FUZZINESS IN MULTISTAGE FUZZY-REASONING

In multistage fuzzy reasonings, vagueness will spread as the stage number of reasoning increases. Previous papers on this subject deal only with some specified implication functions. This paper will consider a more general framework, wherein by studying the effects on spread of vagueness, we will explore those properties requested for implication functions to satisfy. Further, while papers hitherto were concerned only with fuzzy sets with triangle-typed membership functions, we will consider here fuzzy sets of a more general type. We follow here the method proposed by Baldwin, which we denote as ''indirect methods,'' to formulate multistage fuzzy reasonings, and study the relationship between properties of implication functions and the spread of vagueness. Finally, we give quantitative estimates of spread of vagueness.