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 |