On BL-Algebras and its Interval Counterpart

Authors

  • Rui Paiva Instituto Federal de Educação, Ciência e Tecnologia do Ceará - IFCE http://orcid.org/0000-0002-1775-8489
  • Regivan Santiago Federal University of Rio Grande do Norte - UFRN
  • Benjamín Bedregal Federal University of Rio Grande do Norte - UFRN

DOI:

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

Keywords:

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

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.

Author Biographies

Rui Paiva, Instituto Federal de Educação, Ciência e Tecnologia do Ceará - IFCE

Group for Logic, Language, Information, Theory and Applications - LoLITA

Sou graduado em Matemática pela Universidade Estadual do Ceará (UECE), possuo especialização em Ensino de Matemática pela UECE e mestrado acadêmico em Matemática pela Universidade Federal do Ceará (UFC). Atualmente cursando doutorado em Sistemas e Computação pelo Departamento de Informática e Matemática Aplicada da Universidade Federal do Rio Grande do Norte (UFRN). Além disso, sou Professor efetivo do Instituto Federal de Educação, Ciência e Tecnologia do Ceará - IFCE, com experiência na área de Matemática, com ênfase em Geometria e Topologia, e Computação, com ênfase em Matemática Computacional, atuando principalmente nos seguintes temas: variedades de Hadamard, funções de Busemann, teoria geométrica das folheações e Álgebra Universal, Teoria das Categorias, Lógicas não clássicas e Lógica Algébrica.

Regivan Santiago, Federal University of Rio Grande do Norte - UFRN

Group for Logic, Language, Information, Theory and Applications - LoLITA
Department of Informatics and Applied Mathematics - DIMAp

Benjamín Bedregal, Federal University of Rio Grande do Norte - UFRN

Group for Logic, Language, Information, Theory and Applications - LoLITA
Department of Informatics and Applied Mathematics - DIMAp

References

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Published

2019-07-29

How to Cite

Paiva, R., Santiago, R., & Bedregal, B. (2019). On BL-Algebras and its Interval Counterpart. Trends in Computational and Applied Mathematics, 20(2), 241. https://doi.org/10.5540/tema.2019.020.02.241

Issue

Vol. 20 No. 2 (2019)

Section

Original Article

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