HARACTERIZATIONS OF FUZZY STANDARD ELEMENT IN FUZZY LATTICES

HARACTERIZATIONS OF FUZZY STANDARD ELEMENT IN FUZZY LATTICES

P. Khubchandani, J. Khubchandani

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Abstract

In this paper, we introduce the concepts of fuzzy neutral elements, fuzzy join-standard, and fuzzy meet-standard elements in fuzzy lattices. Also, we have proved the fundamental characterization theorem of fuzzy join-standard elements in fuzzy lattices. Moreover, we introduce the concepts of ▽F -standard elements in fuzzy lattices. Further, we have studied the relationship among the fuzzy join-standard, ▽F -standard, fuzzy meet-distributive, and fuzzy atom in fuzzy lattices. Also, we have introduced the notion and notation of fuzzy p-element in the fuzzy lattice.

Keywords

Fuzzy lattices, fuzzy distributive pair, fuzzy semi-distributive pair, fuzzy standard element, ▽F -standard element, fuzzy p-element.