Non-commutative fuzzy structures and pairs of weak negations

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George Georgescu and Andrei Popescu
Fuzzy Sets and Systems 143(1): 129-155 (2004)
Abstract. Weak pseudo BL-algebras (WPBL-algebras) are non-commutative fuzzy structures which arise from pseudo-t-norms (i.e. the non-commutative versions of triangular norms). In this paper, we study the pairs of weak negations on WPBL-algebras, extending the case of weak negations on Esteva–Godo MTL-algebras. A geometrical characterization of the pairs of weak negations in bounded chains is provided.

Our main result characterizes the pairs of weak negations compatible with the multiplication of totally ordered WPBL-algebras giving a way to obtain new examples of WPBL-algebras. We use this to identify all the compatible pairs of weak negations on finite MV-chains.
Fuzzy Sets and Systems, DBLP, BIB

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