THE JOURNAL OF FUZZY MATHEMATICS
  Introduction of The Journal   Instructions to Authors   Archive

The Journal of Fuzzy Mathematics

Volume 12, Number 2, June 2004

CONTENT

DETAILS

Fuzzy Lobachevskian Space and Its Folding

A.E.EI-Ahmady

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

Abstract: In this article we will introduce the definition of the fuzzy Lobachevskian spaces. The folding of this space into itself is discussed, the folding of fuzzy horocycles is deduced. The relations between the retraction of the fuzzy horocycle its folding are obtained. Theorems governing this relations are achieved. The fuzzy deformation retract of a fuzzy horocycle is discussed.

Keywords: Fuzzy Lobachevskian space, folding

On the Weakability of Fuzzy Neighborhood Systems on Various Algebraic Structures

T. M. G. Ahsanullah, Fawzi Al-Thukair

Department of Mathematics, College of Sciences, King Saud University Riyadh 11451, Saudi Arabia Email: tmga@ksu.edu.sa Email: thukair@ksu.edu.sa

M. A. Bashar

Department of Mathematics, University of Dhaka Dhaka 1000,Bangladesh

Abstract: The aim of this article is to investigate the weakability and non- weakability of fuzzy neighborhood systems in a certain class of fuzzy neighborhood Abelian groups, rings and modules. While investigating these phenomenon, we present the notion of locally inversely bounded fuzzy neighborhood ring, and study results relating to the weakability of fuzzy neighborhood system in the class of fuzzy neighborhood rings. In doing so, we observe that the closure operator of the Lowen spaces used in groups, rings, modules along with the notion of Lowen-Wuyts denseness play a pivotal role for further development of the theory.

Keywords: Fuzzy topology, fuzzy neighborhood system, inversely bounded fuzzy sets, groups, rings, modules.

Iterative Computation of Eigenvalues and Corresponding Eigenvectors of A FuzzyMatrix

Makani Das

Department of Mathematics,Assam Engineering College Guwahati-781013,Assam, India

Hemanta K.Baruah

Department of Mathematics, Ganhati University Guwahati-7810134,Assam, India

Abstract: There are quite a few computational algorithms of finding and eigenvector of a square matrix. We have studied the effects of fuzziness in an iterative algorithm of finding the eigenvalues in descending in descending order of absolute values and the corresponding eigenvectors. The findings have been discussed with a small numerical example.

Keywords: Fuzzy eigenvalues, Fuzzy eigenvectors, Fuzzy matrix.

On Fuzzy Quasi Continuous Functions

Eftal Tan

Abstract: The concepts of fuzzy quasi continuous, fuzzy almost-quasi continuous, fuzzy weakly-quasi continuous and fuzzy rarely-quasi continuous functions are introduced and studied in light of the concept of -coincidence in a fuzzy setting. Furthermore two new definitions which are named fuzzy rarely almost-quasi continuous and fuzzy rarely quasi continuous are given such that they are more stronger than fuzzy rarely quasi continuity. Finally, comparative study regarding the mutual interrelations among these maps along with fuzzy maps is made.

Keywords: Fuzzy quasi continuous, Fuzzy almost-quasi continuous, fuzzy weakly-quasi continuous, fuzzy rarely-quasi continuous.

Lebesgue Decompositions of Signed Fuzzy Number-valued Measures and Radon-Nikodym Theorems for Fuzzy Number-valued Intergrals on The Fuzzy Set

Fen-xiaZhao and Guang-Quan Zhang

Department of Basic Courses Education, Tianjin University of Commerce Tianjin, 300134, P.R. China

Abstract: The paper is a continuous discussion about signed fuzzy number-valued measures on the fuzzy set. Based on the previous solutions, the existence of Lebesgue decompositions for signed fuzzy number-valued measures is proved. And, on some conditions, it is also verified that the Radon-Nikodym theorem can be carried over from classical measures to signed fuzzy number-valued measures to singed fuzzy number-valued measures with their corresponding integrals.

Keywords: Fuzzy sets, Fuzzy number, signed fuzzy number-valued measure, Lebesgue decomposition, Radon-Nikodym theorem.

Notes on Transitivity, Negative Transitivity, Semitransitivity and Ferrers Property

Wang Xuzhu and Xue Ye

Department of Mathematics, Taiyuan University of Technology Taiyuan,Shanxi, P.R. China Abstract: In this paper, we focus on the investigation of relationships between T-transitivity, negative S-transitivity, T-S-semitransitivity and T-S-Ferrers relation.

Keywords: T-transitivity, negative S-transitivity; T-S-Ferrers relation; T-S-semitransitivity.

On Covering Dimension of -fuzzy Subsets and -topological Spaces

Dalip Singh Jamwal and Shakeel Ahmed

Department of Mathematics, University of Jammu, Jammu-180006, India e-mail address of first author dalipsj@yahoo.com

Abstract: In this paper, we have introduced the concept of covering dimension of L-fuzzy subsets in L-topology and proved some results which give a relationship between covering dimension of L-fuzzy subsets L-topological spaces. We have also proved some more properties and given some more examples and counter examples of covering dimension in L-topology spaces is equal to the maximum of the covering dimensions of both the spaces by considering an additional condition on the underlying lattice. The concept of covering dimension in L-topology has been introduced in paper[2].

Keywords: L-fuzzy subsets, L-topological spaces, covering dimension, sum space Mathematics subject classification(1991):54A40, 04A72.

A New Approach to The Theory of Fuzzy Groups

Aparna Jain D

epartment of Mathematics, Shivaji college Raja Garden University of Delhi, J.L. Delhi India

Naseem Ajmal

Department of Mathematics, Zakir Hussain College University of Delhi, J.L. Nehru Marg New Delhi, India

Abstract: In this paper, we introduced a new category G of fuzzy groups with object class as the class of all fuzzy groups and a morphism between two G-objects as a family of homomorphisms between their level subgroups with a few obvious chain conditions. We provide complete characterization of the monomorphisms for this category G along with a partial characterization of its epimorphisms. We have shown that this category has uncountably many reflective subcategories.

Keywords: Fuzzy group, level subgroup, homomorphisms, category theory, monomorphism, reflective subcategory.

Weak and Strong Fuzzy Homomorphisms of Groups

B. K. Sarma

Department of Mathematics, India Institute of Technology, Guwahati-1, Assam, India

Tazid Ali

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

Abstract: The concept of fuzzy homomorphisms of groups in the setting of the most generalized form of fuzzy mappings is introduced and the invariance of fuzzy groups under fuzzy homomorphisms is established.

Keywords: Fuzzy relation, Fuzzy subgroup, Fuzzifying mapping, Fuzzy homomorphism.

On Fuzzy Functions and Fuzzy Groups on Fuzzy Spaces

A.A.M. Hassan

Department of Mathematics, Faculty of Sciences, Zagazig University, Zagazig, EGYPT

Abstract: The composition (product) of fuzzy functions that defined over a fuzzy space is defined and used to build the group of all one-to-one fuzzy mappings. The concept of fuzzy (inner) automorphisms on a fuzzy group is introduced and discussed. An isomorphism theorem concerning the fuzzy group and its set of fuzzy inner automorphims is given.

Keywords: Fuzzy spaces, fuzzy groups, fuzzy function, fuzzy automorphims, and fuzzy inner automorphims.

Fuzzy Groups on Fuzzy Spaces, Further Results

A.A.M. Hassan

Department of Mathematics, Faculty of Sciences, Zagazig University, Zagazig, EGYPT

Abstract: The concepts of fuzzy conjugates of a fuzzy element and a fuzzy subspace of a fuzzy group are defined on a fuzzy space. The fuzzy centralizer and fuzzy center of a fuzzy element and a fuzzy subspace are discussed too. Interesting results are obtain in case of induced fuzzy subspaces by a fuzzy subset . Some isomorphism theorems are proved concerning fuzzy quotient groups.

Keywords: Fuzzy spaces, fuzzy groups, induced fuzzy subspaces, fuzzy centralizer, fuzzy center.

On Regularly and Normally Ordered Fuzzy Topological Spaces

E. Roja,M.K. Uma

Dept. of Mathematics, Sri Sarada College For Women Salem-16,Tamil Nadu India

G. Balasubramanian

Dept. of Mathematics, Periyar University Salem-636011 Tamil Nadu, India

Abstract: In this paper new classes of fuzzy topological spaces such as fuzzy pre semi regularly ordered spaces, fuzzy semi normally ordered spaces. Ordered fuzzy semi compact spaces etc are introduced and studied by making use of fuzzy pre semi open sets and ordered fuzzy topology.

Keywords: Ordered M-fuzzy pre semi continuous mappings, ordered fuzzy pre semi open mappings, ordered fuzzy pre semi homeomorphism, fuzzy pre semi regularly ordered spaces, fuzzy pre semi normally ordered spaces, ordered fuzzy pre semi compact spaces etc.

Muti-objective Linear Programming Model with T-fuzzy Variables

Cao Bing-yuan

Department & Institute of Mathematics Shantou University, Guangdong, ZIP 515063, China E-mail: bycao@stu.edu.cn

Abstract: The paper builds a multi-objective linear programming model with T-fuzzy variables after introducing T-fuzzy data into it, gives a method to such a model that can be non-fuzzified, and advances a solution, which tests the effectiveness of the model and method by a numerical example.

Keywords: T-fuzzy data, non-fuzzified, multi-objective, linear programming, algorithm.

A Remark on Common Fixed Point of Four Mappings in A Fuzzy Metric Space

R. P. Pant

Department of Mathematics, Kumaon University, D. S. B. Campus, Nainital-263002,Uttaranchal, India

K.Jha

Department of Mathematical Sciences, Kathmandu University, P.O.Box No.6250, Kathnandu, Nepal. E-mail: jhaknh@yahoo.co.in.

Abstract: The aim of the present paper is to prove a common fixed pointed for four fuzzy mappings in fuzzy metric space, by studying the relationship between the continuity and reciprocal continuity of mappings in fuzzy metric space. This gives an analogue of the results by Balasubramaniam et al.[1].

Keywords: Fuzzy metric space, compatible mappings, R-weakly commuting mappings, reciprocal continuity, fixed pointed theorem. AMS (MOS)Subject Classification: 47 H 10.

On Regularity of Block Fuzzy Matrices

AR. Meenakshi

Department of Mathematics, Annamalai University, Annamalainagar-608002, India.

Abstract: The concept of Schur complement is extended to Fuzzy matrices. Necessary and sufficient conditions are given for the regularity of block fuzzy matrices in terms of the Schur complements of its regular diagonal blocks. A set of conditions for a block matrix to be expressed as the sum of regular block matrices is obtained. Consistency of fuzzy relational equations are discussed.

Keywords: Block fuzzy matrices, Fuzzy relational equations, Schur complements.

-fuzzy -algebras

Jian-ming Zhan and Zhi-song Tan

Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province, 445000, P.R.China E-mail: zhanjianming@hotmail.com

Abstract: In this paper, we introduce the notion of -fuzzy ideals of - -algebras, and investigate some of their properties. Moreover, we give characterizations of -Noether - -algebras. Finally, we study the normalization of -fuzzy ideals.

Keywords: -fuzzy ideals, ideals, - normalization, ( -Neother) - -algebras.

Fuzzy Gradation of Openness

Tapas Kumar Mondal and S.K. Samanta

Department of Mathematics, Visva-Bharati, Santiniketan-731 235, W.Bengal, INDIA E-mail: syamal_123@yahoo.in

Abstract: In this paper we introduce a definition of fuzzy gradation of openness as a mapping from the collection of all fuzzy subsets of to the unit interval [0,1] where the arbitrary union condition and finite intersection condition are taken over fuzzy families of fuzzy subsets of .

Keywords: Fuzzy topology, fuzzy family, gradation of openness, fuzzy gradation of openness.

Fuzzy Normal Ideals of - algebras

Young Bae Jun

Department of Mathematics Education, Gyeongsang National University Chinju(jinju)660-701,Korea E-mail: ybjun@gsnu.ac.kr

Abstract: The fuzzification of normal ideals is considered. A condition for a fuzzy ideal to be a fuzzy normal ideal is given. Relations between -fold fuzzy implicative ideals and fuzzy normal ideals are provided. An extension property for fuzzy normal ideals is established. We prove that the family of fuzzy normal ideals is a completely distributive lattice. Using level subsets of a -algebra with respect to a fuzzy set in ,we construct a fuzzy normal ideal of containing .

Keywords: (fuzzy)normal ideal, -fold fuzzy implicative ideal

Strong Connectedness in -fuzzy Topological Spaces

Y.C.Kim

Department of Mathematics, Kangnung National University, Kangnung, Kangwondo210-702, Korea

A.A. Ramadan Department of Mathematics,College of Sciences, King Saud University, Kingdom of Saudi Arabia

S.E.Abbas Department of Mathematics, Faculty of science, Sohag, Egypt

Abstract: In this paper, the concepts of strong connectedness and I-type of strong connectedness in -fuzzy topological space in Sostak¡¯s sense are introduced and studied. We study some properties of them.

Keywords: -fuzzy topological spaces, strong connected sets, I-type of strongly connected sets

Flags and Equivalence of Fuzzy Subspaces

V. Murali

Department of Mathematics (Pure Applied) Rhodes Univerisity Grahamstown 6140 South Africa

Abstract: This paper considers an equivalence on the set of all fuzzy subspaces of a vector spaces, with a finite number of membership values taken from the unit interval. We prove some results linking equivalence classes of such fuzzy subspaces and chain of crisp subspaces of the vector space. Further we investigate the images and pre-images of fuzzy subspaces under a linear map with regard to equivalence. Whenever the equivalence are not preserved, we have provided suitable counter-examples. The novelty of this paper ,is in the use of flag as a primary tool to study fuzzy subspaces. AMS msc 2000: Primary:08 A72;15A03. Secondary:03E72;06D72.

Keywords: Fuzzy subspaces; flags; sum; product; fuzzy equivalence relation