New results about idempotent semi-t-operators on bounded lattices

Wang, Ya-Ming; Jiang, Dongxue; Dan, Yexing

doi:10.22111/ijfs.2024.49405.8721

Document Type : Research Paper

Authors

¹ School of Mathematics, Southwest Jiaotong University

² Shandong University

³ School of Mathematics, Southwest Jiaotong University, Chengdu, PR China

https://doi.org/10.22111/ijfs.2024.49405.8721

Abstract

More recently, Hua conducted an investigation into the properties and constructions of idempotent semi-t-operators on bounded lattices. In her paper, there were two corollaries (without proof) showing the nonexistence of idempotent semi-t-operators on the bounded lattice which contains one of the eight sublattices mentioned in those corollaries. Unfortunately, it has been discovered that the conclusions drawn from those two corollaries are not entirely correct. This work aims to not only identify the errors in those corollaries through three counterexamples but also supplement all findings pertaining to the existence of idempotent semi-t-operators on any bounded lattice.

Keywords

Main Subjects

Approximate Reasoning

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New results about idempotent semi-t-operators on bounded lattices

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Volume 21, Issue 6November and December 2024Pages 69-82

Volume 21, Issue 6
November and December 2024
Pages 69-82