On fuzzy subalgebras of BE-algebras

Rezaei, Akbar; Saeid, Arsham Borumand

doi:10.1007/s13370-011-0011-4

Cited by 22 publications

(9 citation statements)

References 5 publications

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“…In this section, we present certain definitions and results which are taken mostly from [1], [6], [7], [8] and [9] for the ready reference of the reader.…”

Section: Preliminariesmentioning

confidence: 99%

Weak Implicative Filters of Be-Algebras

Rao¹

2017

Journal of applied mathematics & informatics

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The concept of weak implicative filters is introduced in BEalgebras. Some characterizations of weak implicative filters are derived in terms of filters of a BE-algebra. Fuzzification is applied to the class of weak implicative filters. Some properties of fuzzy weak implicative filters are studied with respect to fuzzy relations and homomorphisms. The notion of triangular normed fuzzy weak implicative filters is introduced in BEalgebras and their properties are studied.

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“…In this section, we present certain definitions and results which are taken mostly from [1], [6], [7], [8] and [9] for the ready reference of the reader.…”

Section: Preliminariesmentioning

confidence: 99%

Weak Implicative Filters of Be-Algebras

Rao¹

2017

Journal of applied mathematics & informatics

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“…They defined and studied the concept of a filter in BE-algebras. In [7] and [6], S. S. Ahn et al and A. Rezaei et al studied fuzzy BE-algebras. G. Dymek and A. Walendziak [1] developed the theory of fuzzy filters in BE-algebras.…”

Section: Introductionmentioning

confidence: 99%

Lukasiewicz Fuzzy BE-algebras and BE-filters

Jun¹,

Ahn²

2022

Eur. J. Pure Appl. Math.

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By applying the concept of Lukasiewicz fuzzy set to BE-algebras, the notions of Lukasiewicz fuzzy BE-algebra and Lukasiewicz fuzzy BE-filter are introduced, and their properties are investigated. Characterizations of Lukasiewicz fuzzy BE-algebra and Lukasiewicz fuzzy BE-filter are discussed, and the relationship between fuzzy BE-algebra (resp., fuzzy BE-filter) and Lukasiewicz fuzzy BE-algebra (resp., Lukasiewicz fuzzy BE-filter) is established. The conditions for the ∈-set, q-set and O-set of Lukasiewicz fuzzy set to be BE-subalgebras are explored. Lukasiewicz fuzzy BE-filter is created by using BE-filter.

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“…R.A. Borzooei et al introduced the concept of a fuzzy filter of a BL-algebra, with respect to a t-norm and proved that there is a correspondence bijection between the set of all Tfuzzy filters of a BL-algebra and the set of all T-fuzzy congruences relations in that BL-algebra [2]. Recently, A. Rezaei et al discussed on (fuzzy) congruence relations in (pseudo) CI/BE-algebras and studied some of their properties [13,14,15].…”

Section: Introductionmentioning

confidence: 99%