On BL-Algebras and its Interval Counterpart - Paiva, Rui; Santiago, Regivan; Bedregal, Benjamín (Trends in Computational and Applied Mathematics, 2019)
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.