PRINCIPAL INTUITIONISTIC FUZZY IDEALS AND FILTERS ON A LATTICE
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Date
2021
Authors
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Journal ISSN
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Publisher
Université de M'sila
Abstract
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.
Keywords: lattice, intuitionistic fuzzy set, principal intuitionistic fuzzy
ideal, principal intuitionistic fuzzy filter.
2010 Mathematics Subject Classification: 03E72, 06B23, 47H10.