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Relation between (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras

100%
Paad A.
Discussiones Mathematicae - General Algebra and Applications
|
2016
|
tom 36
|
nr 1
45-58
EN
In this paper, we study relationships between among (fuzzy) Boolean ideals, (fuzzy) Gödel ideals, (fuzzy) implicative filters and (fuzzy) Boolean filters in BL-algebras. In [9], there is an example which shows that a Gödel ideal may not be a Boolean ideal, we show this example is not true and in the following we prove that the notions of (fuzzy) Gödel ideals and (fuzzy) Boolean ideals in BL-algebras coincide.
2
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Tense Operators on BL-algebras and Their Applications

100%
Paad A.
Bulletin of the Section of Logic
|
2021
|
tom 50
|
nr 3
299-324
EN
In this paper, the notions of tense operators and tense filters in \(BL\)-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense \(BL\)-algebras, tense \(MV\)-algebras and tense Boolean algebras are investigated. Moreover, it is shown that the set of all tense filters of a \(BL\)-algebra is complete sublattice of \(F(L)\) of all filters of \(BL\)-algebra \(L\). Also, maximal tense filters and simple tense \(BL\)-algebras and the relation between them are studied. Finally, the notions of tense congruence relations in tense \(BL\)-algebras and strict tense \(BL\)-algebras are introduced and an one-to-one correspondence between tense filters and tense congruences relations induced by tense filters are provided.
3
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Fuzzy n-fold integral filters in BL-algebras

63%
Borzooei R., Paad A.
Discussiones Mathematicae - General Algebra and Applications
|
2013
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tom 33
|
nr 1
57-71
EN
In this paper, we introduce the notion of fuzzy n-fold integral filter in BL-algebras and we state and prove several properties of fuzzy n-fold integral filters. Using a level subset of a fuzzy set in a BL-algebra, we give a characterization of fuzzy n-fold integral filters. Also, we prove that the homomorphic image and preimage of fuzzy n-fold integral filters are also fuzzy n-fold integral filters. Finally, we study the relationship among fuzzy n-fold obstinate filters, fuzzy n-fold integral filters and fuzzy n-fold fantastic filters
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