• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.111-125
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• 2012

In this paper, we introduce new classes of generalized convex n-set functions called $d$-weak strictly pseudo-quasi type-I univex, $d$-strong pseudo-quasi type-I univex and $d$-weak strictly pseudo type-I univex functions and focus our study on multiobjective subset programming problem. Sufficient optimality conditions are obtained under the assumptions of aforesaid functions. Duality results are also established for Mond-Weir and general Mond-Weir type dual problems in which the involved functions satisfy appropriate generalized $d$-type-I univexity conditions.

• 산업경영시스템학회지
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• 제23권61호
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• pp.41-50
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• 2000

Cell formation(CF) Is to group parts with similar geometry, function, material and process into part families, and the corresponding machines into machine cells. Cell formation solutions often contain exceptional elements(EEs). Also, the following objective functions - minimizing the total costs of dealing with exceptional elements and maximizing total similarity coefficients between parts - have been used in CF modeling. Thus, multiobjective programming approach can be developed to model cell formation problems with two conflicting objective functions. This paper presents an effective cell formation method with fuzzy multiobjective nonlinear mixed-integer programming simultaneously to form machine cells and to minimize the cost of eliminating EEs.

• 대한수학회지
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• 제50권4호
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• pp.727-753
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• 2013

In this paper, we introduce three new broad classes of second-order generalized convex functions, namely, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivex functions, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-pseudosounivex functions, and ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivexity assumptions for a multiobjective programming problem containing arbitrary norms.

• 한국경영과학회지
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• 제21권3호
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• pp.227-236
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• 1996

In this paper an algorithm based on cutting plane approach is developed which constructs all the efficient p-tuples of multiobjective integer linear fractional programming problem. The integer solution is constrained to satisfy and h out of n additional constraint sets. A numerical illustration in support of the proposed algorithm is developed.

• 한국경영과학회지
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• 제18권1호
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• pp.55-69
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• 1993

The tests in a battery can be performed in different sequences, and different sequential testing strategies will have exactly the same overall performances for that battery, but at different expected total costs and expected time consumptions. By using a multiobjective dynamic programming model, we are able to find all noninferior testing strategies for a given battery of tests and a stopping rule.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.139-152
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• 2003

In this paper, we characterize a vector-valued convex set function by its epigraph. The concepts of a vector-valued set function and a vector-valued concave set function we given respectively. The definitions of the conjugate functions for a vector-valued convex set function and a vector-valued concave set function are introduced. Then a Fenchel duality theorem in multiobjective programming problem with set functions is derived.

• 산업경영시스템학회지
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• 제19권39호
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• pp.75-80
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• 1996

Fuzzy approaches used to solve MONLP(Multiobjective Nonlinear Programming Problem) are based on the max-min method of fuzzy sets theory However, since the min operator noncompensatory, these approaches can not guarentee an efficient solution to the problem. In this paper, we presents an algorithm for finding the aggregation operator to find efficient solution. In particular, our presented algorithm is guarentee an efficient solution. On the basis of proposed algorithm, an illustrative numerical example is presented.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.123-137
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• 2009

A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

• 한국안전학회지
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• 제12권1호
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• pp.122-128
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• 1997

A new approach, called "two-phase approach", has been proposed In this study. Using this approach to solve MONLP(multiobjective nonlinear programming problem), the solution process is divied into two phase. In the first phase, the min-operator is used to aggregate the membership degree of fuzzy goals and constraints. In the second phase, the $\gamma$-operator is used to test and find an efficient solution in the sense of nondominated. It has been shown that no matter what the solution of the problem is unique or not, an efficient solution can be always obtained at the second phase. The proposed approach can be applied to industrial safety problem with multiobjective problems. On the basis of proposed approach, an illustrative numerical example is presented.presented.

• 산업경영시스템학회지
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• 제20권41호
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• pp.41-50
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• 1997

In this paper, we presents the method for finding the compensatory solution for fuzzy multiobjective nonlinear programming problem with fuzzy parameters involved in the problem-formulation process and fuzzy equal goals of the decision maker for each of the objective functions. The fuzzy parameters in the objective functions and the constraints characterized by fuzzy numbers. The proposed method can be applied to case with multiobjective problems and guarantee an efficient solution. An illustrative numerical example is presented.