On fuzzy Sheffer strokes: New results and the ordinal sums

Recently, Baczynski et al. introduced the axiomatic definition of fuzzy Sheffer strokes, which is the generalization of the Sheffer stroke operators in classical logic. On the basis of this work, we point out that fuzzy Sheffer strokes can be transformed into common fuzzy logical operators through a fuzzy negation and fuzzy Sheffer strokes can be obtained from two increasing unary operators acting on a given fuzzy Sheffer stroke. We further discuss the relationship between fuzzy Sheffer strokes and overlap functions as well as grouping functions. The main contribution is to present the concept of ordinal sums of fuzzy Sheffer strokes which provides constructing methods of fuzzy Sheffer strokes and analyze some related properties. We argue under which condition a fuzzy Sheffer stroke can be represented as the ordinal sum of a family of fuzzy Sheffer strokes. We relate ordinal sums of fuzzy Sheffer strokes with its induced fuzzy conjunctions and fuzzy disjunctions as well as overlap functions and grouping functions under certain conditions. In the end, we give real-life application examples of fuzzy Sheffer strokes. (c) 2022 Elsevier B.V. All rights reserved.