جستجوی مقالات مرتبط با کلیدواژه "eq-algebra" در نشریات گروه "ریاضی"

In this paper, by considering soft set theory, lattice theory and filter theory of EQ-algebras, we introduce the concepts of intuitionistic soft positive implicative L-prefilter and intuitionistic soft implicative L-prefilter. Next, we give some examples and equivalent conditions to characterize them. Furthermore, the relationships between these two notions are investigated.

Intermediate quantifiers are expressions of natural language, for example “most, almost all, many, a few” using which we quantify a number of some objects in a given universe. We have shown in [23] that all valid syllogisms with intermediate  quantifiers are a consequence of only two algebraic inequalities and one equality. The result was obtained in the formalism  of Lukasiewicz fuzzy type theory whose truth values form a linearly ordered complete MV-algebra. In this paper we will  prove that the same holds if we replace MV-algebra by a much more general IEQ-algebra (involutive EQ-algebra).

In this paper, the notions of $n$-fold obstinate and $n$-fold fantastic (pre)filterin $EQ$-algebras are introduced and the relationship among $n$-fold obstinate, maximal, $n$-fold fantastic, and $n$-fold (positive) implicative prefilters are investigated. Moreover, the quotient $EQ$-algebra induced by an $n$-fold obstinate filter is studied and it is proved that the quotient $EQ$-algebra induced byan $n$-fold fantastic filter of a good $EQ$-algebra with bottom element $0$ is an involutive $EQ$-algebra. Finally, the relationships between types of $n$-fold filters in residuated $EQ$-algebras is shown by diagrams

In this paper, we defined the concepts of fuzzy $n$-fold obstinate (pre)filter and maximal fuzzy (pre)filter of $EQ$-algebras and discussed the properties of them. We show that every maximal fuzzy (pre)filter of $mathcal{LomE}$ is normalized and takes only the values ${0, 1}$. Also we show that in good $EQ$-algebra, if $m$ is a normalized fuzzy (pre)filter of $mathcal{LomE}$, then $m$ is a fuzzy $n$-fold obstinate (pre)filter of $mathcal{LomE}$ if and only if every normalized fuzzy (pre)filter of quotient algebra $mathcal{LomE}/m$ is a fuzzy $n$-fold obstinate (pre)filter of $mathcal{LomE}/m$.
Also, we verify relation between fuzzy obstinate $n$-fold (pre)filters and other fuzzy (pre)filters of $EQ$-algebras.

In this paper, by considering the notion of hoop, were introduced by Bosbach in [7, 8] under the name of complementary semigroups, we show that there are relations among hoops and some of other logical algebras such as residuated lattices, MT L-algebras, BL-algebras, MV-algebras, BCK-algebras, equality algebras, EQ-algebras, R0-algebras, Hilbert algebras, Heyting algebras, Hertz algebras, lattice implication algebras and fuzzy implication algebras. The aim of this paper is to find that under what conditions hoops are equivalent to these logical algebras.

This paper is a study of fuzzy type theory (FTT) with partial functions. Out of several possibilities we decided tointroduce a special value ”∗” that represents ”undefined”. In the interpretation of FTT, this value lays outside of thecorresponding domain. In the syntax it can be naturally represented by the description operator acting on the empty(fuzzy) set, because choosing an element from its kernel gives no result. Among many results, we will show that if, in atheory T, ”∗” is defined or provable then T is contradictory. We will also show completeness in the sense any consistenttheory of FTT with partial functions has a model.

In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) states on EQ-algebras. Moreover we discuss the relations between generalized states on EQ-algebras and internal states on other algebras, respectively. We obtain the following (1) Every state-morphism on a good EQ-algebra E is a G-state from E to the EQ-algebra E0 = ([0,1],∧0,⊙0,∼0,1). (2) Every state operator µ satisfying µ(x)⊙µ(y) ∈ µ(E) on a good EQ-algebra E is a GI-state on E. (3) Every state operator τ on a residuated lattice (L,∧,∨,⊙,→,0,1) can be seen a GI-state on the EQ-algebra (L,∧,⊙,∼,1), where x ∼ y := (x → y) ∧ (y → x). (4) Every GI-state σ on a good EQ-algebra (L,∧,⊙,∼,1) is a internal state on equality algebra (L,∧,∼,1). (5) Every GI-state σ on a good EQ-algebra (L,∧,⊙,∼,1) is a left state operator on BCK-algebra (L,∧,→,1), where x → y = x ∼ x∧y.

In this paper, some new properties of EQ -algebras are investigated. We introduce and study the notion of Boolean center of lattice ordered EQ-algebras with bottom element. We show that in a good ℓEQ-algebra E with bottom element the complement of an element is unique. Furthermore, Boolean elements of a good bounded lattice EQ-algebra are characterized. Finally, we obtain conditions under which Boolean center of an EQ-algebra E is the subalgebra of E