies, will be used to illustrate our algorithm and compare it with the existing methods. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Fully fuzzy linear programming problem multi-objective linear programming problem Lexicographic ordering on triangular fuzzy numbers

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An effective computational attempt for solving fully fuzzy linear programming using MOLP problem

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2019年第2期36卷 59-69页

作者： Ebrahimnejad, Ali Islamic Azad Univ Dept Math Qaemshahr Branch Qaemshahr Iran

This paper is concerned with the solution procedure of a fully fuzzy linear programming (FFLP) problem in which all parameters are represented in terms of triangular fuzzy numbers. According to the existing solution approach and based a new lexicographic ordering on triangular fuzzy numbers, the FFLP problem under consideration is converted into a multi-objective linear programming (MOLP) problem with three-objective functions. This paper provides a new technique for reducing the computational complexity of some current FFLP problems for situations that all imprecise data are represented as nonnegative triangular fuzzy numbers. Finally, using a simple example and one case study the results obtained using the proposed algorithm and those obtained using with the existing methods are compared, demonstrating the reliability and applicability of our algorithm.

关键词： Fully fuzzy linear programming multi-objective linear programming problem lexicographic ordering on triangular fuzzy numbers computational complexity

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Using Goal programming Approach to Solve Fuzzy multi-objective linear Fractional programming problems

Using Goal Programming Approach to Solve Fuzzy Multi-objecti...

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7th IEEE International Conference on Computational Intelligence and Computing Research (ICCIC)

作者： De, P. K. Deb, Moumita Natl Inst Technol Silchar Dept Math Silchar 788010 India

ISBN: (纸本)9781509006120

The aims of the article is to the study fuzzy multi-objective linear fractional programming (FMOLFP) problem by using goal programming approach. At first by using Charnes and Cooper [1] transformation, the FMOLFP problem is transformed to fuzzy multi-objective linear programming (FMOLP) problem. The reduced problem is formulated by goal programming approach to find out the solution of FMOLFP problem. By using our proposed GP approach some pareto optimal solution is obtained for the FMOLFP problem. A numerical example is presented to demonstrate our approach.

关键词： multi-objective linear programming problem Fuzzy multi-objective linear fractional programming problem Goal programming

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Bi-Level linear programming of intuitionistic fuzzy

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SOFT COMPUTING 2021年第13期25卷 8635-8641页

作者： Alessa, Nazek A. Princess Nourah Bint Abdulrahman Univ Dept Math Sci Fac Sci Riyadh Saudi Arabia

In this research paper, we will solve problems of Bi-level linear fractional programming (BL-LFP) by proposing an interactive approach. Based on the imposition of the relationship DM. to obtained adequate solution, DMs will updating the minimal adequate level at upper level permanently, and that is through. Firstly, the decision makers uncertainty is described by introducing the membership function and non-membership function. Secondly, the opting of minimum adequate degree, leads to obtain the adequate solution, with the overall adequate balance considerations among two levels. For more, this paper gives an algorithm of the proposed approach. At the end, we give a numerical example to explain the feasibility of that approach.

关键词： Intuitionistic fuzzy Bi-Level linear Fractional programming Interactive approach multi-objective linear programming problem Satisfying degree

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