On BL-Algebras and its Interval Counterpart

Rui Paiva, Regivan Santiago, Benjamín Bedregal

Abstract


Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modelled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from literature that there is a incompatibility between some algebraic structures and its interval counterpart. This paper shows that such incompatibility is also present in the level of BL-algebras. Here we show both: (1) the impossiblity of match imprecision and the correctness of the underlying BLimplication and (2) some facts about the intervalization of BL-algebras.

Keywords


Fuzzy Logic, BL-Algebras, Intervals, Correctness Principle.

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DOI: https://doi.org/10.5540/tema.2019.020.02.241

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