Duality for MultiobjectiveB-vex Programming Involvingn-Set Functions

AbstractIn the present paper we consider a class of multiobjectiveB-vex programming problems involving differentiableB-vexn-set functions and establish duality results in terms of properly efficient solutions. Further, we relate the problem to a certain saddle point of a Lagrangian and show multiobjective fractional program as a special case of the main problem

Generalized b-invex vector valued functions

The aim of this paper is to provide some first results regarding to the extension to the vector valued case of the b -ìnvex functions. Some definitions will be given for both the nonsmooth case and the differentiable case; the inclusion relationships among the introduced families of functions will be studied and some results regarding to vector valued optimization will be stated

A Linearization Approach to Multiobjective Programming Duality

AbstractDuality for multiobjective programming problems having pseudo-convex objective functions and linear constraints is studied through a linearization approach. Its application to a multiobjective fractional programming problem with different denominators is discussed

An equipment replacement problem with dynamic production planning and capacity considerations

In this paper, we propose a 0-1 integer programming formulation for an equipment replacement problem in which the demand of a product varies from period to period and different types of equipment with different production capacities are available. Since all the variables involved in the model are restricted to have binary values, the model is fairly efficient and hence can be used for large-sized problems. The use of the model is demonstrated with the help of some numerical examples

Matrix games with fuzzy goals and fuzzy payoffs

A two person zero sum matrix game with fuzzy goals and fuzzy payoffs is considered and its solution is conceptualized using a suitable defuzzification function. Also, it is proved that such a game is equivalent to a primal-dual pair of certain fuzzy linear programming problems in which both goals as well as parameters are fuzzy.Fuzzy goal Fuzzy payoff Fuzzy linear programming problem

Portfolio selection subject to experts' judgments

Since Markowitz [Markowitz, H. M. (1952). Portfolio selection. The Journal of Finance, 7, 77-91.], mean-variance theory has assumed that risky-asset returns to be random variables. The theory deals with this uncertainty by further assuming that investors hold homogeneous beliefs regarding the probability distribution governing return uncertainty. While the theory deals with return uncertainty, it fails to address measurement imprecision. In his original work, Markowitz recognized the need to combine randomness with heterogeneous expert judgment resulting in such imprecision. The main objective contributions of the paper are (i) to explore the implications of fuzzy return indeterminacy on mean-variance optimal portfolio choice, (ii) to use bid-ask spread as a proxy measure of the indeterminacy or "fuzzy" nature of random returns, and (iii) to introduce a brief, self-contained glimpse of empirical representations to practitioners unfamiliar with the fuzzy modeling field. Exposition, such as this one, is expected to open new collaborations between other branches of fuzzy mathematics and asset-pricing theories.Portfolio selection Fuzzy-set theory Mean-variance theory Subjective measures Ambiguity-aversion Experts' judgments