This chapter describes a system of fuzzy methods designed to solve a broad range of problems in multiple-criteria evaluation, and also their software implementation, FuzzME. A feature common to all the presented methods is the type of evaluation, well suited to the paradigm of fuzzy set theory. All evaluations take on the form of fuzzy numbers, expressing the extent to which goals of evaluation are fulfilled. The system of fuzzy methods is conceived to allow for different types of interaction among criteria of evaluation. Under no interaction, the fuzzy weighted average, fuzzy OWA operator, or WOWA operator are used to aggregate partial evaluations (depending on the evaluator’s requirements regarding type of evaluation). If interactions appear as redundancy or complementarity, the fuzzified discrete Choquet integral is the appropriate aggregation operator. Under more complex interactions, the aggregation function is defined through an expertly set base of fuzzy rules.
TopBackground
Worldwide, one can witness an ever-increasing interest in high-quality mathematical models of multiple-criteria evaluation (e.g. rating of clients in banks, assessment of universities, comparison of alternative solutions to ecological problems). For the tasks of building evaluation models, setting some of their inputs, and interpreting their outputs, expert knowledge is needed (e.g. evaluations of alternatives according to qualitative criteria, partial evaluating functions for quantitative criteria, choice of a suitable aggregation operator, weights of partial evaluations, rule bases describing multiple-criteria evaluating functions, verbal interpretation of obtained results). With uncertainty being a characteristic feature of any expert information, a suitable mathematical tool for creating such models is the fuzzy set theory (Zadeh, 1965; Dubois & Prade 2000). For practical use of the fuzzy models of multiple-criteria evaluation, their user-friendly software implementation is necessary.
Out of numerous papers and books covering the theory and methods of multiple-criteria evaluation, a large number make use of fuzzy approach (e.g. Bellman & Zadeh, 1970; Yager, 1988; Rommelfanger, 1988; Lai & Hwang, 1994; Carlsson & Fullér, 1996; Talašová, 2003; Ramík & Perzina, 2010). Multiple-criteria evaluation (as a basis for decision making) was even one of the earliest applications of fuzzy sets (Bellman & Zadeh, 1970). In more than 40 years of existence of the fuzzy set theory, several software products for multiple-criteria decision making have been developed that utilize fuzzy modeling principles to different degrees and in different ways, e.g. FuzzyTECH (Von Altrock 1995, 1996; http://www.fuzzytech.com/) and NEFRIT (Talašová, 2000).