On modeling ambiguity through entropy

Abstract

AbstractFirst, a concept of ambiguity function is devised as an analogue of membership function, which directly and intuitively represents the ambiguity as perceived by the agent corresponding to a membership function. The ambiguity function is then deployed to develop an adaptive fuzzy entropy function that gives the overall fuzzy entropy of a fuzzy system as perceived by the agent. The proposed function considers also the agent's specific attitude as well as the given context (e.g., collection of the membership grades with respect to an attribute/criterion or property), both of which inevitably shape our perception of uncertainty. The usefulness of the proposed fuzzy entropy function is shown in multicriteria decision aiding in identifying those criteria that are most effective in distinguishing among the alternatives.