− A new trend in the design of fuzzy rulebased systems is the use of evolutionary multiobjective optimization (EMO) algorithms. This trend is observed in various areas in machine learning. EMO algorithms are often used to search for a number of Pareto-optimal non-linear systems with respect to their accuracy and complexity. In this paper, we first explain some basic concepts in multiobjective o...

h a stochastic and fuzzy environment, a multiobjective fuzzy stopping problem is discussed. The randomness and fuzziness are evaluated by probabilistic expectations and linear ranking functions, respectively. Pareto optimal fuzzy stopping times are given under the assumption of regularity for stopping rules, by using X-optimal stopping times. @ 2003 Elsevier Ltd. All rights reserved. &Fords-Mul...

This paper considers a capacitated vehicle routing problem with fuzzy random travel time and demand (FRVRP). A chance-constrained multiobjective programming is presented based on fuzzy random theory and converted to a crisp equivalent models under some assumptions. To solve such a multiobjective combinatorial optimization problem, this paper presents a hybrid multiobjective particle swarm optim...

In this article, a fuzzy goal programming (GP) and method of approximation is presented for the solution of a multiobjective linear plus linear fractional programming problem. In the proposed approach, membership functions are defined for each fuzzy goal and then a method of variable change on the underand overdeviational variables of the membership functions associated with the fuzzy goals of ...

This paper presents a fuzzy goal programming (GP) procedure for solving a multiobjective linear plus linear fractional programming problem. In the proposed approach GP model for achievement of the highest membership value of each of fuzzy goal defined for the linear plus linear fractional objectives is formulated. In the solution process, the method of variable change on the underand overdeviat...

In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...

This note presents the characterization of the stability set of the first kind for multiobjective nonlinear programming (MONLP) problems with fuzzy parameters either in the constraints or in the objective functions without any differentiability assumptions. These fuzzy parameters are characterized by triangular fuzzy numbers (TFNs). The existing results concerning the parametric space in convex...

This note presents the characterization of the stability set of the first kind for multiobjective nonlinear programming (MONLP) problems with fuzzy parameters either in the constraints or in the objective functions without any differentiability assumptions. These fuzzy parameters are characterized by triangular fuzzy numbers (TFNs). The existing results concerning the parametric space in convex...

The linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conicting in nature. This paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. In this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions to ...

Scalarization of the multiobjective programming problems with fuzzy coefficients using the embedding theorem and the concept of convex cone (ordering cone) is proposed in this paper. Since the set of all fuzzy numbers can be embedded into a normed space, this motivation naturally inspires us to invoke the scalarization techniques in vector optimization problems to evaluate the multiobjective pr...