39 research outputs found

    On ideal theory of hoops

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    summary:In this paper, we define and characterize the notions of (implicative, maximal, prime) ideals in hoops. Then we investigate the relation between them and prove that every maximal implicative ideal of a \vee -hoop with double negation property is a prime one. Also, we define a congruence relation on hoops by ideals and study the quotient that is made by it. This notion helps us to show that an ideal is maximal if and only if the quotient hoop is a simple MV-algebra. Also, we investigate the relationship between ideals and filters by exploiting the set of complements

    Graph of BCI

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    We associate a graph to any subset Y of a BCI-algebra X and denote it by G(Y). Then we find the set of all connected components of G(X) and verify the relation between X and G(X), when X is commutative BCI-algebra or G(X) is complete graph or n-star graph. Finally, we attempt to investigate the relation between some operations on graph and some operations on BCI-algebras

    Constructing a Hoop Using Rough Filters

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    When it comes to making decisions in vague problems, rough is one of the best tools to help analyzers. So based on rough and hoop concepts, two kinds of approximations (Lower and Upper) for filters in hoops are defined, and then some properties of them are investigated by us. We prove that these approximations- lower and upper- are interior and closure operators, respectively. Also after defining a hyper operation in hoops, we show that by using this hyper operation, set of all rough filters is monoid. For more study, we define the implicative operation on the set of all rough filters and prove that this set with implication and intersection is made a hoop

    Module Structure on Effect Algebras

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    In this paper, by considering the notions of effect algebra and product effect algebra, we define the concept of effect module. Then we investigate some properties of effect modules, and we present some examples on them. Finally, we introduce some topologies on effect modules.

    Commutative Generalized Neutrosophic Ideals in BCK-Algebras

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    The concept of a commutative generalized neutrosophic ideal in a BCK-algebra is proposed, and related properties are proved. Characterizations of a commutative generalized neutrosophic ideal are considered. Also, some equivalence relations on the family of all commutative generalized neutrosophic ideals in BCK-algebras are introduced, and some properties are investigated

    Positive Implicative Soju Ideals in BCK-Algebras

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    The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations of positive implicative soju ideal are established. Finally, extension property for positive implicative soju ideal is constructed.This research is supported by a grant of National Natural Science Foundation of China (11571281)

    nn-Fold Filters of EQ-Algebras

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    In this paper, we apply the notion of nn-fold filters to the EQEQ-algebras and introduce the concepts of nn-fold pseudo implicative, nn-fold implicative, nn-fold obstinate, nn-fold fantastic prefilters and filters on an EQEQ-algebra E\mathcal{E}. Then we investigate some properties and relations among them. We prove that the quotient algebra E/F\mathcal{E}/F modulo an 1-fold pseudo implicative filter of an EQEQ-algebra E\mathcal{E} is a good EQEQ-algebra and the quotient algebra E/F\mathcal{E}/F modulo an 1-fold fantastic filter of a good EQEQ-algebra E\mathcal{E} is an IEQIEQ-algebra

    The Prominentness of Fuzzy GE-Filters in GE-Algebras

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    Based on the concept of fuzzy points, the notion of a prominent fuzzy GE-filter is defined, and the various properties involved are investigated. The relationship between a fuzzy GE-filter and a prominent fuzzy GE-filter is discussed, and the characterization of a prominent fuzzy GE-filter is considered. The conditions under which a fuzzy GE-filter can be a prominent fuzzy GE-filter are explored, and conditions for the trivial fuzzy GE-filter to be a prominent fuzzy GE-filter are provided. The conditions under which the ∈t-set and Qt-set can be prominent GE-filters are explored. Finally, the extension property for the prominent fuzzy GE-filter is discussed

    A General Model of Neutrosophic Ideals in BCK/BCI-algebras Based on Neutrosophic Points

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    More general form of (∈, ∈ ∨q)-neutrosophic ideal is introduced, and their properties are investigated. Relations between (∈, ∈)-neutrosophic ideal and (∈, ∈ ∨q(kT ,kI ,kF ))-neutrosophic ideal are discussed. Characterizations of (∈, ∈∨q(kT ,kI,kF ))-neutrosophic ideal are discussed, and conditions for a neutrosophic set to be an (∈, ∈∨q(kT ,kI ,kF ))-neutrosophic ideal are displayed
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