Fuzzy Resembler: An Approach for Evaluation of Fuzzy Sets

Abstract

The efficiency of a fuzzy logic-based system is catalyzed by the system design. Fuzzy sets generalize classical crisp sets by incorporating concepts of membership for a fuzzy variable. Each fuzzy set is associated with linguistic concepts that are germane to a particular application. This paper presents an approach for evaluating the region of certainty and uncertainty represented in design of fuzzy linguistic variables. Fuzzy Resembler (FuzR) attempts to capture the goodness of a fuzzy system design using a geometric approach; it can be used for evaluating the design of fuzzy membership space. FuzR is the ratio between region of certainty to region of uncertainty. From the results, it can be inferred that FuzR presents meaningful observations of a fuzzy variable, characterized by trapezoidal, triangular, and gaussian membership functions. FuzR can be used as a design evaluation parameter for evolving fuzzy systems. Knowledge engineers can use it to optimize design of fuzzy systems in the absence of domain experts. Moreover, the level of abstraction provided by FuzR makes it an intuitive design parameter. The significance of this work lies more in its point-of-view than voracious results; the theory and formulation are still young and much more is yet to be conceptualized and tested.