THE JOURNAL OF FUZZY MATHEMATICS
  Introduction of The Journal   Instructions to Authors   Archive
in Preserving Maps on Stsc-Biquantales

The Journal of Fuzzy Mathematics

Volume 17, Number 2, June 2009

CONTENT

DETAILS

The Fuzzy Fitness Model of Evolving Networks

Shou Wei Li and Xing San Qian

School of Business and Administration, Jiangsu University, Zhengjiang, Jiangsu 212013, P.R.China E-mail: swiedu@hotmail.com

Kaiquan Shi

School of Mathematics and System Science Shandong University, Jinan, Shangdong 250100, PRC

Abstract: Based on the idea that the degree increment of nodes in scale-free networks depends on their age and competition, the evolving model of fitness is presented. The definition of fuzzy fitness is show by membership function. In the paper, the fuzzy fitness model of evolving networks is presented, and then it's analytical results are obtained through mean-field theory. At last, we give some discussion and conclusion about the model.

Keywords: Membership function, fuzzy fitness, mean-field theory,power law distribution

Classification of Chaotic One-Manifolds and Differential Equations

M. El.-Ghoul, A. K. El-Ahmady and A. El-Abed

Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt.

Abstract: In this paper we will introduce a new connection between differential equations and 1-manifolds. The concepts of and unfolding on the 1-manifold will be characterized by using the differential equations. Theorems governing this connection are presented.

On Flou (Intuttionistic) Compact Space

Kandil

Mathematics Department, faculty of Science, Hwlwan University, Egypt E-mail: Aii_Kandil@hotmail.com

O. Tantawy

Mathematics Department, faculty of Science, Zagazig University, Egypt E-mail: Osama_1tantawi@hotmail.com

M. Wafaie

Mathematics Department, faculty of Science, Hwlwan University, Egypt E-mail: m_wafaie@hotmail.com

Abstract: This paper is devoted to generalize the notions of the Cartesian product, the direct sum, the compact, the Lindelof and the countable compact topological space into a flou concept (intuitionistic concept).

Keywords: Fl-compact space-Fl-Lindelof-countable Fl-compact space.

Intuitionistic Fuzzy Implicative Hyper BCK-Ideals of Hyper BCK-Algebra

Young Bae Jun

Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Korea E-mail address: ybjun@gsnu.ac.kr

Eun Hwan Roh

Department of Mathematics Education, Ghinju National University of Education, Jinju 660-756,

Korea

E-mail address: ehroh@cue.ac.kr

Habib Harizavi

Department of Mathematics, University of Sistan and Baluchistan, Zahedan, Iran E-mail address: harizavi@hamoon.usb.ac.ir

Abstract: After he introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. In this paper ,we apply the concept of intuitionistic fuzzy sets implication hyper BCK-ideas of a hyper BCK-algebras. The notion of intuitionistic fuzzy implicative hyper BCK-ideas of a hyper BCK-algebra is introduced and some related properties are investigated. Relations between intuitionistic fuzzy implicative hyper BCK-ideas and intuitionistic fuzzy hyper BCK-ideas are provided. Characterizations of intuitionistic fuzzy implicative hyper BCK-ideas are given. Using a collection of implicative hyper BCK-ideas, intuitionistic fuzzy implicative hyper BCK-ideas are established.

Keywords: Hyper BCK-algebra, intuitionistic fuzzy (implicative) hyper BCK-ideas .

On Chaotic Fundamental Group and Their Foldings

M. El-Ghoul, A. K. El-Ahmady and M. Abu-Saleem

Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

Abstract: In this paper, we introduce the definition of a new type of the fundamental group called chaotic fundamental group. Some types of conditional foldings and unfoldings restricted on elements of the chaotic fundamental groups are obtained. Also the chaotic fundamental groups of the limit of foldings are deduced. The variant and invariant of the chaotic fundamental group under the folding of chaotic manifold into itself are presented. Theorems and corollaries governing these studies are achieved.

Keywords: Manifold, Folding, Chaotic fundamental group.

Linguistic Truth-Value Lattice Implication Algebra LTVLIA

Dan Meng

School of Economics Information engineering, Southwest University of Finance and Economics, Chengdu, Sichuan, China, 610074 E-mail: mengd_t@swufe.edu.cn

Li Zhou

School of Computer Information Technology, Liaoning Normal University Dalian, Liaoning, China, 116029 E-mail: zoulicn@163.com

Yang Xu

Department of Mathematics, Southwest Jiaotong University of Chengdu, Sichuan, China, 610031 E-mail: yangxu@home.swjtu.edu.cn

Abstract: In this paper, a type-I product lattice implication algebra is given firstly. Secondly, some notes on Cartesian product of lattice implication algebra is given. Then, a linguistic truth-value lattice implication algebra LTVLIA is presented. It is an useful and appropriate tool to represent the linguistic information which includes both linear ordered set and non-linear ordered set. The linguistic truth-value lattice implication algebra LTVLIA can provide an appropriate and reasonable interpretation field for the linguistic truth-value lattice-valued proposition logic system LTVLP(X) and linguistic truth-value lattice-valued first-order system and LTVLF(X). Moreover, the linguistic truth-value lattice implication algebra LTVLIA will provide important theoretical foundation and representation model for group decision-making system, sematic web, intelligent search engine, evaluation system with fuzzy and incomparable information. Both linear information and incomparable information can be dealt with in the uniform linguistic truth-value lattice-valued logic system framework.

Z-Implicative Algebra and Fuzzy Z-Ideal

Yun Ping Xiao and Ting Rong Z*

Dept. of Math, college of Science and technology, Huazhong Agricultural University, Wuhan 430070, Hubei, P. R. China E-mail: ztr@mail.hzau.edu.cn

Abstract: In this paper, Based to the relations between N-semisimple algebra and Lattice implication algebra, FI-algebra, BCK-algebra, BCI-algebra, BCC-algebra, and MV-algebra etc. we introduced the concept of Z-implicative. Algebra and their Fuzzy Z-ideal and discussed their some properties.

Keywords: Z-implicative Algebra, Fuzzy Z-ideal, N-semisimple algebra, center idempotent element, Lattice implication algebra.

On Fuzzy BCK-Filters of BCK-Algebras

Meng Biao-Long

Department of Basic Courses, Xian University of Science and Technology, Xian 710054, P. R. China E-mail: mengbl_100@yahoo.com.cn

Abstract: In the present we first discuss relations between fuzzy filters and fuzzy ideals in a bounded BCK-algebra. Suppose X is a bounded BCK-algebra. Let u is a fuzzy subset of X, we define a fuzzy set v of X by v(x)=u(Nx) for all x belongs to X. if u is a fuzzy BCK-filter on X, then v is a fuzzy ideal on X; if X is commutative, then the inverse of the above is also true. Next we give some charaterizations of bounded BCK-algebra X satisfying the condition FACC by fuzzy BCK-filter. Finally we establish Cartesian products of fuzzy BCK-filter.

Keywords: BCK-algebra, fuzzyBCK-filter(ideal), prime fuzzy BCK-filter(ideal), congruence, Cartesian product

Triangular Fuzzy Number in Intuitionistic Fuzzy Environment

Prasun Kumar Nayak

Department of Mathematics, Bankura Christian College, Bankura-722101, INDIA. E-mail: nayak-prasun@rediffmail.com

Abstract: A new concept of triangular fuzzy number is put forward on the basis of intuitionistic fuzzy set (IFS). The approach can be considered together the degree of satisfaction, sufficiency and rejection. The algebra of such triangular fuzzy number in intuitionistic fuzzy environment is also introduced. Numerical example is provided to illustrate the method.

Keywords: Intuitionistic fuzzy set, triangular fuzzy number

Common Fixed Point Theorems for Weakly Compatible Mappings in Fuzzy Metric Space

H. M. Abu-Donia

Faculty of science, King Saud University Duwadimi, K. S. A.

Kh.Abd-Rabou

Department of Mathematics, Faculty of science, Tanta University, Egypt.

Abstract: In this paper we extend results of Fisher [6], S. Sharma [17], S. Sharma and J. k. Tiwari [18]. We proved a common fixed point theorems for four mappings in fuzzy metric, fuzzy 2-metric and fuzzy 3-metric spaces. Weakly compatible mappings, Fuzzy metric, Fuzzy 2-metric and Fuzzy 3-metric spaces-Comon fixed point.

Degeneracy in Fuzzy Linear Programming Problems

T.Allahviranloo*, F.Hosseinzadeh Lotfi, L. Alizadeh and N. A. Kian

Department of Mathematics, Science and Research, Islamic Azad University, Tehran, Iran.

Abstract: In this paper, the Fuzzy Degenerate Solution (FDS) of a Fuzzy Linear Programming problem (FLP) is defined. Fuzzy systems with fuzzy right hand side are assumed. Some techniques that prevent cycling phenomenon are proposed. At the end, the proposed method is illustrated by numerical examples.

Keywords: Fuzzy Linear Programming, Fuzzy Degenerate, Cycling Topological Approach S. Borkotokey Sr. Lecturer in Mathematics, Dibrugarh U Prevention.

Fuzzy Subspaces of A Vector Space:

Aniversity, Dibrugarh, Assam, India-786004 E-mail: surajitor@yahoo.com

Abstract: In this paper, a relationship between a fuzzy topological vector space (ftvs) and the fuzzy topological space consisting of all fuzzy subspaces of the given vector space is established. It has also been obtained that not every element of an ftvs is a fuzzy subspace, however certain restriction on their algebraic structure leads to an equivalence between the two approaches. Further, an existence theorem of a weak isomorphism between a fuzzy subspace and its homeomorphic linear image and related results have been proposed. A solution method for simultaneous fuzzy linear equations has been evolved as a pre-requisite to finding the kernel of this weak isomorphism.

Keywords: Fuzzy topology, fuzzy topological vector space, subspace of a fuzzy vector space.

Length of Fuzzy Interval and Lebesgue Measure

V. D. Sebastian

Sel. Grade Lecturer in Mathematics, Govt. College, Kottayam, Kerala, India

M. S. Samuel

Dept. of Computer Applications, MACFAST, Thiruvalla, Kerala, India.

Abstract: In this paper we define lower semi continuous fuzzy number and length of a fuzzy closed interval. Certain properties of fuzzy length are considered and finally we define the Fuzzy-Lebesgue measure of an arbitrary fuzzy set in R.

Keywords: Fuzzy number, fuzzy interval, t-norm.

The Bi-Matrix Games with Interval Payoffs and Its Nash Equilibrium Strategy

Prasun Kumar Nayak and Madhumangal Pai*

Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, INDIA.

Abstract: In this paper, we consider bi-matrix games with interval pay-offs. First, based on interval number ranking method for such games, we define Nash equilibrium solutions for pure strategies. On the basis of a comparative study on ordering interval numbers, inequality constraints involving interval coefficients are reduced in their satisfactory crisp equivalent forms and a satisfactory solution of the problem is defined. Moreover, we prove that these Nash equilibrium strategies exist in any bi-matrix games with interval pay-offs. Numerical example is also presented to illustrate the methodology.

Keywords: Bi-matrix game, Interval numbers, Interval game, Nash equilibrium.

Mixed Variational Inclusions and T-Resolvent Equations With Fuzzy Mappings

Rais Ahmad, Farhat Usman and Syed Shakaib Irfan*

Department of Mathematics, Aligarh Muslim University, Aligarh-202002,India. E-mail: raisain@lycos.com; shakaibll@rediffmail.com *College of Engineering, P.O. Box6677, Qassim University, Buraidah 51452 Al-Qassim, Kingdom of Saudi Arabia E-mail: shakaibll@rediffmail.com

Abstract: In this work, we consider a new class of mixed variational inclusions with fuzzy mappings (for short, MVIPFM). In connection with MVIPFM, we also consider a generalized resolvent equation with T-resolvent operations and fuzzy mappings, called T-resolvent equation with fuzzy mappings (for short F-T-REP). the existence of a solution of MVIPFM, F-T-REP and convergence of iterative sequences generated by the proposed algorithms are also studied by using the definition of relaxed strongly accretive operators.

Keywords: variational inclusions, T-accretive operators, Relaxed strongly accretive mapping, T-resolvent equations.

Effect Algebra and Fuzzy Logic Algebra Systems*

Jiancheng Zhang

Dept. of Math., Quanzhou Normal University, Fujian, Quanzhou 362000, China;

Dongli Liu+

Institute of Mathematics, Shaanxi Normal University, Xi¡¯an 710062, China.

Abstract: In the paper, we introduce implicative operation in an effect algebra and get some important properties. Through implicative operation, we investigate the relations among effect algebra and fuzzy logic algebra systems MV ¨Calgebra and R0 ¨Calgebra, furthermore prove that a linear lattice ordered effect algebra is not only a MV- algebra, but also a basis R0 ¨Calgebra. In the contrary, R0 ¨Calgebra may also be an effect algebra.

Keywords: Effect algebra; MV ¨Calgebra; R0 ¨Calgebra; Implicative operation

Join Preserving Maps on Stsc-Biquantales

Yong Chan Kim and Nam Gyu Kim

Department of Mathematics, Kangnung National University, Gangneung, 201-702, Korea

Abstract: We investigate the properties of join preserving maps on strictly two-sided, commutative biquantales. Using the properties of join preserving maps, we induce the Zadeh image and preimage operators.

Keywords: Strictly two-sided, commutative biquantales, join preserving maps, (left) right adjointness

On Direct Productof Fuzzy Subrings

Tazid Ali

Department of Mathematics, Dibrugarh University Dibrugarh-4, Assam, India.

Abstract: In this paper the direct product of fuzzy subrings (ideals) has been discussed. We have proved that if the direct product of two fuzzy subsets is a fuzzy subrings (ideal) then at least one of the fuzzy subsets must be a fuzzy subrings (ideal).

Keywords: Direct product of fuzzy subsets, fuzzy subrings, fuzzy ideals.

Some Properties of -Covering Dimension

Shakeel Ahmed Govt.

Degree College Thana Mandi, Tanta Mandi-185212, J and K, INDIA. E-mail: shakeelar2002@yahoo.com

Sandeep Sharma and Renu

Department of Mathematics, University of Jammu, Jammu-180006, INDIA. E-mail: sandeepsh_ju@yahoo.com

Abstract: In this paper we have discussed some more properties of -Covering Dimension.

Keywords: -Covering Dimension, Sum Space, Homomorphism, Good Extension Property.

Isocurvature Folding of Dynamical Manifold

M. El-Ghoul

Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt.

S. I. Nada

Mathematics Department, Faculty of Science, Menoufiya University, Shebeen ElKohom, Menoufiya, Egypt.

S. I. Abo El Fotooh Mathematics Department, Faculty of Science, Al-AzharUniversity for Girls, Cairo, Egypt.

Abstract: In the this we will introduce a new type of foldings of dynamical manifold into itself or into another dynamical manifold, this type preserves the curvature at the corresponding points, we called it isocur-vature folding of dynamical manifold or conditional folding restricted by curvature. The relation between the curvature and the dimension of dynamical manifold is obtained. The relation between the torsion and the dimension of dynamical manifold is discussed.

Keywords: Riemannian manifolds, curvatures.