Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices

Xiaohong Zhang (), Rong Liang and Benjamín Bedregal
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Xiaohong Zhang: Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China
Rong Liang: Department of Mathematics, Shaanxi University of Science & Technology, Xi’an 710021, China
Benjamín Bedregal: Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Natal 59084-100, RN, Brazil

Mathematics, 2022, vol. 10, issue 18, 1-21

Abstract: After the research on naBL-algebras gained by the non-associative t-norms and overlap functions, inflationary BL-algebras were also studied as a recent kind of non-associative generalization of BL-algebras, which can be obtained by general overlap functions. In this paper, we show that not every inflationary general overlap function can induce an inflationary BL-algebra by a counterexample and thus propose the new concept of weak inflationary BL-algebras. We prove that each inflationary general overlap function corresponds to a weak inflationary BL-algebra; therefore, two mistaken results in the previous paper are revised. In addition, some properties satisfied by weak inflationary BL-algebras are discussed, and the relationships among some non-classical logic algebras are analyzed. Finally, we establish the theory of filters and quotient algebras of inflationary general residuated lattice (IGRL) and inflationary pseudo-general residuated lattice (IPGRL), and characterize the properties of some kinds of IGRLs and IPGRLs by naBL-filters, (weak) inflationary BL-filters, and weak inflationary pseudo-BL-filters.

Keywords: fuzzy logic; overlap function; weak inflationary BL-algebra; filter; inflationary pseudo-general residuated lattice (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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