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- W2896743770 abstract "For mathematical fuzzy logic systems, the study of corresponding algebraic structures plays an important role. Pseudo-BCI algebra is a class of non-classical logic algebras, which is closely related to various non-commutative fuzzy logic systems. The aim of this paper is focus on the structure of a special class of pseudo-BCI algebras in which every element is quasi-maximal (call it QM-pseudo-BCI algebras in this paper). First, the new notions of quasi-maximal element and quasi-left unit element in pseudo-BCK algebras and pseudo-BCI algebras are proposed and some properties are discussed. Second, the following structure theorem of QM-pseudo-BCI algebra is proved: every QM-pseudo-BCI algebra is a KG-union of a quasi-alternating BCK-algebra and an anti-group pseudo-BCI algebra. Third, the new notion of weak associative pseudo-BCI algebra (WA-pseudo-BCI algebra) is introduced and the following result is proved: every WA-pseudo-BCI algebra is a KG-union of a quasi-alternating BCK-algebra and an Abel group." @default.
- W2896743770 created "2018-10-26" @default.
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- W2896743770 date "2018-10-08" @default.
- W2896743770 modified "2023-09-25" @default.
- W2896743770 title "The Structure Theorems of Pseudo-BCI Algebras in Which Every Element is Quasi-Maximal" @default.
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- W2896743770 doi "https://doi.org/10.3390/sym10100465" @default.
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