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DEGREE OF VERTICES IN VAGUE GRAPHS
BORZOOEI, R.A.,RASHMANLOU, HOSSEIN The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.5
A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G<sub>1</sub> and G<sub>2</sub> using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.
Degree of Vertices in Vague Graphs
R.A. Borzooei,H. Rashmanlou 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.5
A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs $G_1$ and $G_2$ using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.
(Weak) Implicative Hyper K-ideals
A. Borumand Saeid,R. A. Borzooei,M. M. Zahedi 대한수학회 2003 대한수학회보 Vol.40 No.1
In this note first we define the notions of weak implicative andimplicative hyper K-ideals of a hyper K-algebra H. Then westate and prove some theorems which determine the relationshipbetween these notions and (weak) hyper K-ideals. Also we givesome relations between these notions and all types of positiveimplicative hyper K-ideals. Finally we classify the implicativehyper K-ideals of a hyper K-algebra of order 3.
RESULTS ON HYPERK-ALGEBRAS OF ORDER 3
BORZOOEI, R.A. The Honam Mathematical Society 2005 호남수학학술지 Vol.27 No.2
In this paper, by considering the notion of hyperK-algebras of order 3 (which satisfies the simple or normal condition), we state and prove some theorems which determine the relationships between (weak) hyperK-ideals and positive implicative hyperK-ideals of type $1,{\ldots},8$.
R. A. Borzooei,M. Sabetkish,E. H. Roh,M. Aaly Kologani 한국지능시스템학회 2019 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.19 No.3
In this paper, we introduce the notion of int-soft filters in hoops and related properties are investigated. Characterizations of int-soft filters are discussed and we introduce a congruence relation by using int-soft filter and we show that the quotient is a hoop. Also, we introduce the notions of int-soft n-fold (positive) implicative and int-soft n-fold fantastic filters of hoops, we study some equivalence definitions of them and the relation between them, we prove that every int-soft n-fold positive implicative filter is an int-soft fantastic filter and int-soft implicative filter. Also, we investigate about the quotient structure that is made by them.
CHROMATIC NUMBER OF BIPOLAR FUZZY GRAPHS
TAHMASBPOUR, A.,BORZOOEI, R.A. The Korean Society for Computational and Applied M 2016 Journal of applied mathematics & informatics Vol.34 No.1
In this paper, two different approaches to chromatic number of a bipolar fuzzy graph are introduced. The first approach is based on the α-cuts of a bipolar fuzzy graph and the second approach is based on the definition of Eslahchi and Onagh for chromatic number of a fuzzy graph. Finally, the bipolar fuzzy vertex chromatic number and the edge chromatic number of a complete bipolar fuzzy graph, characterized.
(WEAK) IMPLICATIVE HYPER K-IDEALS
Saeid, A.Borumand,Borzooei, R.A.,Zahedi, M.M. Korean Mathematical Society 2003 대한수학회보 Vol.40 No.1
In this note first we define the notions of weak implicative and implicative hyper K-ideals of a hyper K-algebra H. Then we state and prove some theorems which determine the relationship between these notions and (weak) hyper K-ideals. Also we give some relations between these notions and all types of positive implicative hyper K-ideals. Finally we classify the implicative hyper K-ideals of a hyper K-algebra of order 3.
DERIVATIONS OF MV-ALGEBRAS FROM HYPER MV-ALGEBRAS
Hamidi, M.,Borzooei, R.A. The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.3
In this paper, we investigate some new results in MV-algebras and (strong) hyper MV-algebras. We show that for any infinite countable set M, we can construct an MV-algebra and a strong hyper MV-algebra on M. Specially, for any infinite totally bounded set, we can construct a strong hyper MV-algebra on it. Then by considering the concept of fundamental relation on hyper MV-algebras, we define the notion of fundamental MV-algebra and prove that any MV-algebra is a fundamental MV-algebra. In practical, we show that any infinite countable MV-algebra is a fundamental MV-algebra of itself, but it is not correct for finite MV-algebras.
DERIVATIONS OF MV -ALGEBRAS FROM HYPER MV -ALGEBRAS
( M. Hamidi ),( R. A. Borzooei ) 호남수학회 2016 호남수학학술지 Vol.38 No.3
In this paper, we investigate some new results in MV -algebras and (strong) hyper MV -algebras. We show that for any infinite countable set M, we can construct an MV -algebra and a strong hyper MV -algebra on M. Specially, for any infinite totally bounded set, we can construct a strong hyper MV -algebra on it. Then by considering the concept of fundamental relation on hyper MV -algebras, we define the notion of fundamental MV -algebra and prove that any MV -algebra is a fundamental MV -algebra. In practical, we show that any infinite countable MV -algebra is a fundamental MV -algebra of itself, but it is not correct for finite MV -algebras.