A Fuzzy Decision Making Method for Multi-Objective Problems with a Preference Structure Representation by Fuzzy Connectives

Abstract
The authors propose a new fuzzy decision making method for multi-objective problems. The main feature of this method is the usage of fuzzy connectives to represent the decisionmaker's preference structure. The fuzzy connectives which we adopt are Zimmermann's γ operation and its extensions. These extended operations have much larger descriptivity of the decision-maker's preference structure than the γ operation.Our method is summarized in the following 5 steps.Step 1. The identification of a decision making problem with a fuzzy environment and the construction of an objective hierarchy.Step. 2. A questionnaire procedure: Questionnaire is used to identify the decision-maker's preference structure in each cluster of the objective hierarchy.Step 3. A parameter identification procedure: The parameters of the three fuzzy connectives: γ operation, extension 1, and extension 2 are identified by Quasi Newton Projection Method using the questionnaire results. Then one fuzzy connective is selected among the three as the preference structure model on the basis of AIC's value in each cluster.Step 4. Evaluation of alternatives: The decision-maker assesses the evaluation value of alternatives with respect to the lowest-level objectives. If he cannot assess the unique value, then he uses a fuzzy probability representation.Step 5. Rating and Ranking: The evaluation values with respect to the lowest-level objectives are aggregated using the preference structure model from the bottom level to the upper level in the objective hierarchy. And then the alternatives are ranked.Finally, an application of this method is presented in a company-choice problem for students.

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