379 research outputs found

    Interval valued (\in,\ivq)-fuzzy filters of pseudo BLBL-algebras

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    We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (\in,\ivq)-fuzzy filters of pseudo BLBL-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo BLBL-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of pseudo BLBL-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed

    Classes of filters in generalizations of commutative fuzzy structures

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    summary:Bounded commutative residuated lattice ordered monoids (RR\ell -monoids) are a common generalization of BL\mathit {BL}-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 RR\ell -monoids

    On a New Construction of Pseudo BL-Algebras

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    We present a new construction of a class pseudo BL-algebras, called kite pseudo BL-algebras. We start with a basic pseudo hoop AA. Using two injective mappings from one set, JJ, into the second one, II, and with an identical copy A\overline A with the reverse order we construct a pseudo BL-algebra where the lower part is of the form (A)J(\overline A)^J and the upper one is AIA^I. Starting with a basic commutative hoop we can obtain even a non-commutative pseudo BL-algebra or a pseudo MV-algebra, or an algebra with non-commuting negations. We describe the construction, subdirect irreducible kite pseudo BL-algebras and their classification
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