Abstract
This paper formulates multiobjective linear programming problems where each coefficient of the objective functions is expressed by a random fuzzy variable. Assuming that the decision maker concerns about the probability that each of the objective function values is smaller than or equal to a certain target value, the fuzzy goals of the decision maker for the probabilities are introduced. Then, the possibility-based probability model to maximize the degrees of possibility with respect to the attained probability is considered. For solving transformed deterministic problems efficiently, particle swarm optimization for nonlinear programming problems is introduced. An interactive fuzzy satisficing method is presented for deriving a satisficing solution for a decision maker efficiently by updating the reference probability levels. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.
Highlights
In actual decision making situations, we must often make a decision on the basis of vague information or uncertain data
For handling the decision maker’s vague judgments in multiobjective problems and the randomness of the parameters involved in the objectives and/or constraints, Sakawa and his colleagues incorporated their interactive fuzzy satisficing methods for deterministic problems [5, 10] into multiobjective stochastic programming problems, through the introduction of several stochastic programming models such as expectation optimization [11, 12], variance minimization [11], probability maximization [11, 13, 14] and fractile criterion optimization [11], to derive a satisficing solution for a decision maker from Pareto optimal solution sets
In the remainder of this paper, considering the possible realized values of random parameters are often only ambiguously known to the experts, we focus on multiobjective linear programming problems with random fuzzy variables
Summary
In actual decision making situations, we must often make a decision on the basis of vague information or uncertain data. In multiobjective stochastic programming problems, it is implicitly assumed that uncertain parameters or coefficients can be expressed as random variables in probability theory This means that the realized values of random parameters under the occurrence of some event are assumed to be definitely represented with real values. Special stress is placed on interactive decision making aspects of fuzzy stochastic multiobjective programming for human-centered systems under uncertainty in most realistic situations when dealing with both fuzziness and randomness. Under these circumstances, in this paper, we consider multiobjective linear programming problems involving random fuzzy variables. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method
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