Incline Algebras Research Articles

Neutrosophic equivalence relation applied on incline algebra

Researchers have great interest in working in thefields of fuzzyalgebra and its substructure. Nowadays, the work on fuzzy algebrahas attained the greatest height. Considering the incline algebra in thisstudy, the concept of the neutrosophic equivalence relation in inclinealgebra and its related properties are introduced. Furthermore, thecharacteristic function and chain conditions are also analyzed, withsome results.

Study of Neutrosophic Magnified Translation on Incline Algebra

The concept of magnified translation is studied in Neutrosophic set which is a segregation of mf (membership function) is known as t(truth)mf, i(indeterminate)mf, and f(falsity)mf which has been applied in incline algebra sub - structures and raises with a name called neutrosophic incline substructures are interlinked with the new frame of (nmt) neutrosophic magnified translation. Further, some more engrossing outputs such as homomorphic image, preimage and cartesian product on this neutrosophic magnified translation of incline substructure are investigated.

Jordan generalized left derivations in incline algebras

In this paper, we introduce the concept of generalized left derivations in incline algebras and give some basic properties, which will be helpful to extend some results of algebra to generalized left derivations in incline algebras. At the end, we prove under some certain conditions that a Jordan generalized left derivation in incline algebra [Formula: see text] is a generalized left derivation in [Formula: see text].

Application of MBJ - Neutrosophic Set on Filters of Incline Algebra

The concept of fuzzy set has been generalized to many kinds and one among them is neutrosophic set which is a developed from intuitionistic fuzzy set by adding a components called indeterminate function between truth and falsity membership function. This neutrosophic set also moved a step forward and shows a variation in indeterminate function alone as an interval valued indeterminate function and other functions remains same and this is named as MBJ - neutrosophic set. Here, this work on the MBJ - neutrosophic set merged with incline algbera and introduces the idea of MBJ - neutrosophic filter of an incline algebraic structure and is engrossing with several results. Also, the level, cartesian product, projection, characteristic function and chain conditions are also disputed.

On symmetric bi-generalized derivations of incline algebras

On symmetric bi-generalized derivations of incline algebras

English

English

Permuting tri-f-derivations of incline algebras

Permuting tri-f-derivations of incline algebras

On generalized right derivations of incline algebras

In this paper, we introduce the concept of a generalized right derivation, which is a generalization of right derivation in incline algebras and give some properties of incline algebras. Also, the concept of D-ideal is introduced in an incline algebra with respect to a generalized right derivation.

Symmetric bi-f-derivations of incline algebras

In this paper, we introduce the concept of a symmetric bi-f-derivation in incline algebras and give some properties of incline algebras. Also, we characterize KerD(K) and Fa(K) by symmetric bi-f-derivations in incline algebras. Mathematics Subject Classication: 06F35, 03G25, 08A30

On generalized f-derivations of incline algebras

On generalized f-derivations of incline algebras

ON RIGHT f-DERIVATIONS OF INCLINE ALGEBRAS

Abstract. In this paper, we introduce the concept of a rightderivation in incline algebras and give some properties of inclinealgebras. Also, the concept of d-ideal is introduced in an inclinealgebra with respect to right derivation. 1. IntroductionZ. Q. Cao, K. H. Kim and F. W. Roush [4] introduced the notionof incline algebras in their book and later it was developed someauthors [1, 2, 3, 5]. Ahn et al [1] introduced the notion of quotientincline and obtained the structure of incline algebras. N. O. Alshehri [3]introduced the notion of derivation in incline algebra. Incline algebra is ageneralization of both Boolean and fuzzy algebra and it is a special typeof semiring. It has both a semiring structure and a poset structure. Itcan also be used to represent automata and other mathematical systems,to study inequalities for non-negative matrices of polynomials. In thispaper, we introduce the concept of a right derivation in incline algebrasand give some properties of incline algebras. Also, the concept of d-idealis introduced in an incline algebra with respect to right derivation.2. PreliminariesAn incline algebra is a set K with two binary operations denoted by + and satisfying the following axioms:(K1) x+ y = y + x;(K2) x+ (y + z) = (x+ y) + z;

Graphs and matroids weighted in a bounded incline algebra.

Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.

ON RIGHT DERIVATIONS OF INCLINE ALGEBRAS

In this paper, we introduce the concept of a right derivation in incline algebras and give some properties of incline algebras. Also, the concept of d-ideal is introduced in an incline algebra with respect to right derivation.

On t−derivations of incline algebras

On t−derivations of incline algebras

Generalized derivations of incline algebras

In this paper we introduce the notion of generalized derivation of incline algebras, and we prove some result on generalized derivation of an incline and integral incline.

On Generalized Transitive Matrices

Transitivity of generalized fuzzy matrices over a special type of semiring is considered. The semiring is called incline algebra which generalizes Boolean algebra, fuzzy algebra, and distributive lattice. This paper studies the transitive incline matrices in detail. The transitive closure of an incline matrix is studied, and the convergence for powers of transitive incline matrices is considered. Some properties of compositions of incline matrices are also given, and a new transitive incline matrix is constructed from given incline matrices. Finally, the issue of the canonical form of a transitive incline matrix is discussed. The results obtained here generalize the corresponding ones on fuzzy matrices and lattice matrices shown in the references.

Maximum order-index of matrices over commutative inclines: an answer to an open problem

This paper proves that the maximum order-index of n × n matrices over an arbitrary commutative incline equals ( n − 1) 2 + 1. This is an answer to an open problem “Compute the maximum order-index of a member of M n ( L)”, proposed by Cao, Kim and Roush in a monograph Incline Algebra and Applications, 1984, where M n ( L) is the set of all n × n matrices over an incline L.

Inclines and incline matrices: a survey

Inclines are additively idempotent semirings in which products are less than or equal to either factor. Thus they generalize Boolean and fuzzy algebra. We outline results obtained in a book with Cao [Cao, Kim, Roush, Incline Algebra and Applications, John Wiley & Sons, New York, 1984] on algebraic structure of inclines themselves, matrices over inclines, topological and convergence results, and some applications. This survey paper represents our talk at the 10th annual ILAS conference at Auburn University, June 2002.

Fuzzy subinclines (ideals) of incline algebras

The fuzzification of subinclines (ideals) in inclines are considered, and some related properties are investigated. We also state the product of fuzzy subinclines (ideals), and the projections of fuzzy subinclines (ideals). We discuss fuzzy relations, fuzzy characteristic subinclines (ideals).

Boolean, fuzzy, incline algebra and applications : K.H. Kim, Mathematical Social Sciences, Alabama State University, Montgomery, AL 36195, U.S.A.

Boolean, fuzzy, incline algebra and applications : K.H. Kim, Mathematical Social Sciences, Alabama State University, Montgomery, AL 36195, U.S.A.