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2015 International Conference on Automation,Mechanical Control and Computational Engineering(AMCCE 2015)

作者： Fachao Li Jingduo Jie School of Ecnomics and Management Hebei University of Science and Technology

ISBN: (纸本)9781510803084

Crisp multi-objective programming has been applied successfully in many fields. But in real applications, the decision environment often exists randomness and the objectives are fuzzy. So it is significant and valuable to establish a fuzzy multi-objective programming model under random environment. In this paper, we use fuzzy number to represent the fuzzy events and fuzzy objectives. Firstly, the general formula of effect probability based on continuous distributions is given combined with effect theory, and a special one based on normal distribution is further given. Secondly, an effect probability-based fuzzy multi-objective programming(abbreviated as FMO-EP) model is proposed by regarding fuzzy objectives as fuzzy events. Finally, the effectiveness and interpretability of FMO-EP is proved through a case.

关键词： FMO-EP effect probability multi-objective programming fuzzy number decision

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multi-objective AND GOAL-programming APPROACHES AS A DISTANCE FUNCTION MODEL

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1985年第3期36卷 249-251页

作者： ROMERO, C UNIV CORDOBA CORDOBASPAIN

This note shows that virtually all the multi-objective and goal-programming approaches can be thought of as special cases of a general distance-function model. Although the outcome of this paper cannot be considered completely new, it can, however, help increasing conceptual clarity and precision in future dialogue, showing the actual links between multi-objective programming, goal programming and traditional mathematical programming.

关键词： compromise programming distance functions goal programming multi-objective programming

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On neutrosophic multi-level multi-objective linear programming problem with application in transportation problem

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2023年第2期44卷 2251-2267页

作者： Fathy, E. Ammar, E. Helwan Univ Fac Sci Dept Math Cairo Egypt Tanta Univ Fac Sci Dept Math Tanta Egypt

In this research, we use the harmonic mean technique to present an interactive strategy for addressing neutrosophic multi-level multi-objective linear programming (NMMLP) problems. The coefficients of the objective functions of level decision makers and constraints are represented by neutrosophic numbers. By using the interval programming technique, the NMMLP problem is transformed into two crisp MMLP problems, one of these problems is an MMLP problem with all of its coefficients being upper approximations of neutrosophic numbers, while the other is an MMLP problem with all of its coefficients being lower approximations of neutrosophic numbers. The harmonic mean method is then used to combine the many objectives of each crisp problem into a single objective. Then, a preferred solution for NMMLP problems is obtained by solving the single-objective linear programming problem. An application of our research problem is how to determine the optimality the cost of multi-objective transportation problem with neutrosophic environment. To demonstrate the proposed strategies, numerical examples are solved.

关键词： Neutrosophic number multi-level linear programming multi-objective programming harmonic mean technique

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A new fuzzy clustering algorithm based on multi-objective mathematical programming

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TOP 2015年第1期23卷 168-197页

作者： Sadi-Nezhad, Soheil Khalili-Damghani, Kaveh Norouzi, Ameneh Islamic Azad Univ Sci & Res Branch Dept Ind Engn Tehran Iran Islamic Azad Univ South Tehran Branch Dept Ind Engn Tehran Iran

This paper presents a new fuzzy clustering approach based on an efficient fuzzy distance measurement and multi-objective mathematical programming. As the human intuitions implies, it is not rational to measure the distance between two fuzzy clusters by a crisp measurement. Unfortunately, most of the existing fuzzy clustering approaches, consider the distance between two fuzzy clusters as a crisp value. This will yield a rounding error and is assumed a pitfall. In this paper, an efficient fuzzy distance measurement is developed in order to measure distance between multi-dimensional fuzzy clusters as a fuzzy measure. The triangle fuzzy numbers (TFNs) are used to develop the applicable fuzzy clustering approach. Then, multi-objective mathematical programming is utilized to optimize the center, and left and right spreads of fuzzy clusters which are calculated as TFNs. More formally, the advantages of proposed fuzzy clustering in comparison with existing procedure is (a) developing an efficient fuzzy distance measurement, and (b) optimizing the center and spread of the fuzzy clusters using multi-objective mathematical programming. An illustrative random simulated instance is supplied in order to present the mechanism and calculations of the proposed fuzzy clustering approach. The performance of proposed fuzzy clustering approach is compared with an existing Fuzzy C-means approach in the literature on several benchmark instances. Then, the Error Ratio is defined to compare the performance of both methods and comprehensive statistical analysis and hypothesis test are accomplished to test the performance of both methods. Finally, a real case study, called group decision making multi-possibility multi-choice investment partitioning problem, is discussed in order to illustrate the efficacy and applicability of the proposed approach in real world problems. The proposed approach is straightforward, its quality is as well as existing approach in the literature and its results ar

关键词： Fuzzy clustering Fuzzy distance measurement multi-objective programming Investment selection

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A robust augmented ε-constraint method (AUGMECON-R) for finding exact solutions of multi-objective linear programming problems

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OPERATIONAL RESEARCH 2022年第2期22卷 1291-1332页

作者： Nikas, Alexandros Fountoulakis, Angelos Forouli, Aikaterini Doukas, Haris Natl Tech Univ Athens Sch Elect & Comp Engn Decis Support Syst Lab Iroon Politech 9 Athens 15780 Greece

Systems can be unstructured, uncertain and complex, and their optimisation often requires operational research techniques. In this study, we introduce AUGMECON-R, a robust variant of the augmented epsilon-constraint algorithm, for solving multi-objective linear programming problems, by drawing from the weaknesses of AUGMECON 2, one of the most widely used improvements of the epsilon-constraint method. These weaknesses can be summarised in the ineffective handling of the true nadir points of the objective functions and, most notably, in the significant amount of time required to apply it as more objective functions are added to a problem. We subsequently apply AUGMECON-R in comparison with its predecessor, in both a set of reference problems from the literature and a series of significantly more complex problems of four to six objective functions. Our findings suggest that the proposed method greatly outperforms its predecessor, by solving significantly less models in emphatically less time and allowing easy and timely solution of hard or practically impossible, in terms of time and processing requirements, problems of numerous objective functions. AUGMECON-R, furthermore, solves the limitation of unknown nadir points, by using very low or zero-value lower bounds without surging the time and resources required.

关键词： Augmecon epsilon-constraint multi-objective programming Optimisation Pareto

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Fuzzy goal programming approach to solve fully fuzzy multi-objective quadratic programming problem

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2024年第2期15卷 705-712页

作者： Tadesse, Admasu Acharya, M. M. Acharya, Srikumar Sahoo, Manoranjan KITT Univ Sch Appl Sci Dept Math Bhubaneswar India

The focus of this paper is to suggest a solution methodology for a fully fuzzy multi-objective quadratic programming problem. Solving the provided mathematical model using known classical methods is extremely difficult. To solve the present mathematical programming problem, three major approaches are suggested. In first step, we used arithmetic operations between two fuzzy parameters and variables. The importance is given in the next step to handle fuzzy part of objective functions by ranking functions and after the completion of the second step, the fuzzy part of the fuzzy constraints tackled by the inequality property of between two triangular fuzzy numbers. Finally, the transformed multi-objective quadratic mathematical programming problem is solved using a weighted fuzzy goal programming approach. The final solution of the suggested model is derived using existing methodology and softwares. The working procedures of the proposed method is further discussed using numerical example.

关键词： multi-objective programming Triangular fuzzy number Weighted fuzzy goal programming Fuzzy decision variables Quadratic programming Fuzzy quadratic programming

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A multi-objective Stochastic programming Approach for Project Time, Cost and Quality Trade-off Problem (TCQTP)

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JORDAN JOURNAL OF CIVIL ENGINEERING 2016年第4期10卷 553-563页

作者： Ahadian, Behrooz Veisy, Omid Azizi, Vahid Islamic Azad Univ Dept Ind Engn Najaf Abad Branch Esfahan Iran Univ Tehran Dept Ind Engn Tehran Iran Khajeh Nasir Toosi Univ Technol Fac Ind Engn Tehran Iran

Generally, in project time, cost and quality trade-off problems, the decision maker (DM) has to take different conflicting objectives into account in order to find an optimal solution. In project management literature, many models have been developed for project crashing and project time-cost trade-off, but only a few of them consider quality as an objective. This article employs a chance constrained compromise programming approach (CCCP) to solve the time, cost and quality trade-off problem (TCQTP). The purpose of this paper is to present and test a new model for the project time, cost and quality problem. In fact, we try to find the optimal decrease in cost and duration of activities while maximizing quality under uncertainty conditions. In order to expect more realistic outcomes for the problem of uncertainties in project activities, time should be taken into account. Therefore, we assume the activity duration as a random and normally distributed parameter. An example of a project network, consisting of 6 nodes and 7 activities, is analyzed under different uncertainty levels.

关键词： Project management Chance-constrained compromise programming multi-objective programming Time cost and quality trade-off Linear programming

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Non-smooth multi-objective fractional programming problem involving higher order functions

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INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS 2019年第4期10卷 351-363页

作者： Kharbanda, Pallavi Agarwal, Divya Higher Educ Dept Math Panchkula India Amity Univ Amity Inst Appl Sci Dept Math Noida India

In this paper, a new generalised class of higher order (F, alpha, rho, d)-V-type I function is introduced for a non-smooth multi-objective fractional programming problem involving support functions. The newly defined class extends several known classes in the literature has been justified through a non-trivial example. In the framework of new concept, we determine conditions under which a fractional function becomes higher order (F, alpha, rho, d)-V-type I function and do some computational work to substantiate the analysis. Further, we establish Karush-Kuhn-Tucker type sufficient optimality conditions and derive various duality results for higher order Mond-Weir type and Schaible type dual programs.

关键词： multi-objective programming (F, alpha, rho, d)-V-type I function fractional programming nonlinear programming efficient solution

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Sensitivity in multi-objective programming under homogeneity assumptions

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Journal of multi-Criteria Decision Analysis 1999年第3期8卷 133-138页

作者： Balbás, A. Ballvé, M. Jiménez Guerra, P. Departamento de Economía de la Empresa Universidad Carlos III de Madrid Madrid 126 28903 C/Madrid Spain Departamento de Matemáticas Fundamentales Facultad de Ciencias UNED Madrid 28040 C/Senda del Rey s/n Spain

Duality theory is applied to measure the sensitivity of a multi-objective programming problem. Since the dual problem does not always measure primal sensitivity, the paper states necessary and sufficient conditions (homogeneity conditions) to guarantee the existence and uniqueness of a pair of solutions (primal and dual) such that the dual solution provides the primal sensitivity. © 1999 John Wiley & Sons, Ltd.

关键词： Duality theory Homogeneity assumptions multi-objective programming

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Solution of multi-objective Linear programming Problems in Intuitionistic Fuzzy Environment 2

Solution of Multi-Objective Linear Programming Problems in I...

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2nd International Conference on Soft Computing for Problem Solving (SocProS)

作者： Bharati, S. K. Nishad, A. K. Singh, S. R. Banaras Hindu Univ Dept Math Varanasi 221005 Uttar Pradesh India

ISBN: (纸本)9788132216025;9788132216018

In the paper, we give a new method for solution of multi-objective linear programming problem in intuitionistic fuzzy environment. The method uses computation of the upper bound of a non-membership function in such way that the upper bound of the non-membership function is always less than the upper bound of the membership function of intuitionistic fuzzy number. Further, we also construct membership and non-membership function to maximize membership function and minimize non-membership function so that we can get a more efficient solution of a probabilistic problem by intuitionistic fuzzy approach. The developed method has been illustrated on a problem, and the result has been compared with existing solutions to show its superiority.

关键词： multi-objective programming Positive ideal solution Intuitionistic fuzzy sets Intuitionistic fuzzy optimization

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