64 research outputs found
Classes of filters in generalizations of commutative fuzzy structures
summary:Bounded commutative residuated lattice ordered monoids (-monoids) are a common generalization of -algebras and Heyting algebras, i.e. algebras of basic fuzzy logic and intuitionistic logic, respectively. In the paper we develop the theory of filters of bounded commutative -monoids
Normal filters in residuated lattices
Residuated lattices play an important role in the study of fuzzy logic. In the present paper, we introduce the notion of a normal filter in a residuated lattice and give some characterizations of them. We state and prove some theorems and examples which determine the relationship between this notion and the other types of filters of a residuated lattice. Finally we investigate the relation between the set of dense elements and normal filters of a residuated lattice
Normal filters in residuated lattices
Residuated lattices play an important role in the study of fuzzy logic. In the present paper, we introduce the notion of a normal filter in a residuated lattice and give some characterizations of them. We state and prove some theorems and examples which determine the relationship between this notion and the other types of filters of a residuated lattice. Finally we investigate the relation between the set of dense elements and normal filters of a residuated lattice.</span
Some Types of Generalized Fuzzy -Fold Filters in Residuated Lattices
Fuzzy filters and their generalized types have been extensively studied in the literature. In this paper, a one-to-one correspondence between the set of all generalized fuzzy filters and the set of all generalized fuzzy congruences is established, a quotient residuated lattice with respect to generalized fuzzy filter is induced, and several types of generalized fuzzy n-fold filters such as generalized fuzzy n-fold positive implicative (fantastic and Boolean) filters are introduced; examples and results are provided to demonstrate the relations among these filters
Some Types of Generalized Fuzzy n
Fuzzy filters and their generalized types have been extensively studied
in the literature. In this paper, a one-to-one correspondence between the set of all generalized fuzzy filters and the set of all generalized fuzzy congruences is established, a quotient residuated lattice with respect to generalized fuzzy filter is induced, and several types of generalized fuzzy n-fold filters such as generalized fuzzy n-fold positive implicative (fantastic and Boolean) filters are introduced; examples and results are provided to demonstrate the relations among these filters
An investigation on the -fold IVRL-filters in triangle algebras
summary:The present study aimed to introduce -fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of -fold (positive) implicative IVRL-extended filters and -fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the -fold IVRL-extended filters, -fold (positive) implicative algebras, and the Gödel triangle algebra were discussed
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