Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets by Florentin Smarandache, Xiaohong Zhang, Mumtaz Ali

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Interval-Valued General Residuated Lattice-Ordered Groupoids and Expanded Triangle Algebras by Xiaohong Zhang, Rong Liang

“…However, their corresponding interval-valued algebraic structure has not been studied yet. On the other hand, with the development of non-commutative (non-associative) fuzzy logic, the study of residuated lattice theory is gradually deepening. …”
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Regular Partial Residuated Lattices and Their Filters by Nan Sheng, Xiaohong Zhang

“…In this paper, we mainly study the related algebraic structure of fuzzy partial logic. First, we provide the definitions of regular partial t-norms and regular partial residuated implication (rPRI) through the general forms of partial t-norms and partial residuated implication. …”
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Pseudo General Overlap Functions and Weak Inflationary Pseudo BL-Algebras by Rong Liang, Xiaohong Zhang

“…The legend reveals IPGRLs include all non-commutative algebraic structures involved in the article.…”
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Filters in Strong BI-Algebras and Residuated Pseudo-SBI-Algebras by Xiaohong Zhang, Xiangyu Ma, Xuejiao Wang

“…Furthermore, in order to describe the characteristics of the algebraic structure corresponding to the non-commutative fuzzy logics, we extend strong BI-algebra to the non-commutative case, and propose the concept of pseudo-strong BI (SBI)-algebra, which is the common extension of quantum B-algebras, pseudo-BCK/BCI-algebras and other algebraic structures. …”
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Neutrosophic Extended Triplet Group Based on Neutrosophic Quadruple Numbers by Qiaoyan Li, Yingcang Ma, Xiaohong Zhang, Juanjuan Zhang

“…In this paper, we explore the algebra structure based on neutrosophic quadruple numbers. …”
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Generalized Neutrosophic Extended Triplet Group by Yingcang Ma, Xiaohong Zhang, Xiaofei Yang, Xin Zhou

“…Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. …”
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Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups by Xiaohong Zhang, Florentin Smarandache, Xingliang Liang

“…From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures. In this paper, we further study neutrosophic duplet sets, neutrosophic duplet semi-groups, and cancellable neutrosophic triplet groups. …”
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The Structure Theorems of Pseudo-BCI Algebras in Which Every Element is Quasi-Maximal by Xiaoying Wu, Xiaohong Zhang

“…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. …”
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