• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.245-257
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• 2009

A mixed type dual for multiobjective variational problem involving higher order derivatives is formulated and various duality results under generalized invexity are established. Special cases are generated and it is also pointed out that our results can be viewed as a dynamic generalization of existing results in the static programming.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.1
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• pp.163-175
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• 1997

This paper presents the algorithm for finding the compensatory solution for fuzzy multiobjective nonlinear programming problem using $\gamma$-operator. The proposed algorithm can be applied to all cases with multiobjective problems since the interactive process with a decision maker is simple, various uncertainties involved on decision making are eliminated and all the objectives are well balanced. On the basis of proposed algorithm, an illustrative numerical example is presented.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.603-619
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• 2009

Wolfe and Mond-Weir type dual to a nondifferentiable continuous programming containing support functions are formulated and duality is investigated for these two dual models under invexity and generalized invexity. A close relationship of our duality results with those of nondifferentiable nonlinear programming problem is also pointed out.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.359-375
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• 2014

In this paper, a multiobjective nondifferentiable fractional programming problem (MFP) is considered where the objective function contains a term involving the support function of a compact convex set. A vector valued (generalized) ${\alpha}$-univex function is defined to extend the concept of a real valued (generalized) ${\alpha}$-univex function. Using these functions, sufficient optimality criteria are obtained for a feasible solution of (MFP) to be an efficient or weakly efficient solution of (MFP). Duality results are obtained for a Mond-Weir type dual under (generalized) ${\alpha}$-univexity assumptions.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.99-111
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• 2014

In this paper, we have taken step in the direction to establish weak, strong and strict converse duality theorems for three types of dual models related to multiojective fractional programming problems involving ($H_p$, r)-invex functions.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1157-1165
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• 2011

The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.2
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• pp.67-78
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• 1997

In general, two types fuzziness of human judgements should be incorporated in multiobjective programming problems. One is the expert's ambigjous understanding of the nature of the parameters in the problem formulation process and the other is the fuzzy goals of the decision maker for each of the objective functions. In this paper, we present a new interactive fuzzy approach for obtaining the satisficing solution which efficiently reflect both types of fuzziness. An illustrative numerical example nonlinear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.419-423
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• 2013

In this paper we present a robust duality theory for generalized convex programming problems under data uncertainty. Recently, Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362-1373] established a robust duality theory for generalized convex programming problems in the face of data uncertainty. Furthermore, we extend results of Jeyakumar, Li and Lee for an uncertain multiobjective robust optimization problem.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.797-804
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• 1998

A pair of multiobjective generalized symmetric dual non-linear programming problems and weak strong and converse dual-ity theorems for these problems are established under generalized $\rho-(\eta,0)$-invexity assumptions. Several known results are obtained as special cases.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.15 no.26
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• pp.13-19
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• 1992

MODM(multiobjective decision-making)problem is very complex system for the analysist and decision maker. Therefore, it requires suitable MODM method to solve multiobjective decision-making problem. This paper presents an interactive fuzzy decision making method for solving multiobjective nonlinear programming problems with fuzzy goals and $\alpha$-cut set of fuzzy numbers. In our interactive method, if the decision maker specifies the degree $\alpha$of the objective value and the imprecise goals, λ-mux problem is solved. To examplify the proposed method, an interactive computer programming written in FORTRAN and an illustrate numerical example along with computer outputs are presented.