This paper deals with the stability of multiobjective nonlinear programming problems with ordinary and fuzzy parameters in the objective functions. These fuzzy parameters are characterized by fuzzy numbers. The existi...
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This paper deals with the stability of multiobjective nonlinear programming problems with ordinary and fuzzy parameters in the objective functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the qualitative analysis of the notions (solvability set, stability sets of the first kind and of the second kind) in parametric nonlinearprogramming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of alpha-pareto optimality. An algorithm for obtaining any subset of the parametric space which has the same corresponding alpha-pareto optimal solution is also presented. An illustrative example is given to clarify the obtained results.
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 optimal...
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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.
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 funct...
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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.
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