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INTERACTIVE FUZZY DECISION-MAKING FOR multiobjective nonlinear-programming USING AUGMENTED MINIMAX PROBLEMS

FUZZY SETS AND SYSTEMS 1986年第1期20卷 31-43页

作者： SAKAWA, M YANO, H KAGAWA UNIV COLL ECONDEPT INFORMAT SCITAKAMATSUKAGAWA 760JAPAN

An interactive fuzzy decision-making method for solving multiobjective nonlinear programming problems is presented in this paper by assuming that the decision maker (DM) has fuzzy goals for each of the objective functions. The fuzzy goals of the DM are quantified by eliciting corresponding membership functions through the interaction with the DM. Having determined the membership functions, if the DM specifies his reference membership values, the augmented minimax problem is solved and the DM is supplied with the corresponding Pareto-optimal solution together with the trade-off rates between the membership functions. Then by considering the current values of the membership functions as well as the trade-off rates, the DM responds by updating his reference membership values. In this way the compromise or satisficing solution for the DM can be derived efficiently from among a Pareto-optimal solution set. On the basis of the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the computer outputs.

关键词： multiobjective nonlinear programming Interactive decision making Fuzzy goals Membership functions Pareto-optimal solutions Interactive computer programs

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Stability achievement scalarization function for multiobjective nonlinear programming problems

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APPLIED MATHEMATICAL MODELLING 2008年第6期32卷 1044-1055页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Dept Math Tanta Egypt

In this paper, we present a method to determine the stability of nondominated criterion vectors using a modified weighted achievement scalarization metric. This method is based on the application of a particular objective function which scalarizes and parameterizes the original multiobjective nonlinear programming problem. Also, we show that this modified weighted achievement metric coincides with the metric introduced by Choo and Atkins [E.-U. Choo, D.R. Atkins, Proper efficiency in nonconvex multicriteria programming, Math. Oper. Res. 8 (1983) 467-470] and Kaliszewski [L Kaliszewski, A modified weighted Tchebycheff metric for multiple objective programming, Comput. Oper. Res. 14 (1987) 315-323] in cases when sets of all criterion vectors are finite or polyhedral. (c) 2007 Elsevier Inc. All rights reserved.

关键词： multiobjective nonlinear programming achievement scalarization function nondominated solutions stability

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STABILITY OF multiobjective nonlinear-programming PROBLEMS WITH FUZZY PARAMETERS IN THE CONSTRAINTS

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FUZZY SETS AND SYSTEMS 1995年第3期74卷 343-351页

作者： KASSEM, MAE AMMAR, EI Department of Mathematics Faculty of Science Tanta University Tanta Egypt

This paper deals with the stability of multiobjective nonlinear programming problems with fuzzy parameters in the constraint functions. These fuzzy parameters are characterized by fuzzy numbers. Qualitative and quantitative analysis of the basic notions like the set of feasible parameters, the solvability set, the stability sets of the first kind and of the second kind, will be reformulated under the concept of alpha-pareto optimality. An illustrative example is given to clarify the obtained results.

关键词： multiobjective nonlinear programming STABILITY PARAMETRIC ANALYSIS FUZZY programming FUZZY NUMBERS ALPHA-PARETO OPTIMALITY

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Interactive stability cutting-plane algorithm for multiobjective nonlinear programming problems

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APPLIED MATHEMATICS AND COMPUTATION 2007年第2期192卷 446-456页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Dept Math Tanta Egypt

In this paper, we introduce an interactive stability cutting-plane algorithm for determining a best-compromise solution to a multiobjective nonlinear programming problems in situations with an implicitly defined utility function. The method is called "interactive stability cutting-plane compromise programming (ISCPCP)". The cutting-planes which I am going to derive, are based on suitable pairwise trade-offs between the objective functions, as prescribed by the decision maker (DM) at each iterate generated by the algorithm. This algorithm requires no line searches, and generates iterates that are all contained in the efficient frontier. This feature facilitates the preference judgment of the decision maker, and permits an analyst to terminate short of optimality with an efficient near-optimal solution. Also, we investigate the stability of its efficient solutions which are obtained by using this algorithm. An illustrating example is presented to clarify this algorithm. (C) 2007 Elsevier Inc. All rights reserved.

关键词： cutting-plane algorithm multiobjective nonlinear programming trade-off method best-compromise solution stability

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Stability of multiobjective nonlinear programming problems with random variables in the objective functions

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FUZZY SETS AND SYSTEMS 1999年第2期102卷 247-252页

作者： Kassem, MAEH Tanta Univ Fac Sci Dept Math Tanta Egypt

This paper deals with multiobjective nonlinear programming problems with random variables in the objective functions. These random variables are characterized by possibility density functions. The existing results concerning the qualitative analysis of basic notions in parametric nonlinear programming problems are reformulated to study the stability sets of the first, second, third and fourth kind for multiobjective nonlinear programming problems under the concept of a-possibility efficient. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： multiobjective nonlinear programming random variables stability parametric programming

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Interactive Fuzzy Goal programming Based on Taylor Series to Solve multiobjective nonlinear programming Problems With Interval Type-2 Fuzzy Numbers

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2018年第4期26卷 2434-2449页

作者： Dalman, Hasan Bayram, Mustafa Istanbul Gelisim Univ Dept Comp Engn TR-34310 Istanbul Turkey

This paper presents an interactive fuzzy goal programming (FGP) approach for solving multiobjective nonlinear programming problems (MONLPP) with interval type-2 fuzzy numbers (IT2 FNs). The cost and time of the objective functions, the resources, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered problem is first transformed into an equivalent crisp MONLPP, and then the transformed MONLPP is converted into an equivalent multiobjective linear programming problem. By using a procedure based on Taylor series, this problem is reduced into a single objective linear programming problem that can be easily solved by Maple 2017 optimization toolbox. Finally, the proposed solution procedure is illustrated by two numerical examples.

关键词： Fuzzy goal programming (FGP) interactive approach interval type-2 (IT2) fuzzy sets multiobjective nonlinear programming Taylor series

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A FUZZY DUAL DECOMPOSITION METHOD FOR LARGE-SCALE multiobjective nonlinear-programming PROBLEMS

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FUZZY SETS AND SYSTEMS 1994年第1期67卷 19-27页

作者： SAKAWA, M YANO, H NAGOYA MUNICIPAL WOMENS COLL NAGOYA 464JAPAN

In this paper, we propose a fuzzy dual decomposition method for large-scale multiobjective nonlinear programming problems (LS-MONLPs) with the block angular structure. By considering the vague nature of human judgements, we assume that the decision maker (DM) may have a fuzzy goal for each of the objective functions in the LS-MONLP. After eliciting the corresponding membership function for each of the objective functions through the interaction with the DM, an extended primal problem and the corresponding extended dual problem are formulated. Then a two-level optimization algorithm for the extended dual problem is proposed for deriving the compromise solution for the DM to the LS-MONLP. Based on the proposed algorithm, FORTRAN programs are developed and an illustrative numerical example is demonstrated.

关键词： multiobjective nonlinear programming DECISION MAKING LARGE-SCALE programming DECOMPOSITION METHODS BLOCK ANGULAR STRUCTURE

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Interactive Fuzzy Decisionmaking for multiobjective nonlinear programming Problems with Fuzzy Parameters

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IFAC Proceedings Volumes 1987年第5期20卷 371-376页

作者： M. Sakawa H. Yano Department of Computer Science Faculty of Engineering Iwate University. Ueda Morioka Iwate 020 Japan Department of Information Science College of Economics Kagawa University Takamatsu Kagawa 760 Japan

In this paper, in order to deal with the multiobjective nonlinear programming problems with fuzzy parameters characterized by fuzzy numbers, the concept of α-multiobjective nonlinear programming and α-Pareto optimality is introduced on the basis of the a-level sets of the fuzzy numbers. Then by assuming that the fuzzy goals of the decision maker (DM) for each of the objective functions in α-multiobjective nonlinear programming can be quantified by eliciting the corresponding membership functions, a new interactive fuzzy decisionmaking method to derive the satisficing solution of the DM efficiently from among an α-Pareto optimal solution set is presented.

关键词： Decision theory man-machine systems multiobjective nonlinear programming fuzzy programming fuzzy numbers

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Interactive stability of multiobjective integer nonlinear programming problems

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期176卷 230-236页

作者： ElShafel, Mervat Mohamed Kamel Helwan Univ Fac Sci Dept Math Cairo Egypt

In this paper we present a solution method for fuzzy multiobjective integer nonlinear programming (FMOINLP) problems and the stability of this solution. An interactive stability compromise programming method for solving (FMOINLP) problems by using the compromise weights from the pay-off table of membership function for each objective function is presented. (c) 2005 Elsevier Inc. All rights reserved.

关键词： integer programming multiobjective nonlinear programming fuzzy parameters fuzzy number membership functions branch-and bound method stability set of the first kind interactive decision making parametric programming interactive decision making compromise weights interactive compromise programming

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Second-order necessary and sufficient optimality conditions for multiobjective interval-valued nonlinear programming

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APPLICABLE ANALYSIS 2025年第4期104卷 691-718页

作者： Tung, Le Thanh Can Tho Univ Coll Nat Sci Dept Math Can Tho Vietnam

In this article, the second-order optimality conditions for nonlinear programming with multiple interval-valued objective functions (in brief, NPMIOF) are studied. In the first part, the second- and first-order necessary optimality conditions for some types of efficient solutions of NPMIOF are established under of Abadie second- and first-order constraint qualifications. In the next part, we investigate both primal and dual second-order sufficient optimality conditions. Our second-order necessary conditions enhance the previous results. The second-order sufficient optimality conditions are new.

关键词： multiobjective nonlinear programming interval-valued objective functions second-order necessary and sufficient optimality conditions second-order Abadie constraint qualifications

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