Clifford's order based on non-commutative operations

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Liu Z. Q.

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Journal Paper

Paper Information

Journal: Iranian Journal of Fuzzy Systems Year:2024 | Volume:21 | Issue:3 Page(s): 77-90

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Information Journal Paper

Title

Clifford's order based on non-commutative operations

Author(s)

Liu Z. Q. | Issue Writer Certificate

Keywords

Partial order

Aggregation operator

Poset

semi-t-operator

Semi-uninorm

Abstract

Based on the classical works of Clifford inducing Partial order from semigroups, recently, Gupta and Jayaram explored the order $\sqsubseteq_{F}$ from an associative operation $F$ through \emph{local left identity} (\textbf{LLI}). Inspired by their works, we further present an order $\sqsubseteq^{*}_F$ obtained from non-commutative operation $F$ which has the \emph{local right identity} (\textbf{LRI}) since the non-commutativity of $F$ implies that the local left and right identity may be different for each element, which means that both orders may not coincide in the same domain. Firstly, we determine an equivalent characterization for two orders induced by non-commutative operation $F$. Secondly, we investigate both orders induced by semi-t-operators and deeply study their properties. Finally, we characterize both orders obtained from Semi-uninorm (resp. semi-nullnorm) under the condition that Semi-uninorm (resp. semi-nullnorm) is locally continuous.

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