Name
Abstract | ||
|---|---|---|
naBL-algebras are non-associative generalizations of BL-algebras obtained from non-associative t-norms (nat-norms). In the present paper we propose a further generalization of BL-algebras where associativity is not required. Such generalization is based on a subclass of bivariate general overlap functions called inflationary. We call this non-associative generalization inflationary BL-algebras, and we discuss the main differences between the latter and the more specific class of inflationary BL-algebras. We show that the class naBL of non-associative BL-algebras obtained from general overlap functions contains the class naT of naBL-algebras obtained by nat-norms, and we provide a pictorial representation that summarizes these facts. We also prove some related properties, as well as a version of the well-known Chinese Remainder Theorem for these algebras but, under certain restrictions. Moreover, the notions of pseudo-automorphisms, automorphisms and their action on general overlap functions are used to obtain conjugated inflationary BL-algebras, as well as to obtain inflationary BL-algebras by distorting nat-norms by pseudo-automorphisms and, in the converse direction, to obtain naBL-algebras from inflationary BL-algebras via automorphisms. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.fss.2020.12.018 | Fuzzy Sets and Systems |
Keywords | DocType | Volume |
General overlap functions,Inflationary BL-algebras,Pseudo-automorphisms,Non-associative residuated lattices,BL-algebras,Residuation principle | Journal | 418 |
ISSN | Citations | PageRank |
0165-0114 | 1 | 0.35 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rui Paiva | 1 | 1 | 1.36 |
| Regivan H. Nunes Santiago | 2 | 1 | 3.39 |
| Benjamín Bedregal | 3 | 1 | 0.35 |
| Umberto Rivieccio | 4 | 103 | 14.47 |