Synthesis using fuzzy set theory and a Dempster-Shafer-based approach to compromise decision-making with multiple-attributes applied to risk control options selection

In decision-making there are always some parameters that are inaccurately known, meaning that the decision-making process must be based on subjective opinions. One of the useful aspects of fuzzy set theory is its ability to represent mathematically a class of decision problems called multiple objective decisions, with involvement of many vague (and thus fuzzy) goals and constraints. The objective of the fuzzy set decision methodology is to obtain an optimal decision in the sense that some set of goals is attained while observing (i.e., not violating) a simultaneous set of constraints. This paper presents a decision-making model as applied to multiple-attribute decision-making problems, which may be useful to decision-makers in many real-world problems. The proposed decision-making framework is a synthesis using an approach developed by Zadeh and Bellman in 1970 [1] and later extended by Yager, in 1977 [2], together with the Dempster-Shafer theory of evidence [3]. While dealing with a multiple-attribute decision-making problem the decision-maker may have to compromise with available alternatives, none of which may satisfy exactly his ultimate ideal best. The decision mechanism is constrained by the uncertainty and imprecision inherent in the determination of the relative importance of each attribute element and the classification of existing alternatives. The classification of alternatives is addressed through expert evaluation of the degree to which each attribute element is contained in each available alternative. The implementation of pairwise comparison and a ratio-scale quantification method by the decision-maker is performed to determine the relative importance of each attribute element. Then the 'belief and plausibility' that an alternative will satisfy the decision-maker's ideal 'best' are derived and combined to rank the available alternatives. Two examples in maritime safety engineering are presented to demonstrate the proposed framework.