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

The Journal of Fuzzy Mathematics

Volume 11, Number 4, December 2003

CONTENT

DETAILS

Topics in Fuzzy Metric Spaces Massound

Amini and Reza Saadatic

Departement of Mathematic Shahid Beheshti University Evin 19839-Tehran.Iram

Abstact: We define adherent and accumulation points of a set in a fuzzy metric space and prove Sierpinsky Theorem and Hine Therom for fuzzy metric spaces.

Keywords: Fuzzy metric spaces , simerpinsky theorem , henie theorem .

Fuzzy Semi-topogenous Orders

A.A.Ramadan B.

Departement of Mathematic , King Soud University Burieda 818999 , Kingdom of Saudi Arabia

M . El-Dardery

Departement of Mathematic, Faculty of Science, Cairv University Faiyum,Egypt

Y.C. Kim

Departement of Mathematic,kagunung National University Kangnung ,Kangwondo,210-702,Korea

Abstract: We introduce the concept of fuzzy (semi-) topogenous orders in the framework of fuzzy (supra) topology, fuzzy (supra) interior operator and fuzzy (supra-) quasiproximity.Some fundmamental properties of them are established. We study a natural relationship between fuzzy (semi-) topogenous structure, fuzzy (supra) topology, fuzzy (supra) interior operator and fuzzy (quasi) proximity.

Keywords: Fuzzy (semi-) topogenous orders, fuzzy (supra) interior operator, fuzzy (supra) topology and fuzzy (supra-) quasi-proximity.

On Fuzzy Syntopogenous Structures

A.A.Ramadan B.

Departement of Mathematic , King Soud UniversityC.Burieda 818999 , Kingdom of Saudi Arabia

D.M . El-Dardery E.

Departement of Mathematic, Faculty of Science, Cairv University Faiyum,Egypt

Y.C. Kim Departement of Mathematic,kagunung National University Kangnung ,Kangwondo,210-702,Korea

Abstract: We introduce the concept of smooth syntopogenous stuctures in the framework of fuzzy topologies, fuzzy proximities and fuzzy uniformities. We investigate some fundamental properties of them. Firnally, We study a natural relationship among smooth syntopogenous structures, fuzzy topologies, fuzzy proximityies and fuzzy topologies.

Keywords: Fuzzy topogenous orders, Fuzzy (syn-) topogenous structure, smooth syntopogenous stuctures, fuzzy topologies, fuzzy (quasi-) topologies, fuzzy (quasi-) uniformities.

Fuzzy Implications Suitable for Triple I Based Fuzzy Reasoning

Daowu Pei

Faculty of Science, Xi¡¯an Jiaotong university Xi¡¯an 710049,P. R. Chnia Departement of Mathematic,Yangcheng Teachers College Y,angcheng 224002,P.R.China E-mail:dwpei@sina.com

Abstract: This paper focuses on fuzzy implications suitable for triple I based reasoning.Two kids of generalized R-implication are introuduced, and their properties are discussed.

Keywords: Fuzzy logic, triple I based fuzzy reasoning,generalized R-impication, generalized t-norm.

Isomorphism Theorems of Generalized Fuzzy Quotient Rings

Bingxue Yao

School of Mathematics and System Science,Shangdong University Jinan 250100,P.R.China Department of Mathematics and System Science,Liaocheng UniversityLiaocheng252059,P.R.China

Yong Li and Kaiquan Shi

School of Mathematics and System Science,Shangdong University Jinan 250100,P.R.China

Abstract: The concept of fuzzy semiideals and generalized fuzzy quotient rings are introduced.Some properties of fuzzy semiideals discussed. At last,several isomorphism theorems of generalized fuzzy quotient rings are established.

Keywords: Fuzzy semiideal, generalized fuzzy quotient ring,homomorphism,isomorphism.

On Charaterizing Notions of Characterized Spaces

S. Abd-Allah and M.El-Essawy

Department of Mathematics,Faculty of Science,El-Mansoura University El-Mansoura,Egypt

Abstract: Basic result on the characterized spaces are presented obtained in applying the theory of fuzzy filters developed in [6] and using results given in [1].There are mainly investigated notions defined for characterized spaces which can be used for their characterization.They are called characterizing notions.In some cases the notions we consider are characterizing under some assumptions on the characterized spaces.Examples of characterizing notions which do not need any assumption are those of -fuzzy neighborhood of a fuzzy filter,of the -interior of a fuzzy filter and of the set of -inner points of a fuzzy filter. The notions of -open fuzzy filter are characterizing for idempotent characterized spaces.Futher characterizing notions are presented obtained by restricting to valued and superior principal fuzzy filters.

Keywords: Characterized Spaces,idempotent characterized spaces,stratified sna strongly stratified characterized spaces,fuzzy filter pretopologies, -fuzzy neighborhood operators, -interior operators, -open and projectively -open fuzzy filters, -inner points of fuzzy filters.

The Structure and a-resolution Field of Indecomposable Extremely Simple Forms of Lattic-valued Proposition Logic LP(X)

Wei Wang ,Yang Xu and KeYum Qin

Department of Applied Mathematics,Southwest jiaotong University Chengdu610031,Sichuan,P.R.China

Abstract: In this present paper,the -resolution field of indecomposable extremely simple forms of lattice-valued propositional logic LP(X) is focused.The properties and the -resolution field of indecomposable extremely simple forms are investigated,the conclusion that every formula of LP(X) is equivalent to a generalized conjunctive(disjunctive) normal form is proved,and some important results of -resolution field of indecomposable extremely simple forms are obtained.

Keywords: Propositional variable,generalized literal,extremely simple form,indecomposable extremely simple form.

Lattic Implication Algebras and Their Filters

Xuefang ,Wang Yang Xu and Keyun Qin

Department of Applied Mathematics,Southwest jiaotong University Chengdu610031,Sichuan,P.R.China

Abstract: Lattice implication algebra is an algebraic structure that is established by combing lattice and implication algebra.In this paper,we further investigate on some properties of implication algebras and their filters.

Keywords: Lattice-valued logic, lattice implication algebras,filters,implicative filters.

Fuzzying Topogenous Structures

M. Azab Abd-Allah

Department of Mathematics,Faculty of Science Assiunt University,Assiut,Egypt E-mail:mazab57@hotmai.com

Abstract: We will define the fuzzifying topogenous spaces and investigate some of their properties.We will prove the existences of initial topogenous structures.

Fuzzy BZ ¨Cideals and Anti-grounped Ideals

Xiao Hong Zhang

Department of Mathematics,Faculty of Science Ningbo University,Ningbo315211Zhejiang,PeoplesP.R.China

Department of Computer Science and Engineering,Northwestern Polytechnical University Xian 710072,Shaanxi Province,P.R.China E-mail:zxhonghz@263.net

Abstract: The aim of this paper is to introduce the notions of fuzzy BZ-ideal and fuzzy antigrouped ideals of BZ-algebras and investigate their properties.We prove that every fuzzy BZ-ideal of a BZ-algebra is a fuzzy BCI-ideal,but the converse is not true by providing an example (proved by using the software mathematica),and shou that in a BCI-algebra the notion of fuzzy BZ-ideal and BCI-algebra the notion of fuzzy anti-grouped ideal and fuppy p-ideal coincide.We give several characterizations of fuzzy BZ-ideals and fuzzy anti-grouped ideals.There are the generalization of the related results in [3],[4],[5],[6],[7],[8] from BCI,BCC-algebras.to BZ-algebras. Finally we prove the following interesting result:let be a fuzzy BZ-idea of a BZ-algebras X(a fuzzy BCI ¨Cideal of BCI ¨Calgebra X),then there exits a fuzzy antigrouped ideal(a fuppy p-ideal) of X such that for any .

Keywords: BZ-algebra, fuzzy BZ-ideal, fuzzy anti-grouped ideals, fuppy p-ideal.

Some Good Dilutions of Compactness in Sostak¡¯s Fuzzy Topology

Y.C. Kim

Department of Mathematics,Kangnung Nation University Kangwondo,Korea

A.A.Ramadan

Department of Mathematics,Faculty of Science Beni-Suef,Egypt

S.E.Abbas

Department of Mathematics, Faculty of Science Sohag,Egypt

Abstract: The ain of this paper is to introduce good definitions of compactness,almost compactness,near compactness,weak compactness,and S-closedness in fuzzy topological spaces in Sostak¡¯s sense.These compactness related concepts are defined for arbitrary fuzzy sets and some of their properties studiesd.

Keywords: Fuzzy compactness,,fuzzy almost compactness,fuzzy near compactness,fuzzy weak compactness,good extension.

Operations on Fuzzy Multifunctionns and Fuzzy Maxiimum Principle

Ismat Beg

Department of Mathematics,Lahore University of Manngement Science 54792-Lahore,Pakistan E-mail:ibeg@lums.edu.pk

Abstract: We study basic operations on fuzzy multifunction defined between fuzzy topological spaces.Many interesting relations basic operations and upper and lower henicontinuity are proved.As application we proved fuzzy maximal principle for fuzzy multifunctions.

Keywords: Fuzzy multifunction,fuzzy hemicontinuity,fuzzy maximumprinciple,analysis.

Fuzzy Matrices and Linear Transformtions on Fuzzy Verctor Spaces

A.R. Meemnakshi and CInbam

Department of Mathematics,Annamalai University Annamalainagar-608002,India

Abstract: We introduce the concept of standard fuzzy linear combination of vectors in terma of the unique standard basis in a finitely generated subspace of a fuzzy vector space.By using this we proved that there is a one to one correspondence between the set of all linear transformations on a finitely generated subspace of a fuzzy vector space to the set of all fuzzy matrices.

Keywords: Fuzzy matrix,fuzzy relational equation, fuzzy vector space, linear transformation.

Differentiation of Fuzzy Functions

John N. Mordeson

Department of Mathematics,Compute Science,Creighton University Omaha,Nebraska68178,U.S.A

Abstract: We give a different definition of differentiability of a fuzzy function.Our definition of differentiability is such that it corresponds to a particular definition of Riemann integrability of a fuzzy function.It also has the benefit of allowing the theory to be put into an an algebraic setting.The definition yields in a natural way a measure of fuzziness of a fuzzy function.This measure of fuzziness of a fuzzy function is used to show that the derivative of a fuzzy function can be considered sa a fuzzy linear transformation of a space of differentiable fuzzy functionto the space of fuzzy numbers.This particular type of a fuzzy linear transformation is of the same type as the occurringin the integration of fuzzy function.This is of importance since it indicates what type of fuzzy linear transformation should be used in the development of modern Galois theory involing higher derivations and high order derivations.We also give conditions under which a differential equation of the first order involving fuzzy function has a unique solution.

Keywords: Derivative, fuzzy function,fuzzy number, fuzzy linear transformation,Lipschitz condition.

Necessary and Sufficient Conditions for Oscillations of the Delay Difference Equation

M..El-attar£¬E.M. El-Abd and SH.El-Bendary

Department of Mathematics,Faculty of Science Tanta University,Egypt

-semi Group in Fuzzy Setting

Baldev Baberjiee and Surajit Borkotokey

Department of Mathematics,Dibrugarh University Dibrugarh,Assam,786004 India E-mai:b-banerjee@lycos.com E-mail:surajitbor@yahoo.com

Abstract: In this paper,we have introduced the concept of a fuzzy -ideal of a -semigroup and discussed some of their properties.The concept of the ( ) cuts in a -semigroup has been introduced and studied some of their characteristics.

Keywords: -semigroup,fuzzy, -ideal, ( ) cut.

-structure of FTS: Fuzzy Paracompact Spaces(I)

Hu Cheng-ming

International Fuzzy Mathematics Institute P.O.Box4067,El Monte CA91734,USA

Abstract: In paper [1,2],the auther introduced -cover, -refinement and some kinds of fuzzy compactness.Using these conceptions,we will introduce F-paracompact and give some characterizations of its.In paper [5],we introduced S- paracompact and proved that every (or F-regular) S- paracompact fuzzy topological space is a product-induced space.This is a kind of important fuzzy topological spaces [3,4,5].Every product-induced space is topologically isomorphic with a classical product topological space.Now,we will give the -stucture of S- paracompact and point out that the F- paracompact and S- paracompact are equivalent in the finest product-induced spaces.

Keywords: -cover, -refinement,locally finite of -sets, F- paracompact,pseudo-open fuzzy set, S- paracompact, product-induced spaces.