Using General Fuzzy Number to Handle Uncertainty and Imprecision in Group Decision-Making
In order to handle uncertain or imprecise opinions of decision makers in group decision-making, this paper proposes an integrated fuzzy group decision-making algorithm and a related method. The method allows decision makers using linguistic terms to descr
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Abstract: In order to handle uncertain or imprecise opinions of decision makers in group decision-making, this paper proposes an integrated fuzzy group decision-making algorithm and a related method. The method allows decision makers using linguistic terms to describe their fuzzy opinions, including their fuzzy preferences for alternative solutions, fuzzy judgments for solution selection criteria and fuzzy weights of group members in a group decision-making. This method deals with simultaneously and aggregates the three groups of linguistic terms to arrive a group consensus decision. The group consensus decision is the most acceptable one for the group as a whole. Particularly, the proposed algorithm uses general fuzzy number to describe the uncertainty and imprecision happened to decision individuals and decision processes. It can therefore use any forms of fuzzy number including triangular fuzzy number, rectangle fuzzy number and continuous fuzzy number to describe the fuzziness in a group decision-making when applying the group decision-making method.
1 Introduction Group decision-making often involves the selection for a most satisfactory solution from among a set of alternative solutions. The most satisfactory solution is selected under a set of selection criteria by a group of decision makers. Consequently, the aim in making a group decision is to select a most satisfactory solution that is the most acceptable for the group of individuals as a whole (Bui 1989). When a decision is to be made in a group, the analysis must be extended to account for conflict and aggregation among all group members. Three main conflicts are identified in group decision-making. First, there may be a group leader, or leaders, who playa dominant role in a group decision-making, or some group members play more important roles than others. Thus, the group members D. Ruan et al. (eds.), Intelligent Sensory Evaluation © Springer-Verlag Berlin Heidelberg 2004
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G. Zhang and J. Lu
do not have equal importance (weight) in a decision activity. Second, preferences of group members for alternative solutions would be expected to vary from one to another. Third, group members often have different judgments for priorities of selection criteria. For example, group members may give different priorities for decision objectives in a multi-objective decision problem where decision objectives are used as selection criteria. Therefore determining a most satisfactory solution in a group requires a whole aggregation of individual weights, preferences and judgments for solutions and selection criteria. There is no rule for combining these individual properties into a group preference unless interpersonal comparison of utilities is allowed (Iz and Jelassi 1990). In a group decision-making practice, the three main conflicts, individual weights, preferences and judgments, are hardly described by precise values, often are expressed by way of linguistic variables/terms which reflect imprecise values (Marimin et al. 1998). For example, 'personal weight' i
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