A Fuzzy Decision Maker

One of the most useful aspects of fuzzy set theory is its ability to represent mathematically a class of decision problems called multiple objective decisions (MODs). This class of problems often involves many vague and ambiguous (and thus fuzzy) goals and constraints. The object of the fuzzy decision methodology is to obtain a decision, optimum in the sense that some set of goals is attained while observing (i.e. not violating) a simultaneous set of constraints. This paper presents one possible fuzzy decision-making model developed by L.A. Zadeh and Richard Bellman [1] and later extended by Ronald R. Yager [5], which has proved to be useful to decision makers in many "real-world" problems. The latter fuzzy decision making method is used when the goals or objectives and the constraints are not of equal importance to the decision maker. The methodology for weighting the importances of the decision components is an exponential weighting, which are obtained using a method of paired comparisons developed by T.L. Saaty [3]. The weighting methodology is based on finding the eigenvector associated with the maximal eigenvalue of a paired comparison matrix, which is obtained from simple, binary decisions (i.e. which of two things is more important) and a fuzzyily-guessed-at scale of how much more important (on a scale of 1 to 9) one factor is than another. This last step characterizes the decision maker and properly reflects his/her biases with an easily obtained vector of exponents. A further extension of the decision making methodology was made by Yager [6] in 1981, in which partially ordered sets of fuzzy ratings could be used in the decision process as opposed to cardinal numbers. A simple BASIC program incorporating Yager's first methodology [5] was first published by Whaley [4] in 1979.