Search results for: regular ordered semigroup

Authors: Jian Tang

Abstract:

Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S. Finally, characterizations of regular ordered semigroups and intra-regular ordered semigroups by means of the lower part of (∈ ,∈ ∨q)-fuzzy left ideals, (∈,∈ ∨q)-fuzzy right ideals and (∈,∈ ∨q)- fuzzy (generalized) bi-ideals are given.

Keywords: Ordered semigroup, regular ordered semigroup, intraregular ordered semigroup, (∈, ∈ ∨q)-fuzzy left (right) ideal of an ordered semigroup, (∈, ∈ ∨q)-fuzzy (generalized) bi-ideal of an ordered semigroup.

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Authors: Jian Tang

Abstract:

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semigroups. Furthermore, we introduce the notion of semiprime fuzzy ideals of ordered semigroup S and establish the relations between completely semiprime fuzzy ideals and semiprime fuzzy ideals of S. Finally, we give a characterization of prime fuzzy ideals of an ordered semigroup S and show that a nonconstant fuzzy ideal f of an ordered semigroup S is prime if and only if f is twovalued, and max{f(a), f(b)} = inf f((aSb]), ∀a, b ∈ S.

Keywords: Ordered fuzzy point, fuzzy left (right) ideal of anordered semigroup, completely semiprime fuzzy ideal, semiprimefuzzy ideal, prime fuzzy ideal.

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Authors: Jian Tang

Abstract:

In this paper, we first introduce the concepts of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S. Furthermore, we give some characterizations of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S by the ordered fuzzy points and fuzzy subsets of S.

Keywords: Ordered semigroup, ordered fuzzy point, weakly prime fuzzy left ideal, weakly quasi-prime fuzzy left ideal.

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Authors: S.K.Sardar, B.Davvaz, S.Kayal, S.K.Majumdar

Abstract:

The purpose of this note is to obtain some properties of (∈,∈ ∨q)- fuzzy bi-ideals in a Γ-semigroup in order to characterize regular and intra-regular Γ-semigroups.

Keywords: Regular Γ-semigroup, belong to or quasi-coincident, (∈, ∈ ∨q)-fuzzy subsemigroup, (∈, ∈ ∨q)-fuzzy bi-ideals.

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Authors: Samit Kumar Majumder

Abstract:

In this paper the concept of Q-fuzzification of ideals of Γ-semigroups has been introduced and some important properties have been investigated. A characterization of regular Γ-semigroup in terms of Q-fuzzy ideals has been obtained. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between Q-fuzzy ideals of a Γ-semigroup and that of its operator semigroups.

Keywords: Q-Fuzzy set, Γ-semigroup, Regular Γ-semigroup, Q-Fuzzy left(right) ideal, Operator semigroups.

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Authors: Enxiao Yuan, Xiaomin Zhang

Abstract:

It is known that a left C-wrpp semigroup can be described as curler structure of a left band and a C-wrpp semigroup. In this paper, we introduce the class of weakly left C-wrpp semigroups which includes the class of weakly left C-rpp semigroups as a subclass. We shall particularly show that the spined product of a left C-wrpp semigroup and a right normal band is a weakly left C-wrpp semifroup. Some equivalent characterizations of weakly left C-wrpp semigroups are obtained. Our results extend that of left C-wrpp semigroups.

Keywords: Left C-wrpp semigroup, left quasi normal regular band, weakly left C-wrpp semigroup.

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Authors: Sujit Kumar Sardar Manasi Mandal Samit Kumar Majumder

Abstract:

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun and S.Z. Song introduced the notion of intuitionistic fuzzy points. In this paper we find some relations between the intuitionistic fuzzy ideals of a semigroup S and the set of all intuitionistic fuzzy points of S.

Keywords: Semigroup, Regular(intra-regular) semigroup, Intuitionistic fuzzy point, Intuitionistic fuzzy subsemigroup, Intuitionistic fuzzy ideal, Intuitionistic fuzzy interior ideal, Intuitionistic fuzzy semiprime ideal, Intuitionistic fuzzy prime ideal.

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Authors: Zelalem Teshome Wale

Abstract:

The notions of I-vague groups with membership and non-membership functions taking values in an involutary dually residuated lattice ordered semigroup are introduced which generalize the notions with truth values in a Boolean algebra as well as those usual vague sets whose membership and non-membership functions taking values in the unit interval [0, 1]. Moreover, various operations and properties are established.

Keywords: Involutary dually residuated lattice ordered semigroup, I-vague set and I-vague group.

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Authors: Zelalem Teshome Wale

Abstract:

The notions of I-vague normal groups with membership and non-membership functions taking values in an involutary dually residuated lattice ordered semigroup are introduced which generalize the notions with truth values in a Boolean algebra as well as those usual vague sets whose membership and non-membership functions taking values in the unit interval [0, 1]. Various operations and properties are established.

Keywords: Involutary dually residuated lattice ordered semigroup, I-vague set, I-vague group and I-vague normal group.

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Authors: Shin-Shin Kao, Hsiu-Chunj Pan

Abstract:

Given a graph G. A cycle of G is a sequence of vertices of G such that the first and the last vertices are the same. A hamiltonian cycle of G is a cycle containing all vertices of G. The graph G is k-ordered (resp. k-ordered hamiltonian) if for any sequence of k distinct vertices of G, there exists a cycle (resp. hamiltonian cycle) in G containing these k vertices in the specified order. Obviously, any cycle in a graph is 1-ordered, 2-ordered and 3- ordered. Thus the study of any graph being k-ordered (resp. k-ordered hamiltonian) always starts with k = 4. Most studies about this topic work on graphs with no real applications. To our knowledge, the chordal ring families were the first one utilized as the underlying topology in interconnection networks and shown to be 4-ordered. Furthermore, based on our computer experimental results, it was conjectured that some of them are 4-ordered hamiltonian. In this paper, we intend to give some possible directions in proving the conjecture.

Keywords: Hamiltonian cycle, 4-ordered, Chordal rings, 3-regular.

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Authors: Liew Siaw Yee, Tahir Ahmad

Abstract:

In this paper, the Fuzzy Autocatalytic Set (FACS) is composed into Omega Algebra by embedding the membership value of fuzzy edge connectivity using the property of transitive affinity. Then, the Omega Algebra of FACS is a transformation semigroup which is a special class of semigroup is shown.

Keywords: Fuzzy autocatalytic set, omega algebra, semigroup, transformation semigroup.

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Authors: Xiaomin Zhang

Abstract:

In this paper, the class of weakly left C-wrpp semigroups which includes the class of weakly left C-rpp semigroups as a subclass is introduced. To particularly show that the spined product of a left C-wrpp semigroup and a right normal band which is a weakly left C-wrpp semifroup by virtue of left C-full Ehremann cyber groups recently obtained by authors Li-Shum, results obtained by Tang and Du-Shum are extended and strengthened.

Keywords: Left C-semigroup, left C-wrpp semigroup, left quasinormal band, weakly left C-wrpp semigroup

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Authors: D.R Prince Williams

Abstract:

In this paper,we introduce a notion of fuzzy ideals in near-subtraction semigroups and study their related properties.

Keywords: subtraction algebra, subtraction semigroup, an ideal, near-subtraction semigroup, fuzzy level set, fuzzy ideal, fuzzy homomorphism.

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Authors: José M. Merigó, Anna M. Gil-Lafuente

Abstract:

Different types of aggregation operators such as the ordered weighted quasi-arithmetic mean (Quasi-OWA) operator and the normalized Hamming distance are studied. We introduce the use of the OWA operator in generalized distances such as the quasiarithmetic distance. We will call these new distance aggregation the ordered weighted quasi-arithmetic distance (Quasi-OWAD) operator. We develop a general overview of this type of generalization and study some of their main properties such as the distinction between descending and ascending orders. We also consider different families of Quasi-OWAD operators such as the Minkowski ordered weighted averaging distance (MOWAD) operator, the ordered weighted averaging distance (OWAD) operator, the Euclidean ordered weighted averaging distance (EOWAD) operator, the normalized quasi-arithmetic distance, etc.

Keywords: Aggregation operators, Distance measures, Quasi- OWA operator.

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Authors: S.Krishnamoorthy, R.Arul Doss

Abstract:

We introduce the notion of commuting regular Γ- semiring and discuss some properties of commuting regular Γ- semiring. We also obtain a necessary and sufficient condition for Γ-semiring to possess commuting regularity.

Keywords: Commutative Γ-semiring, Idempotent Γ-semiring, Rectangular Γ-band, Commuting regular Γ-semiring, Clifford Γ-semiring.

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Authors: José M. Merigó, Anna M. Gil-Lafuente

Abstract:

We study different types of aggregation operators such as the ordered weighted averaging (OWA) operator and the generalized OWA (GOWA) operator. We analyze the use of OWA operators in the Minkowski distance. We will call these new distance aggregation operator the Minkowski ordered weighted averaging distance (MOWAD) operator. We give a general overview of this type of generalization and study some of their main properties. We also analyze a wide range of particular cases found in this generalization such as the ordered weighted averaging distance (OWAD) operator, the Euclidean ordered weighted averaging distance (EOWAD) operator, the normalized Minkowski distance, etc. Finally, we give an illustrative example of the new approach where we can see the different results obtained by using different aggregation operators.

Keywords: Aggregation operators, Minkowski distance, OWA operators, Selection of strategies.

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Authors: K. Kannan, D. Narasimhan, K. Chandrasekhara Rao, R. Ravikumar

Abstract:

The aim of this paper is to introduce the concepts of τ1τ2-regular generalized star star closed sets , τ1τ2-regular generalized star star open sets and study their basic properties in bitopological spaces.

Keywords: τ1τ2-regular closed sets, τ1τ2-regular open sets, τ1τ2-regular generalized closed sets, τ1τ2-regular generalized star closed sets, τ1τ2-regular generalized star star closed sets.

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Authors: Ismat Beg, Asma Rashid Butt

Abstract:

Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn  x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x  y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x  y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0  x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.

Keywords: Fixed point, partially ordered set, metric space, set valued mapping.

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Authors: Mahdiyeh Abbasi, Akbar Golchin

Abstract:

It is well-known that, using principal weak flatness property, some important monoids are characterized, such as regular monoids, left almost regular monoids, and so on. In this article, we define a generalization of principal weak flatness called GP-Flatness, and will characterize monoids by this property of their right (Rees factor) acts. Also we investigate new classes of monoids called generally regular monoids and generally left almost regular monoids.

Keywords: G-left stabilizing, GP-flatness, generally regular, principal weak flatness.

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Authors: Munehiro Iwami

Abstract:

A property is persistent if for any many-sorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property. Zantema showed that termination is persistent for term rewriting systems without collapsing or duplicating rules. In this paper, we show that the Zantema's result can be extended to term rewriting systems on ordered sorts, i.e., termination is persistent for term rewriting systems on ordered sorts without collapsing, decreasing or duplicating rules. Furthermore we give the example as application of this result. Also we obtain that completeness is persistent for this class of term rewriting systems.

Keywords: Theory of computing, Model-based reasoning, term rewriting system, termination

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Authors: Santirat Nansaarng, Sittichai Kaewkuekool, Supreeya Siripattanakunkajorn

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This research was to study a comparison of inspector-s performance between regular and complex visual inspection task. Visual task was simulated on DVD read control circuit. Inspection task was performed by using computer. Subjects were 10 undergraduate randomly selected and test for 20/20. Then, subjects were divided into two groups, five for regular inspection (control group) and five for complex inspection (treatment group) tasks. Result was showed that performance on regular and complex inspectors was significantly difference at the level of 0.05. Inspector performance on regular inspection was showed high percentage on defects detected by using equal time to complex inspection. This would be indicated that inspector performance was affected by visual inspection task.

Keywords: Visual inspection task, regular and complex task.

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Authors: Ezequiel Herruzo, Juan José Cruz, José Ignacio Benavides, Oscar Plata

Abstract:

This paper describes a new algorithm of arrangement in parallel, based on Odd-Even Mergesort, called division and concurrent mixes. The main idea of the algorithm is to achieve that each processor uses a sequential algorithm for ordering a part of the vector, and after that, for making the processors work in pairs in order to mix two of these sections ordered in a greater one, also ordered; after several iterations, the vector will be completely ordered. The paper describes the implementation of the new algorithm on a Message Passing environment (such as MPI). Besides, it compares the obtained experimental results with the quicksort sequential algorithm and with the parallel implementations (also on MPI) of the algorithms quicksort and bitonic sort. The comparison has been realized in an 8 processors cluster under GNU/Linux which is running on a unique PC processor.

Keywords: Parallel algorithm, arrangement, MPI, sorting, parallel program.

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Authors: Ryuya Uda

Abstract:

On existing online shopping on the web, SSL and password are usually used to achieve the secure trades. SSL shields communication from the third party who is not related with the trade, and indicates that the trader's web site is authenticated by one of the certification authority. Password certifies a customer as the same person who has visited the trader's web site before, and protects the customer's privacy such as what the customer has bought on the site. However, there is no forensics for the trades in those cased above. With existing methods, no one can prove what is ordered by customers, how many products are ordered and even whether customers have ordered or not. The reason is that the third party has to guess what were traded with logs that are held by traders and by customers. The logs can easily be created, deleted and forged since they are electronically stored. To enhance security with digital forensics for electronic commerce on the web, I indicate a secure method with cellular phones.

Keywords: Cellular Phone, Digital Forensics, ElectronicCommerce, Information Security

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Authors: José M. Merigó, Montserrat Casanovas

Abstract:

We consider different types of aggregation operators such as the heavy ordered weighted averaging (HOWA) operator and the fuzzy ordered weighted averaging (FOWA) operator. We introduce a new extension of the OWA operator called the fuzzy heavy ordered weighted averaging (FHOWA) operator. The main characteristic of this aggregation operator is that it deals with uncertain information represented in the form of fuzzy numbers (FN) in the HOWA operator. We develop the basic concepts of this operator and study some of its properties. We also develop a wide range of families of FHOWA operators such as the fuzzy push up allocation, the fuzzy push down allocation, the fuzzy median allocation and the fuzzy uniform allocation.

Keywords: Aggregation operators, Fuzzy numbers, Fuzzy OWAoperator, Heavy OWA operator.

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Authors: K. V. Geetha, N. R. Mangalambal

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Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounded convergence assigned to the dual spaces. We apply Laplace transformation to the ordered linear space of Laplace transformable generalized functions. We ultimately aim at finding solutions to nonhomogeneous nth order linear differential equations with constant coefficients in terms of generalized functions and comparing different solutions evolved out of different initial conditions. Method. The above aim is achieved by • Defining the spaces La,b, L(w, z). • Assigning an order relation on these spaces by identifying a positive cone on them and studying the properties of the cone. • Defining an order relation on the dual spaces La,b, L(w, z) of La,b, L(w, z) and assigning a topology to these dual spaces which makes the order dual and the topological dual the same. • Defining the adjoint of a continuous map on these spaces and studying its behaviour when the topology of bounded convergence is assigned to the dual spaces. • Applying the two-sided Laplace Transformation on the ordered linear space of generalized functions W and studying some properties of the transformation which are used in solving differential equations. Result. The above techniques are applied to solve non-homogeneous n-th order linear differential equations with constant coefficients in terms of generalized functions and to compare different solutions of the differential equation.

Keywords: Laplace transformable generalized function, positive cone, topology of bounded convergence

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Authors: Antonio Breda d’Azevedo

Abstract:

Regularity has often been present in the form of regular polyhedra or tessellations; classical examples are the nine regular polyhedra consisting of the five Platonic solids (regular convex polyhedra) and the four Kleper-Poinsot polyhedra. These polytopes can be seen as regular maps. Maps are cellular embeddings of graphs (with possibly multiple edges, loops or dangling edges) on compact connected (closed) surfaces with or without boundary. The n-dimensional abstract polytopes, particularly the regular ones, have gained popularity over recent years. The main focus of research has been their symmetries and regularity. Planification of polyhedra helps its spatial construction, yet it destroys its symmetries. To our knowledge there is no “planification” for n-dimensional polytopes. However we show that it is possible to make a “surfacification” of the n-dimensional polytope, that is, it is possible to construct a restrictedly-marked map representation of the abstract polytope on some surface that describes its combinatorial structures as well as all of its symmetries. We also show that there are infinitely many ways to do this; yet there is one that is more natural that describes reflections on the sides ((n−1)-faces) of n-simplices with reflections on the sides of n-polygons. We illustrate this construction with the 4-tetrahedron (a regular 4-polytope with automorphism group of size 120) and the 4-cube (a regular 4-polytope with automorphism group of size 384).

Keywords: Maps, representation, polytopes.

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Authors: Lokendra K. Balyan

Abstract:

In this paper, we present an algorithm for computing a Schur factorization of a real nonsymmetric matrix with ordered diagonal blocks such that upper left blocks contains the largest magnitude eigenvalues. Especially in case of multiple eigenvalues, when matrix is non diagonalizable, we construct an invariant subspaces with few additional tricks which are heuristic and numerical results shows the stability and accuracy of the algorithm.

Keywords: Schur Factorization, Eigenvalues of nonsymmetric matrix, Orthoganal matrix.

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Authors: Zhengnan Shi

Abstract:

In this paper, we consider the problem of Popular Matching of strictly ordered preference lists. A Popular Matching is not guaranteed to exist in any network. We propose an IDbased, constant space, self-stabilizing algorithm that converges to a Maximum Popular Matching an optimum solution, if one exist. We show that the algorithm stabilizes in O(n5) moves under any scheduler (daemon).

Keywords: self-stabilization, popular matching, algorithm, distributed computing, fault tolerance

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Authors: Asep Bayu Dani Nandiyanto, Asep Suhendi, Yutaka Kisakibaru, Takashi Ogi, Kikuo Okuyama

Abstract:

An ordered porous antimony-doped tin oxide (ATO) film was successfully prepared using a simple coating process with colloidal templates. The facile production was effective when a combination of 16-nm ATO (as a model of an inorganic nanoparticle) and polystyrene (PS) spheres (as a model of the template) weresimply coated to produce a composite ATO/PS film. Heat treatment was then used to remove the PS and produce the porous film. The porous film with a spherical pore shape and a highly ordered porous structure could be obtained. A potential way for the control of pore size could be also achieved by changing initial template size. The theoretical explanation and mechanism of porous formation were also added, which would be important for the scaling-up prediction and estimation.

Keywords: Porous structure film; ATO particle; Ultra-low refractive index; vertical drop method; Low-density material;

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Authors: Ahmed Mansouri, Naoji Matsumoto

Abstract:

This research is a comparative study of complexity, as a multidimensional concept, in the context of streetscape composition in Algeria and Japan. 80 streetscapes visual arrays have been collected and then presented to 20 participants, with different cultural backgrounds, in order to be categorized and classified according to their degrees of complexity. Three analysis methods have been used in this research: cluster analysis, ranking method and Hayashi Quantification method (Method III). The results showed that complexity, disorder, irregularity and disorganization are often conflicting concepts in the urban context. Algerian daytime streetscapes seem to be balanced, ordered and regular, and Japanese daytime streetscapes seem to be unbalanced, regular and vivid. Variety, richness and irregularity with some aspects of order and organization seem to characterize Algerian night streetscapes. Japanese night streetscapes seem to be more related to balance, regularity, order and organization with some aspects of confusion and ambiguity. Complexity characterized mainly Algerian avenues with green infrastructure. Therefore, for Japanese participants, Japanese traditional night streetscapes were complex. And for foreigners, Algerian and Japanese avenues nightscapes were the most complex visual arrays.

Keywords: Streetscape, Nightscape, Complexity, Visual Array, Affordance, Cluster Analysis, Hayashi Quantification Method.

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