Bipolar Representations of Optimism and Pessimism in Multiple Criteria Decision Analysis Based on Interval-Valued Fuzzy Sets--- A Comparative Analysis of Point Operators and Its Applications

Multiple criteria decision analysis (MCDA) problems are an important research field in decision science, management science, systems engineering, and operations research. Since classical MCDA methods cannot effectively handle problems with imprecise information, the theory of fuzzy sets has been used to resolve this difficulty. But in reality, it may not always be certain that the evaluation of membership values. In view that there are many real life situations where due to insufficiency in information availability, interval-valued fuzzy sets (IVFSs), separately introduced by Zadeh and Sambuc in 1975, are appropriate to deal with such problems. In this research project, the vagueness and incomplete preference information problems in MCDA will be dealt with the IVFS theory and new interval-valued fuzzy decision methods will be propounded for decision aiding. Valuable applications of IVFSs have been developed in the field of multiple criteria analysis. However, what seems to be lacking is the influence of dispositional optimism and pessimism on subjective judgments that accompanies the decision making process. Optimism and pessimism are fundamental constructs that reflect how people respond to their perceived environment and how to construe and affect subjective judgments. Optimistic decision makers interpret their decision situations positively and expect favorable outcomes, whereas pessimistic decision makers expound their decision situations negatively and anticipate unfavorable outcomes. From this perspective, an appropriate method is necessary to draw the influences of optimism and pessimism on decision making processes. The frequently used methods of handling optimism and pessimism in MCDA are Hurwicz’s and Yager’s approaches. Despite their wide usage, a critical issue has been raised about unidimensionality. Numerous psychological researches and empirical findings have convincingly supported that optimism and pessimism do not represent opposite poles on a single, bipolar dimension, but they are conceived as two partially independent dimensions instead. Considering the nature of bipolarity, the focus of this research is a two-dimensional approach by adequately employing the degrees of membership and non-membership based on IVFSs. The research period of this project is three years, and the topic for each year is as follow: (i) An Interval-Valued Fuzzy MCDA Method Based on Bipolar Models of Optimism and Pessimism; (ii) A Comparative Study in Optimistic and Pessimistic Multicriteria Decision Analysis Based on Interval-Valued Fuzzy Sets; and (iii) An Outcome-Oriented Approach to Multicriteria Decision Analysis with Interval- Valued Fuzzy Optimistic/Pessimistic Operators. For the first-year research, this study develops optimistic and pessimistic estimations with several fuzzy point operators to draw the influences of optimism and pessimism on multicriteria decision making for the sake of a better fit than the unidimensional model. Given a typology from empirical grounds, the appropriate point operators specific to each type are suggested to identify adaptational outcomes. Base upon a series of new score functions, a useful method for MCDA is provided to efficiently facilitate decision analysis with a multimeasure approach. For the second-year research, we intend to extend compensatory models in MCDA, including compromising models, outranking models, and scoring models, for the sake of appropriate for the interval-valued fuzzy environment. Furthermore, we design several computational experiments to compare ranking orders yielded by different methods. We examine several comparison indices, including the consistency rate of total orders, the contradiction rate of the best choice, and the inversion rate between the better choices and worse ones. Finally, we provide a second-order regression model to highlight the effects of variant parameter settings on average Spearmen correlation coefficients. For the third-year research, an empirical study will be conducted to validate the feasibility and applicability of the current method. Real-world applications on consumer decision problems will be conducted to examine the feasibility and validity of the proposed interval-valued fuzzy decision methods as well. We apply the proposed methods on limited and extensive decision making problems in a hedonic or utilitarian manner. We anticipate that the proposed method can add insight on the influences of optimism and pessimism in decision analysis studies. These new methods not only improve the existing methods of MCDA but also explore new directions for the permeation of the IVFS theory to application areas in practice.

Project ID:PF9907-7884
External Project ID:NSC99-2410-H182-022-MY3