States and Measures on Hyper BCK-Algebras

Journal of Applied Mathematics ◽

10.1155/2014/397265 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Xiao-Long Xin ◽

Pu Wang

Keyword(s):

Congruence Relation ◽

Basic Properties ◽

Mv Algebra ◽

Regular Congruence ◽

Bosbach State

We define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra(H,∘,0,e)and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a∘-compatibledregular congruence relationθand aθ-compatibledinf-Bosbach stateson(H,∘,0,e). By inducing an inf-Bosbach states^on the quotient structureH/[0]θ, we show thatH/[0]θis a bounded commutative BCK-algebra which is categorically equivalent to an MV-algebra. In addition, we introduce the notions of hyper measures (states/measure morphisms/state morphisms) on hyper BCK-algebras, and present a relation between hyper state-morphisms and Bosbach states. Then we construct a quotient hyper BCK-algebraH/Ker(m)by a reflexive hyper BCK-idealKer(m). Further, we prove thatH/Ker(m)is a bounded commutative BCK-algebra.

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States on Pseudo-BCI Algebras

European Journal of Pure and Applied Mathematics ◽

10.29020/nybg.ejpam.v10i3.2779 ◽

2017 ◽

Vol 10 (3) ◽

pp. 455-472 ◽

Cited By ~ 2

Author(s):

Xiao Long Xin ◽

Yi Jun Li ◽

Yu Long Fu

Keyword(s):

Basic Properties ◽

Mv Algebra ◽

Bosbach State

In this paper, we discuss the structure of pseudo-BCI algebras and get that any pseudo-BCI algebra is a union of it's branches. We introduce the notion of local bounded pseudo-BCI algebras and study some related properties. Moreover we define two operations $\wedge_1$, $\wedge_2$ in a local bounded pseudo-BCI algebra $A$ and two local operations $\vee_1$ and $\vee_2$ in $V(a)$ for $a\in M(A)$. We show that in a local $\wedge_1$($\wedge_2$)-commutative local bounded pseudo-BCI algebra $A$, $(V(A),\wedge_1,\vee_1)$($(V(A),\wedge_2,\vee_2)$) forms a lattice for all $a\in M(a)$. We define a Bosbach state on a local bounded pseudo-BCI algebra. Then we give two examples of local bounded pseudo-BCI algebras to show that there is local bounded pseudo-BCI algebras having a Bosbach state but there is some one having no Bosbach states. Moreover we discuss some basic properties about Bosbach states. If $s$ is a Bosbach state of a local bounded pseudo-BCI algebra $A$, we prove that $A/ker(s)$ is equivalent to an MV-algebra. We also introduce the notion of state-morphisms on local bounded pseudo-BCI algebras and discuss the relations between Bosbach states and state-morphisms. Finally we give some characterization of Bosbach states.

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New definition of MV-semimodules

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-211130 ◽

2021 ◽

pp. 1-12

Author(s):

Simin Saidi Goraghani ◽

Rajab Ali Borzooei ◽

Sun Shin Ahn

Keyword(s):

Basic Properties ◽

Mv Algebra ◽

Definition Of ◽

Torsion Free

In recent years, A. Di Nola et al. studied the notions of MV-semiring and semimodules and investigated related results [9, 10, 12, 26]. Now in this paper, by using an MV-semiring and an MV-algebra, we introduce the new definition of MV-semimodule, study basic properties and find some examples. Then we study A-ideals on MV-semimodules and Q-ideals on MV-semirings, and by using them, we study the quotient structures of MV-semimodule. Finally, we present the notions of prime A-ideal, torsion free MV-semimodule and annihilator on MV-semimodule and we study the relations among them.

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On EMV-Semirings

Mathematica Slovaca ◽

10.1515/ms-2017-0265 ◽

2019 ◽

Vol 69 (4) ◽

pp. 739-752 ◽

Cited By ~ 2

Author(s):

R. A. Borzooei ◽

M. Shenavaei ◽

A. Di Nola ◽

O. Zahiri

Keyword(s):

Distributive Lattice ◽

Algebraic Structure ◽

Maximal Ideal ◽

Boolean Algebras ◽

Algebraic Extension ◽

Theoretic Approach ◽

Basic Properties ◽

Mv Algebra ◽

Definition Of ◽

Generalized Boolean Algebras

Abstract The paper deals with an algebraic extension of MV-semirings based on the definition of generalized Boolean algebras. We propose a semiring-theoretic approach to EMV-algebras based on the connections between such algebras and idempotent semirings. We introduce a new algebraic structure, not necessarily with a top element, which is called an EMV-semiring and we get some examples and basic properties of EMV-semiring. We show that every EMV-semiring is an EMV-algebra and every EMV-semiring contains an MV-semiring and an MV-algebra. Then, we study EMV-semiring as a lattice and prove that any EMV-semiring is a distributive lattice. Moreover, we define an EMV-semiring homomorphism and show that the categories of EMV-semirings and the category of EMV-algebras are isomorphic. We also define the concepts of GI-simple and DLO-semiring and prove that every EMV-semiring is a GI-simple and a DLO-semiring. Finally, we propose a representation for EMV-semirings, which proves that any EMV-semiring is either an MV-semiring or can be embedded into an MV-semiring as a maximal ideal.

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Involution Abel–Grassmann’s Groups and Filter Theory of Abel–Grassmann’s Groups

Symmetry ◽

10.3390/sym11040553 ◽

2019 ◽

Vol 11 (4) ◽

pp. 553 ◽

Cited By ~ 1

Author(s):

Xiaohong Zhang ◽

Xiaoying Wu

Keyword(s):

Congruence Relation ◽

Filter Theory ◽

Basic Properties ◽

New Concepts ◽

Structure Theorems

In this paper, some basic properties and structure characterizations of AG-groups are further studied. First, some examples of infinite AG-groups are given, and weak commutative, alternative and quasi-cancellative AG-groups are discussed. Second, two new concepts of involution AG-group and generalized involution AG-group are proposed, the relationships among (generalized) involution AG-groups, commutative groups and AG-groups are investigated, and the structure theorems of (generalized) involution AG-groups are proved. Third, the notion of filter of an AG-group is introduced, the congruence relation is constructed from arbitrary filter, and the corresponding quotient structure and homomorphism theorems are established.

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Anti Fuzzy Equivalence Relation on Rings with Respect to t-conorm C

Earthline Journal of Mathematical Sciences ◽

10.34198/ejms.3120.119 ◽

2019 ◽

pp. 1-19 ◽

Cited By ~ 1

Author(s):

Rasul Rasuli

Keyword(s):

Equivalence Relation ◽

Congruence Relation ◽

Basic Properties ◽

Fuzzy Congruence

In this paper, by using t-conorms, we define the concept of anti fuzzy equivalence relation and anti fuzzy congruence relation on ring R and we investigate some of their basic properties. Also we define fuzzy ideals of ring R under t-conorms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring. Next we investigate this concept under homomorphism of new introduced ring.

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Hyper Homomorphism and Hyper Product of Hyper UP-algebras

European Journal of Pure and Applied Mathematics ◽

10.29020/nybg.ejpam.v13i3.3704 ◽

2020 ◽

Vol 13 (3) ◽

pp. 483-497

Author(s):

Rohaima M. Amairanto ◽

Rowena Isla

Keyword(s):

Congruence Relation ◽

Regular Congruence

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.

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Ideals in residuated lattices

Carpathian Journal of Mathematics ◽

10.37193/cjm.2021.01.06 ◽

2021 ◽

Vol 37 (1) ◽

pp. 53-63

Author(s):

DUMITRU BUŞNEG ◽

DANA PICIU ◽

ANCA-MARIA DINA

Keyword(s):

Fuzzy Sets ◽

Binary Relation ◽

Congruence Relation ◽

Natural Generalization ◽

Residuated Lattices ◽

Algebraic Analysis ◽

Deductive Systems ◽

Mv Algebra ◽

The Relationship ◽

Mv Algebras

"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."

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On the Essence and Tipology of International Public Goods

Voprosy Ekonomiki ◽

10.32609/0042-8736-2005-3-131-141 ◽

2005 ◽

pp. 131-141

Author(s):

V. Mortikov

Keyword(s):

Economic Policy ◽

Social Construction ◽

Public Goods ◽

Public Good ◽

Global Public Goods ◽

Club Goods ◽

Basic Properties ◽

International Public Goods ◽

Regional Public Goods ◽

Joint Products

The basic properties of international public goods are analyzed in the paper. Special attention is paid to the typology of international public goods: pure and impure, excludable and nonexcludable, club goods, regional public goods, joint products. The author argues that social construction of international public good depends on many factors, for example, government economic policy. Aggregation technologies in the supply of global public goods are examined.

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