Fuzzy Congruence Relations in Generalized Almost Distributive Fuzzy Lattices

This paper defines the fuzzy congruence relation of GADFL (Generalized nearly distributive fuzzy lattices). The ideas of θ - ideal and θ - Prime ideal are introduced in GADFL, and the fuzzy congruence relation is used to explain these ideals. AMS subject classification: 06D72, 06F15, 08A72.

Norms over intuitionistic fuzzy congruence relations on rings

In this paper, by using norms, we define the concept of intuitionistic fuzzy equivalence relations and intuitionistic fuzzy congruence relations on ring R and we investigate some assertions. Also we define intuitionistic fuzzy ideals of ring R under norms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring.

Sheffer Stroke Nelson Algebras

In this study, Sheffer stroke Nelson algebras (briefly, s-Nelson algebras), (ultra) ideals, quasi-subalgebras and quotient sets on these algebraic structures are introduced. The relationships between s-Nelson and Nelson algebras are analyzed. Also, it is shown that a s-Nelson algbera is a bounded distributive modular lattice, and the family of all ideals forms a complete distributive modular lattice. A congruence relation on s-Nelson algebra is determined by its ideal and quotient s-Nelson algebras are constructed by this congruence relation. Finally, it is indicated that a quotient s-Nelson algebra defined by the ultra ideal is totally ordered and that the cardinality of the quotient is less than or equals to 2.

Filters of strong Sheffer stroke non-associative MV-algebras

In this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved.

Ideals in residuated lattices

"The notion of ideal in residuated lattices is introduced in [Kengne, P. C., Koguep, B. B., Akume, D. and Lele, C., L-fuzzy ideals of residuated lattices, Discuss. Math. Gen. Algebra Appl., 39 (2019), No. 2, 181–201] and [Liu, Y., Qin, Y., Qin, X. and Xu, Y., Ideals and fuzzy ideals in residuated lattices, Int. J. Math. Learn & Cyber., 8 (2017), 239–253] as a natural generalization of that of ideal in MV algebras (see [Cignoli, R., D’Ottaviano, I. M. L. and Mundici, D., Algebraic Foundations of many-valued Reasoning, Trends in Logic-Studia Logica Library 7, Dordrecht: Kluwer Academic Publishers, 2000] and [Chang, C. C., Algebraic analysis of many-valued logic, Trans. Amer. Math. Soc., 88 (1958), 467–490]). If A is an MV algebra and I is an ideal on A then the binary relation x ∼I y iff x^{*}Ꙩ y; x Ꙩy^{*} ∈ I , for x; y ∈ A; is a congruence relation on A. In this paper we find classes of residuated lattices for which the relation ∼ I (defined for MV algebras) is a congruence relation and we give new characterizations for i-ideals and prime i-ideals in residuated lattices. As a generalization of the case of BL algebras (see [Lele, C. and Nganou, J. B., MV-algebras derived from ideals in BL-algebras, Fuzzy Sets and Systems, 218 (2013), 103–113]), we investigate the relationship between i-ideals and deductive systems in residuated lattices."

Construction of some algebras of logics by using intuitionistic fuzzy filters on hoops

<abstract><p>In this paper, we define the notions of intuitionistic fuzzy filters and intuitionistic fuzzy implicative (positive implicative, fantastic) filters on hoops. Then we show that all intuitionistic fuzzy filters make a bounded distributive lattice. Also, by using intuitionistic fuzzy filters we introduce a relation on hoops and show that it is a congruence relation, then we prove that the algebraic structure made by it is a hoop. Finally, we investigate the conditions that quotient structure will be different algebras of logics such as Brouwerian semilattice, Heyting algebra and Wajesberg hoop.</p></abstract>

Hyper Homomorphism and Hyper Product of Hyper UP-algebras

In this paper, we investigate the concept of regular congruence relation on hyper UP-algebras and establish some homomorphism theorems on such algebras. We also examine the notion of hyper product of hyper UP-algebras.

Rough sets based on fuzzy ideals in distributive lattices

In this paper, we present a rough set model based on fuzzy ideals of distributive lattices. In fact, we consider a distributive lattice as a universal set and we apply the concept of a fuzzy ideal for definitions of the lower and upper approximations in a distributive lattice. A novel congruence relation induced by a fuzzy ideal of a distributive lattice is introduced. Moreover, we study the special properties of rough sets which can be constructed by means of the congruence relations determined by fuzzy ideals in distributive lattices. Finally, the properties of the generalized rough sets with respect to fuzzy ideals in distributive lattices are also investigated.

Soft Set Theory Applied to Hoops

In this paper, we introduced the concept of a soft hoop and we investigated some of their properties. Then, we established different types of intersections and unions of the family of soft hoops. We defined two operations ⊙ and → on the set of all soft hoops and we proved that with these operations, it is a hoop and also is a Heyting algebra. Finally we introduced a congruence relation on the set of all soft hoops and we investigated the quotient of it.