In this article, two-person zero-sum games are investigated in the fuzzy environment. Several models constructed by Maeda in the symmetrical fuzzy environment are extended to the models in the asymmetric fuzzy environment. The existence of equilibrium strategies for these extended models is proposed in the asymmetric fuzzy environment. However, in some cases, Nash equilibrium strategies may not...

So far the focus of almost all multior many-objective performance metrics has been the convergence and distribution of solutions in the objective space (Pareto-surface). Pareto-surface metrics such as IGD, HV, and Spread are simple and provide knowledge about the overall performance of the solution set. However, these measures do not provide any insight into the distribution or spread of a solu...

Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if ...

This paper revisits the college admissions problem and studies the efficiency, incentive, and monotonicity for colleges. We show that max-min criterion that is stronger than substitutability, together with the quota-saturability that requires having enough acceptable applicants, guarantees weak Pareto efficiency and strategy-proofness for colleges under the colleges-proposing deferred acceptanc...

 Evolutionary multi-objective optimization (EMOO) finds a set of Pareto solutions rather than any single aggregated optimal solution for a multi-objective problem. The purpose of this paper is to describe a newly developed evolutionary approach --Paretobased multi-objective differential evolution (MODE). In this paper, the concept of differential evolution, which is well-known in the continuou...

In this paper, we give some new generalized convexities with the tool–right upper-Diniderivative which is an extension of directional derivative. Next, we establish not only Karush-KuhnTucker necessary but also sufficient optimality conditions for mathematical programming involving new generalized convex functions. In the end, weak, strong and converse duality results are proved to relate weak ...

The analytical form of general affine transform families with givenmaximum likelihood estimators for the affine parameters is determined. In this context, the simultaneous maximum likelihood equations of the affine parameters in the generalised Pareto distribution cannot have a common solution. This pathological situation is removed by extending it to a four parameter family, called Pareto type...

This paper proposes a practical methodology for the solution of multi-objective system reliability optimization problems. The new method is based on the sequential combination of multi-objective evolutionary algorithms and data clustering on the prospective solutions to yield a smaller, more manageable sets of prospective solutions. Existing methods for multiple objective problems involve eithe...

We consider situations in which a group takes a collective decision by aggregating individual’s judgments on a set of criteria according to some agreed-upon decision functions. Assuming the criteria and the decision to be binary, we demonstrate that, except when the aggregation rule is dictatorial or the decision rule is particularly simple, such reason-based social choice must violate the Pare...