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International Conference on Information Communication and Embedded Systems (ICICES)

作者： Biswas, Animesh Bose, Koushik Dewan, Shyamali Univ Kalyani Dept Math Kalyani 741235 W Bengal India Bhairab Ganguly Coll Dept Math Kolkata 700056 India

ISBN: (纸本)9781467357869;9781467357876

This paper presents a fuzzy goal programming procedure to solve multiobjective quadratic bilevel programming problems, where all the parameters involved in objectives of each level decision maker and in system constraints are fuzzily defined. In model formulation process the fuzzy numbers associated with the parameters are described by using the concept of alpha-cut of fuzzy numbers. Then the model is decomposed on the basis of the tolerance limits of fuzzy numbers. Individual decision at each objective at each level is found in isolation to find the fuzzy goals of the objectives. Then a fuzzy goal programming model is developed to minimize the group regret of degree of satisfactions of both the decision makers and to achieve the highest degree (unity) of each of the membership goals for overall benefit of the organization. In the decision process Taylor's series linear approximation technique is applied to make the quadratic membership goals to its equivalent linear form. To establish the efficiency of the proposed approach a numerical example is solved.

关键词： Bilevel programming Quadratic programming multiobjective programming Fuzzy Numbers Fuzzy Goal programming Linear Approximation Technique

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第三章多目标规划(multiobjective programming)

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环境科学丛刊 1987年第11期 16-33页

(一)多目标问题的基本特征真实系统,不论大小,都是多目标和多宗旨的。同时考虑多个目标(或指标)最优化的问题称为多目标优化问题或向量极值问题。

关键词：多目标规划分析者数学规划 multiobjective programming 多目标决策问题决策者决策个体目标值目标函数值目标函数偏差变量

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Deterministic Equivalents for Use in multiobjective, Stochastic programming

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IFAC Proceedings Volumes 1980年第3期13卷 31-40页

作者： A. Goicoechea School of Industrial Engineering and Management Oklahoma State University Stillwater Oklahoma USA

The existence of a decision situation is postulated in which there are p resources to be allocated so that satisfactory levels for q objective functions can be attained. This paper considers a decision situation in the reclamation and management of lands that have been strip-mined for coal. A multiobjective, stochastic technique labeled PROTRADE is suggested to help a decision maker achieve satisfactory levels for several objective functions. Risk enters the problem in the form of random variables in the objective functions. The emphasis is in the development of non normal dctcrministic equivalents for use in multiobjective techniques such as Protrade.

关键词： Non-normal deterministic equivalents stochastic programming multiobjective programming decision analysis coal strip-mining land reclamation management

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A unified approach for fuzzy multiobjective stochastic programming with Cauchy and extreme value distributed fuzzy random variables

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INTELLIGENT DECISION TECHNOLOGIES-NETHERLANDS 2018年第1期12卷 81-91页

作者： De, Arnab Kumar Dewan, Shyamali Biswas, Animesh Govt Coll Engn & Text Technol Dept Math Serampore India Bhairab Ganguly Coll Dept Math Kolkata India Univ Kalyani Dept Math Kalyani 741235 W Bengal India

A new technique for solving fuzzy multiobjective chance constrained programming problems associated with Cauchy distributed and extreme value distributed fuzzy random variables is developed in this paper. The proposed methodology includes both fuzziness and randomness under one roof. At first fuzzy programming model is constructed from the fuzzy probabilistic model applying chance constrained programming methodology and alpha-cuts. Then using the method of defuzzification with probability density function of the corresponding membership functions the fuzzy model is converted into the deterministic one. Afterward by setting the imprecise aspiration level for each of the individual objectives, the membership functions are defined to measure the degree of achievements of the goal levels of the objectives. Finally, a weighted fuzzy goal programming technique is applied to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing under deviational variables in the decision making context. To illustrate the proposed approach, a practical application is considered and solved and then the achieved solution is compared with the other existing technique.

关键词： Chance constrained programming Cauchy distribution defuzzification extreme value distribution fuzzy goal programming fuzzy random variable multiobjective programming

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New Global Semiparametric Sufficient Efficiency Conditions in multiobjective Fractional programming with Generalized (F, b, phi, rho, theta, ) - Univex n-Set Functions

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JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2014年第5-6期17卷 409-431页

作者： Stancu-Minasian, I. M. Stancu, Andreea Madalina Romanian Acad Inst Math Stat & Appl Math Gheorghe Mihoc Caius Iacob Calea 13 Septembrie nr 13 Bucharest 050711 5 Romania

We consider some types of generalized convexity and discuss new global semiparametric sufficient efficiency conditions for a multiobjective fractional programming problem involving n-set functions.

关键词： multiobjective programming n-set function optimality condition generalized convexity fractional programming

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A Fuzzy Goal programming Approach for Quadratic multiobjective Bilevel programming under Fuzzy Environment

A Fuzzy Goal Programming Approach for Quadratic Multiobjecti...

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International Conference on Information Communication and Embedded Systems

作者： Animesh Biswas Koushik Bose Shyamali Dewan Department of Mathematics University of Kalyani Kalyani 741235 India Department of Mathematics Bhairab Ganguly College Belghoria Kolkata 700056 India

ISBN: (纸本)9781467357869

This paper presents a fuzzy goal programming procedure to solve multiobjective quadratic bilevel programming problems, where all the parameters involved in objectives of each level decision maker and in system constraints are fuzzily defined. In model formulation process the fuzzy numbers associated with the parameters are described by using the concept of α-cut of fuzzy numbers. Then the model is decomposed on the basis of the tolerance limits of fuzzy numbers. Individual decision at each objective at each level is found in isolation to find the fuzzy goals of the objectives. Then a fuzzy goal programming model is developed to minimize the group regret of degree of satisfactions of both the decision makers and to achieve the highest degree (unity) of each of the membership goals for overall benefit of the organization. In the decision process Taylor's series linear approximation technique is applied to make the quadratic membership goals to its equivalent linear form. To establish the efficiency of the proposed approach a numerical example is solved.

关键词： Bilevel programming Quadratic programming multiobjective programming Fuzzy Numbers Fuzzy Goal programming Linear Approximation Technique

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On strong KKT type sufficient optimality conditions for nonsmooth multiobjective semi-infinite mathematical programming problems with equilibrium constraints

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OPERATIONS RESEARCH LETTERS 2016年第1期44卷 148-151页

作者： Pandey, Yogendra Mishra, S. K. Banaras Hindu Univ Dept Math Varanasi 221005 Uttar Pradesh India

In this paper, we consider a nonsmooth multiobjective semi-infinite mathematical programming problems with equilibrium constraints (MOSIMPECs). We introduce the concept of Mordukhovich stationary point for the nonsmooth multiobjective semi-infinite mathematical programming problems with equilibrium constraints in terms of the Clarke subdifferentials. Further, we establish that the M-stationary conditions introduced in this paper are strong KKT type sufficient optimality conditions for the nonsmooth multiobjective semi-infinite mathematical programming problems with equilibrium constraints under generalized invexity assumptions. We also illustrate our result with an example. (C) 2016 Published by Elsevier B.V.

关键词： multiobjective programming Mathematical programming problems with equilibrium constraints Optimality conditions Semi-infinite programming Generalized invexity

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An interactive fuzzy satisficing method based on fractile criterion optimization for multiobjective stochastic integer programming problems

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EXPERT SYSTEMS WITH APPLICATIONS 2010年第8期37卷 6012-6017页

作者： Kato, Kosuke Sakawa, Masatoshi Katagiri, Hideki Perkgoz, Cahit Hiroshima Inst Technol Fac Appl Informat Sci Hiroshima 7315193 Japan Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan ASELSAN Inc TR-06172 Yenimahalle Ankara Turkey

In this paper, we focus on multiobjective integer programming problems involving random variable coefficients in objective functions and constraints. Using the concept of chance constrained conditions, such multiobjective stochastic integer programming problems are transformed into deterministic ones based on the fractile criterion optimization model. As a fusion of stochastic programming and fuzzy one, we introduce fuzzy goals representing the ambiguity of the decision maker's judgments into them and define M-theta-efficiency, a new concept of efficient solution, as a fusion of stochastic approaches and fuzzy ones. Then, we construct an interactive fuzzy satisficing method using genetic algorithms to derive a satisficing solution for the decision maker which is guaranteed to be M-theta-efficient by updating the reference membership levels. Finally, the efficiency of the proposed method is demonstrated through numerical experiments. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： multiobjective programming Stochastic programming Fuzzy programming Integer programming Fractile criterion optimization Efficient solution

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Genetic based fuzzy goal programming for multiobjective chance constrained programming problems with continuous random variables

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2006年第2期83卷 171-179页

作者： Jana, R. K. Biswal, M. P. Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

Solution procedure consisting of fuzzy goal programming and stochastic simulation-based genetic algorithm is presented, in this article, to solve multiobjective chance constrained programming problems with continuous random variables in the objective functions and in chance constraints. The fuzzy goal programming formulation of the problem is developed first using the stochastic simulation-based genetic algorithm. Without deriving the deterministic equivalent, chance constraints are used within the genetic process and their feasibilities are checked by the stochastic simulation technique. The problem is then reduced to an ordinary chance constrained programming problem. Again using the stochastic simulation-based genetic algorithm, the highest membership value of each of the membership goal is achieved and thereby the most satisfactory solution is obtained. The proposed procedure is illustrated by a numerical example.

关键词： chance constrained programming fuzzy goal programming multiobjective programming continuous random variable genetic algorithm

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New efficiency conditions for multiobjective interval-valued programming problems

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INFORMATION SCIENCES 2017年 420卷 235-248页

作者： Osuna-Gomez, R. Hernandez-Jimenez, B. Chalco-Cano, Y. Ruiz-Garzon, G. Univ Seville Fac Matemat Dept Estadist & IO C Tarfia S-N E-41012 Seville Spain Univ Pablo Olavide Area Estadist & IO Dept Econ Metodos Cuantitat & H Econ Seville Spain Univ Tarapaca Inst Alta Invest Casilla 7D Arica Chile Univ Cadiz Dept Estadist & IO Campus Jerez Jerez de la Frontera 11405 Spain

In this paper, we focus on necessary and sufficient efficiency conditions for optimization problems with multiple objectives and a feasible set defined by interval-valued functions. A new concept of Fritz-John and Karush-Kuhn-Tucker-type points is introduced for this mathematical programming problem based on the gH-derivative concept. The innovation and importance of these concepts are presented from a practical and computational point of view. The problem is approached directly, without transforming it into a real-valued programming problem, thereby attaining theoretical results that are more powerful and computationally more efficient under weaker hypotheses. We also provide necessary conditions for efficiency, which have been inexistent in the relevant literature to date. The identification of necessary conditions is important for the development of future computational optimization techniques in an interval-valued environment. We introduce new generalized convexity notions for gH-differentiable interval-valued problems which are a generalization of previous concepts and we prove a sufficient efficiency condition based on these concepts. Finally, the efficiency conditions for deterministic programming problems are shown to be particular instances of the results proved in this paper. The theoretical developments are illustrated and justified through several numerical examples. (C) 2017 Elsevier Inc. All rights reserved.

关键词： multiobjective programming Interval-valued functions Generalized Hukuhara differentiability Fritz-John and Karush-Kuhn-Tucker efficiency conditions

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