Principal Intuitionistic Fuzzy Ideals and Filters on a Lattice

Boudaoud Sarra; Zedam Lemnaouar; Milles Soheyb

doi:10.7151/dmgaa.1325

Discussiones Mathematicae - General Algebra and Applications (Jun 2020)

Principal Intuitionistic Fuzzy Ideals and Filters on a Lattice

Boudaoud Sarra,
Zedam Lemnaouar,
Milles Soheyb

Affiliations

Boudaoud Sarra: Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of M’sila, Algeria
Zedam Lemnaouar: Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of M’sila, Algeria
Milles Soheyb: Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of M’sila, Algeria

DOI: https://doi.org/10.7151/dmgaa.1325
Journal volume & issue: Vol. 40, no. 1
pp. 75 – 88

Abstract

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In this paper, we generalize the notion of principal ideal (resp. filter) on a lattice to the setting of intuitionistic fuzzy sets and investigate their various characterizations and properties. More specifically, we show that any principal intuitionistic fuzzy ideal (resp. filter) coincides with an intuitionistic fuzzy down-set (resp. up-set) generated by an intuitionistic fuzzy singleton. Afterwards, for a given intuitionistic fuzzy set, we introduce two intuitionistic fuzzy sets: its intuitionistic fuzzy down-set and up-set, and we investigate their interesting properties.

Published in Discussiones Mathematicae - General Algebra and Applications

ISSN: 1509-9415 (Print); 2084-0373 (Online)
Publisher: University of Zielona Góra
Country of publisher: Poland
LCC subjects: Science: Mathematics
Website: https://www.dmgaa.uz.zgora.pl

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