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A fuzzy approach for the intuitionistic multi-objective linear fractional programming problem using a bisection method

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2025年第2期49卷 1-24页

作者： Kara, Nurdan Kocken, Hale Gonce Akdemir, Hande Gunay Natl Def Univ TR-34334 Istanbul Turkiye Yildiz Tech Univ Dept Math Engn TR-34220 Istanbul Turkiye Giresun Univ Dept Math TR-28200 Giresun Turkiye

In this paper, intuitionistic fuzzy multi-objective linear fractional programming problems (IFMOLFPs) with several fractional criteria, including profit/cost, profit/time, or profitability ratio maximization, are considered. Moreover, all parameters, with the exception of the decision variables, are characterized as triangular intuitionistic fuzzy numbers. The component-wise optimization method is employed to transform IFMOLFP into an equivalent crisp multi-objective linear fractional problem. Then, we use an iterative fuzzy methodology that integrates linear programming with a bisection approach. The proposed approach addresses single-objective and real-life multi-objective organizational planning problems, which are approached using various methods in the literature. It is used for non-linear membership functions in solving these problems. Furthermore, the values obtained using the ranking function are compared. Ultimately, the decision-maker selects the most appropriate solution technique based on the weights of the objective functions.

关键词： multi-objective linear programming Fractional programming Fuzzy programming Intuitionistic fuzzy number Bisection method Membership function

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A decentralized coordination algorithm for multi-objective linear programming with block angular structure

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ENGINEERING OPTIMIZATION 2021年第2期53卷 185-205页

作者： Okpoti, Evans Sowah Jeong, In-Jae Hanyang Univ Dept Ind Engn Seoul South Korea

This article considers linear multi-objective programming problems with block angular structure, which are analogous to multi-disciplinary optimization environments where disciplines must collaborate to achieve a common overall goal. In this decentralized environment, a mechanism to guide locally optimized decision makers' solutions to a Pareto-optimal solution without sharing the entire local information is developed. The mechanism is based on an augmented Lagrangian approach to generate a solution and is separated into two phases: phase I determines an ideal point for each of the single objectives and phase II searches for a compromise solution starting from a single ideal point. Theoretical results show that the algorithm converges and the solution generated is Pareto optimal. The algorithm's effectiveness is demonstrated via an illustrative example and a real-world bi-objective re-entrant flow-shop production planning problem. The real-world experimental results showed that the decentralized method had an average 50% better performance compared to other centralized methods.

关键词： Collaborative optimization decentralized coordination multi-objective linear programming block angular structure multi-agent

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Involving Fuzzy Orders for multi-objective linear programming

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MATHEMATICAL MODELLING AND ANALYSIS 2012年第3期17卷 366-382页

作者： Grigorenko, Olga Univ Latvia LV-1002 Riga Latvia

This paper presents a solution approach for multi-objective linear programming problem. We propose to involve fuzzy order relations to describe the objective functions where in "classical" fuzzy approach the membership functions which illustrate how far the concrete point is from the solution of individual problem are studied. Further the global fuzzy order relation is constructed by aggregating the individual fuzzy order relations. Thus the global fuzzy relation contains the information about all objective functions and in the last step we find a maximum in the set of constrains with respect to the global fuzzy order relation. We illustrate this approach by an example.

关键词： multi-objective linear programming fuzzy order relation aggregation of fuzzy relations

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Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach

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APPLIED MATHEMATICAL MODELLING 2010年第9期34卷 2377-2387页

作者： Baky, Ibrahim A. Benha Univ Dept Basic Sci Benha Higher Inst Technol El Kalyoubia Egypt

In this paper, two new algorithms are presented to solve multi-level multi-objective linear programming (ML-MOLP) problems through the fuzzy goal programming (FGP) approach. The membership functions for the defined fuzzy goals of all objective functions at all levels are developed in the model formulation of the problem: so also are the membership functions for vectors of fuzzy goals of the decision variables, controlled by decision makers at the top levels. Then the fuzzy goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtain the most satisfactory solution for all decision makers. The first suggested algorithm groups the membership functions for the defined fuzzy goals of the objective functions at all levels and the decision variables for each level except the lower level of the multi-level problem. The second proposed algorithm lexicographically solves MOLP problems of the ML-MOLP problem by taking into consideration the decisions of the MOLP problems for the upper levels. An illustrative numerical example is given to demonstrate the algorithms. (C) 2009 Elsevier Inc. All rights reserved.

关键词： multi-objective linear programming multi-level programming problems Goal programming Fuzzy programming Fuzzy goal programming

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Solving intuitionistic fuzzy multi-objective linear programming problem and its application in supply chain management

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APPLICATIONS OF MATHEMATICS 2023年第3期68卷 269-287页

作者： Hassanpour, Hassan Hosseinzadeh, Elham Moodi, Mahsa Univ Birjand Dept Math Birjand *** Iran Kosar Univ Bojnord Imam Hassan Hosp Dept Math Arkan Rd Bojnord *** Iran

The aim of this paper is solving an intuitionistic fuzzy multi-objective linear programming problem containing intuitionistic fuzzy parameters, intuitionistic fuzzy maximization/minimization, and intuitionistic fuzzy constraints. To do this, a linear ranking function is used to convert the intuitionistic fuzzy parameters to crisp ones first. Then, linear membership and non-membership functions are used to manipulate intuitionistic fuzzy maximization/minimization and intuitionistic fuzzy constraints. Then, a multi-objective optimization problem is formulated containing maximization of membership functions and minimization of non-membership functions. To solve this problem, the minimax and weighted sum methods are used. Then, the described procedure is summarized as an algorithm to solve the problem, and a numerical example is solved by the proposed method. Finally, to investigate the capability and performance of the model, a supplier selection problem, which is one of the important applications in supply chain management, is solved by the proposed algorithm.

关键词： multi-objective linear programming intuitionistic fuzzy set accuracy function membership function non-membership function supplier selection

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Supplier selection and order allocation problem using a two-phase fuzzy multi-objective linear programming

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APPLIED MATHEMATICAL MODELLING 2013年第22期37卷 9308-9323页

作者： Nazari-Shirkouhi, Salman Shakouri, Hamed Javadi, Babak Keramati, Abbas Univ Tehran Coll Engn Dept Ind Engn Tehran Iran

The aim of this paper is to solve a supplier selection problem under multi-price level and multi-product using interactive two-phase fuzzy multi-objective linear programming (FMOLP) model. The proposed model attempts to simultaneously minimize total purchasing and ordering costs, a number of defective units, and late delivered units ordered from suppliers. The piecewise linear membership functions are applied to represent the decision maker's fuzzy goals for the supplier selection and order allocation problem, and can be resulted in more flexibility via an interactive decision-making process. To demonstrate effectiveness of the proposed model, results of applying the proposed model are shown by a numerical example. The analytical results show that the proposed approach is effective in uncertain environments and provide a reliable decision tool for integrated multi-objective supplier selection problems. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Supplier selection multi-objective linear programming Fuzzy sets multi-price level multi-product

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linear coordination method for fuzzy multi-objective linear programming problems with convex polyhedral membership functions

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INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 2004年第3期12卷 269-285页

作者： Phruksaphanrat, B Ohsato, A Thammasat Univ Fac Engn Dept Ind Engn Pathum Thani 12121 Thailand Nagaoka Univ Technol Dept Management & Informat Syst Sci Nagaoka Niigata 9402188 Japan

A fuzzy multi-objective decision-making with nonlinear membership functions is proposed in this paper by assuming that the decision maker has a fuzzy goal for each objective function. The fuzzy goals can be quantified by convex polyhedral membership functions, which are expressed by linguistic terms. The concept of the convex cone is used to formulate a normalized convex polyhedral penalty function, which can also be considered conversely as a convex polyhedral membership function. The most desirable value of membership functions are selected to be reference membership values of achievement of convex polyhedral membership functions that can be viewed as the extension of the idea of reference point method. The formulated model can be solved by existing linear programming solvers and can find the satisficing solution for the decision maker, which can be derived efficiently from among an M-Pareto optimal solution set together with the trade-off rates between the membership functions. The proposed model uses convex polyhedral membership functions to represent vague aspirations of the decision maker. It enriches the existing satisficing methods for fuzzy multi-objective linear programming in. a more practical way with the effective method based on convex cone.

关键词： linear coordination multi-objective linear programming fuzzy goals linguistic terms convex polyhedral membership functions M-Pareto optimal solutions

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Resource allocation based on context-dependent data envelopment analysis and a multi-objective linear programming approach

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COMPUTERS & INDUSTRIAL ENGINEERING 2016年 101卷 81-90页

作者： Wu, Jie Zhu, Qingyuan An, Qingxian Chu, Junfei Ji, Xiang Univ Sci & Technol China Sch Management Hefei 230026 Anhui Peoples R China Cent S Univ Sch Business Changsha 410083 Hunan Peoples R China Univ Technol Troyes Charles Delaunay Inst Ind Syst Optimizat Lab F-10004 Troyes France Univ Technol Troyes CNRS UMR 6281 F-10004 Troyes France

This paper discusses a mechanism for the allocation of resources among a set of decision making units (DMUs) which are managed by a centralized control unit in an organization. Data envelopment analysis (DEA) and multi-objective linear programming (MOLP) are integrated to deal with this resource allocation problem. Also, context-dependent DEA is introduced to identify the changed production possibility set after resource allocation, which determines the production plans that are feasible with input increase or decrease in general. For the centralized unit, the MOLP approach is proposed to simultaneously maximize total output and effectiveness while minimizing the total allocated variable input consumption. Among these objectives, the effectiveness is determined by the output growth rate for all DMUs, which can reflect the effects obtained by allocating the input resources that are not used up, such as new equipment. In addition, we restrict the production of limited resources to the new most productive scale size (MPSS) region where the DMUs have the best economic characteristics. Finally, an example is employed to illustrate the approach. (C) 2016 Published by Elsevier Ltd.

关键词： Resource allocation Data envelopment analysis multi-objective linear programming Most productive scale size

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A NEW APPROACH FOR SOLVING FULLY FUZZY linear FRACTIONAL programming PROBLEMS USING THE multi-objective linear programming

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RAIRO-OPERATIONS RESEARCH 2017年第1期51卷 285-297页

作者： Das, Sapan Kumar Mandal, Tarni Edalatpanah, S. A. Natl Inst Technol Jamshedpur Dept Math Jamshedpur 831014 Bihar India Ayandegan Inst Higher Educ Dept Appl Math Tonekabon Iran

This paper deals with developing an efficient algorithm for solving the fully fuzzy linear fractional programming problem. To this end, we construct a new method which is obtained from combination of Charnes-Cooper scheme and the multi-objective linear programming problem. Furthermore, the application of the proposed method in real life problems is presented and this method is compared with some existing methods. The numerical experiments and comparative results presented promising results to find the fuzzy optimal solution.

关键词： Fully fuzzy linear programming linear fractional programming linear programming multi-objective linear programming triangular fuzzy number

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On a generalized fuzzy goal optimization for solving fuzzy multi-objective linear programming problems

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2007年第1期18卷 83-97页

作者： Lu, Jie Wu, Fengjie Zhang, Guangquan Univ Technol Sydney Fac Informat Technol Sydney NSW 2007 Australia

Many organizational decision problems can be formulated by multi-objective linear programming (MOLP) models. Referring to the imprecision inherent in human judgments, uncertainty may be incorporated in the parameters of an MOLP model when it is established, which is called a Fuzzy MOLP (FMOLP) problem. What is an optimal solution for an FMOLP problem is the first issue to deal with in this study. The second issue is how to effectively derive an optimal solution for an FMOLP problem since uncertainty is also reflected in a solution process of an FMOLP problem. By introducing three types of comparison of fuzzy numbers and an adjustable satisfactory degree alpha in this study, a new solution concept of FMOLP is given. For handling the second issue, this study develops an interactive fuzzy goal optimization method which provides an interactive fashion with decision makers during their solution process and allows decision makers to give their fuzzy goals in any forms of membership functions. An illustrative example gives the details of the solution concept and the proposed method.

关键词： optimization fuzzy programming multi-objective linear programming interactive decision-making method

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