Various generalizations of fuzzy reasoning are frequently used in decision making. While in many application areas it is natural to assume that truth degrees of a property and its complement sum up to 1, such an assumption appears problematic, e.g., in modeling ignorance. Therefore, in some generalizations of fuzzy sets, degrees of membership in a set and in its complement are separated and are no longer required to sum up to 1. In frequent cases, this separation of positive and negative evidences for concept membership is more natural.
As we discuss in the current paper, symbolic explanations of results of such forms of reasoning provide additional important information. In the present paper we address two related questions: (i) given generalized fuzzy connectives and a finite set of truth values τ, find a finitely-valued logic over τ, explaining fuzzy reasoning, and (ii) given a finitely-valued logic, find a fuzzy semantics, explained by the given logic. We also show examples illustrating usefulness of the approach.
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