On the Interpretability and Compact Representation of Linguistic Fuzzy Systems

Finding the compromise between computational complexity and adaptation potential of linguistic fuzzy systems is important in several fields of application of fuzzy systems including fuzzy modeling and control. This paper considers the role of popular sand t-norms in fuzzy inference function in this aspect and presents some recently acquired results. First, it is shown that with simultaneous application of product implication and sum aggregation, it is sufficient to consider symmetrical triangular output MFs, which also makes output-side transparency a default property. Secondly, analytical inference function for linguistic fuzzy systems utilizing minimum implication is derived for several cases of output MFs. Finally, some aspects of maximum aggregation are observed. It appears that computational complexity and transparency are somewhat compatible and the compromise is thus attainable as adaptability potential is difficult to realize when inference algorithm becomes too complex because of lack of capable methods and inherent mathematical limitations.