Fuzzy sets and approximate reasoning in decision and control

Issues in the use of fuzzy set theory for decision and control are examined. The basic methodology for representing multicriterion decision-making (MCDM) functions with fuzzy sets is examined. A procedure for aggregating criteria which judge the alternatives with linear orderings is analyzed. It is shown that, by providing an ordering over the criteria, a fair procedure can be obtained for aggregation of linear orders. Two issues central to use of fuzzy logic control are investigated. The problem of aggregating the outputs of the individual rules is examined to form overall controller fuzzy output. Two families of aggregation procedures are proposed, one based on an orlike aggregation and one based on an andlike aggregation. Defuzzification is discussed. A parameterized family of defuzzification operators based upon the BADD transformation is introduced. The operation of nonmonotonic intersection is studied, and it is shown that it can form the basis for the introduction of a prioritization among criteria in fuzzy MCDM