THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 9, Number 1, March 2001

CONTENT

DETAILS

Product Operation in the Category of L-fuzzy Groups

Tang Jiangang

Department of Mathematics.Yili Teacher¡¯s College Yining,Xinjiang ,P.R.China)

Zhang Xunfeng

Centre of computer,Yili Radio and TV University Yining,,Xinjiang ,P.R.China)

Abstract: First the concept of L-fuzzy groups is introduced which takes the category of fuzzy groups given in [2] as it is subcategory. Then we prove that the category of L-fuzzy groups is closed under the product operation .Furthermore,we establish a necessary and sufficient condition under which the product of L-fuzzy group is the product of groups.Finally we yield the concrete structure and some of the product of L-fuzzy groups.

Keywords: L-fuzzy group,Category of L-fuzzy groups,Product.

On fixed Point Theorems for Fuzzy Mappings*

Wu Jian-rong

Department of Mathematics,Harbin Institute of Technology Harbin,150001,P.R.China

Abstract: The relation between fixed points of fuzzy mappings and those of set-valued mappings is pointed out.Fixed point results for fuzzy mappings are obtained. The common fixed point theorems for fuzzy mappings and single-valued mapping are proved.

Keywords: Fixed point,common fixed point,nonexpansive mapping,contractive-type fuzzy mapping,upper semicontiunous fuzzy mapping.

Fuzzy Ideals of Pogroupoids

Young Bae Jun

Department of Mathematics Education Gyeongsang National University,Chinju 660-701,Korea e-mai:ybjun@nongae.gsnu.ac.kr

Hee Sik Kim

Department of Mathematics Hanyang University.Seoul 133-791,Korea e-mail:heekim@gemail.hanyang.ac.kr

Abstract: The fuzzification of the concept of an ideal in a pogroupoid is considered,and then some fundamental results concerning this notion are discussed.

Keywords: (Extended)pogroupoid,poset,(fuzzy)ideal,level ideal.

On Some Weakly Forms of Fuzzy Continuous Mappings In Fuzzy Bitopological Spaces

A.M.Zahran

Department of Mathematics, Faculty of science Al Azhar University,Assiut 71511,Egypt.

Abstract: In this paper first,we show that by counterexamples some results,which appeared in the article(Some Weakly Forms of Fuzzy Continuous Mappings in Fuzzy Bitopological Spaces,J. of Fuzzy Mathematics 5(2)(1997),455-468)are incorrect and the proofs of some Theorems are incorrect too.Secondly we shall reestablish these results until become corrected.Finally,we introduce the concept of fuzzy pairwise r-weakly continuous mapping which weaker than fuzzy pairwise weakly continuous mapping,by using the concepts of fuzzy weakly open(closed)sets in fuzzy bitopological spaces.

Keywords: Fuzzy pairwise weakly semicontinuous(semiopen,semiclosed)mappings,fuzzy pairwixe weakly continuous(open,closed)mappings,and fuzzy pairwise r-weakly continuous mappings.

Reduced Fuzzy Primary Decompositions For Fuzzy Ideals

Ali Jaballah

Department of Mathematics The Unibersity of Waikatto, Hamilton,NEW ZEALAND Email jaballah@waikato.ac.nz

And

Deparment of Mathematics,Qatar University, PO Box 2713,Doha,State of Qatar Email ajaballah@qu.edu.qa

Abstract: Several characterizations for reduced fuzzy primary decompositions of fuzzy ideals are given,then sharp upper bounds for the number of primary components in such fuzzy primary decompositions are obtained.

Keywords: Commutative ring,composition series,Artinian ring,fuaay ideal,reduced fuzzy primay decomposition.

The Absolute Value of Fuzzy Number and Its Basic Properties*

Li Fachao,Su Lianqing,Yu Xiangdong,Qiu Jiqing

Department of Basic Science,Hebei University of Science and Technology Shijiazhuang,050018,P.R.China

Wu Congxin

Department of Mathematics,Harbin Institute of Technology Harbin,150006,P.R.China

Abstract: In this paper,we introduce the notion of absolute value of fuzzy number,further,we discuss the basic properties of absolute value of fuzzy number about algebra operations.

Keywords: Fuzzy numbers,absolute value,algera operations.

On Fuzzy Ideals of Gamma Near-rings

Yong Bae Jun

Department of Mathematics Education Gyeongsang National Unibersity,Chinju 660-701,Korea E-mail: ybjun@nongae.gsnu.ac.kr

Kyung Ho Kim

Department of Mathematics Chungju National University,Chungju 380-702,Korea E-mail: ghkim@gukwon.chungju.ac.kr

Mehmet Ali Ozturk

Department of Mathematics,Faculty of Arts and Science Cumhuriyet Uitversity,58140 Sivas,Turkey E-mail: maozturk@cumhuriyet.edu.tr

Abstract: The aim of this paper is to introduce the notion of fuzzy characteristic left (resp.right)ideals and normal fuzzy left(resp.right)ideals of ¦£-near-rings,and to study some of their properties.

Keywords: ¦£-near-ring,(normal)fuzzy left (right)ideal,fuzzy characteristic left(right) ideal,¦£-near-ring homomorphism.

On L-smooth Compactness

A.A.Ramadan* and S.E.Abbas**

*Department of Mathematic,Faculty of Science.Beni-Suef,Egypt

**Department of Mathematic,Faculty of Science.Sohag.Egypt

Abastract: The aim of this paper is to introduce good definitions of smooth almost,light and near compactness in smooth L-fuzzy topological spaces,where L is a fuzzy lattice.These compactness-related concepts are defined for arbitrary L-fuzzy sets and some of their properties studied.

Keywords: Fuzzy lattice,smooth fuzzy topology,¦Á-Scott continuous function,smooth almost,light and near compactness,good extension.

Best Approximation in Fuzzy Metric Spaces

P.Veeramani

Department of Mathematics ,Indian Institute of Technology. Madras,Chennai 600 036,India. e-mail:pvmani@pallava.iitm.ernet.in

Abstract: We study the problems of best approximation in fuzzy metric spaces.As every metric induces a fuzzy metric the results obtained in this paper are more general than the corresponding results of metric spaces.

Keywords: Fuzzy metric space,topology,best approximation

The wallman extension in fuzzifying topology

Daowen Qiu

Department of Computer Science and Technology Tsinghua Unibersity Beijing,100084,P.R.China

Zhujun Fan

Department of mathematics Zhonghan University,Guangzhou 510275,P.R.China

Abstract: In this paper,we introduce the concepts of ultrafilter and the Waliman extension,and establish some of their fundamental properties in fuzzifying topology.

Keywords: Fuzzifying topology,ultrafilter,comactification.

Projective Limit of L-fuzzy Locally Convex Topological Vector Spaces*

Cong-hua Yan

Department of Mathematies,Nanjing Normal University. Nanjing Jiangsu,210097,P.R.China

Abstract: In this paper,some propertis of L-fuzzy projective topologies determined by a family of L-fuzzy linear order-homomorphisms [3] in L-fuzzy locally convex topological vector spaces were studied. Then we gibe the definition projective limit and discuss the properties of projective limit space. Finally,a projective limit representative theorem of a separated L-fuzzy locally convex topological vector space is obtained.

Keywords: L-fuzzy linear order-homomorphism,L-flctvs,projective topology,projective limit.

A General Theorem on Selectors of Fuzzy Multifunctions*

Lsmat Beg

Department of Mathematics, Kuwait University,Kuwait E-mail: ibeg@math-l.sci.kuniv.end.kw.

Abstract: We proved the existence of selectors for fuzzy multifunctions defined on fuzzy ordered sets under suitable concitions. A fixed point theorem for fuzzy order preserving fuzzy multifunctions is also obtained.

Keywords: Fuzzy multifunction,selector,fuzzy relation,fuzzy order,fixed point.

On Fuzzy Basically Disconnected Spaces

G.Tangaraaj

Department of Mathematics,Jawahar Science College, Neyveli-607 803,Tamilnadu,India.

G.Balasubramanian

Department of Mathematics,Periyar University Salem-636011,Tamilnadu,India.

Abstract: In this paper we introduce a new class of fuzzy topological space called fuzzy basicallly disconncted spaces.Besides giving several characterizations some interesting properties of these spaces are also given.

Keywords: Fuzzy extremally disconnected,Strong F¦Ò-fuzzy continuous,Fuzzy basically disconnected,Fuzzy P-space,Fuzzy semiregularisation.

On Fuzzy Function Spaces

D.N.Georgiou

Department of Mathematics. University of Patras,96500 Patras,Greece

Abstract: In this paper we define and study fuzzy topologies on the set FC(Y,Z)of all fuzzy continuous functions from a fuzzy topogical space Y into a fuzzy topological space Z.

Keywords: Fuzzy sets,fuzzy topology,fuzzy continuous functions and function spaces.

Linear Fuzzy Multivalued Operators

Ismat Beg

Department of Mathematics,Kuwait University.KUWAIT. E-mail: ibeg@math-l.sci.kuniv.edu.kw.

Abstract: We introduced the notion of linear fuzzy multivalued operators and studied the algebra of linear fuzzy multivalued operators.We also obtained the laws governing addition and scalar multiplication of linear fuzzy multivalued operators combined with the operations of composition and inversion.

Keywords: Linear fuzzy multivalued operator,linear fuzzy relation,fuzzy multivalued function.

On the Completion of Fuzzy Normed Spaces*

Jin-xuan Fang

Department of Mathematics,Nanjing Normal University Nanjing,Jiangsu 210097,China

Abstract: This paper deals with the completeness of fuzzy normed spaces. A theorem on the completion of a fuzzy normed space is proved.

Keywords: Fuzzy norms, complete fuzzy normed spaces, completion.

Extension of Certain Fuzzy Ideals of Semigroups On Strong Semilattices

Shuk Yee Lee and K.p.Shum*

Department of Mathematics The Chinese University of Hong Kong,Shatin,N.T.,Hong Kong

Abstract: In this paper,we extend a fuzzy set from the minimum component of a strong semilattice of semigroups to the whole semigroup.With this approach,we are able to construct fuzzy semiroups from small ones to large one,and a number of related results on fuzzy ideals in the literature are hence extended in this way.

Keywords: Fuzzy ideals, Strong semilattice of semigroups, Extension of fuzzy ideals.

Degrees and Fuzzy Generalized Closed Sets

T.Fukutake, H.Harada,M.Kojima,H.Maki*and F.Tamari

Deparment of Mathematics,Fukuoka University of Education Akama,Munakata, Fukuoka 811-4192 Japan *Wakagidai 2-10-13,Fukuma-cho Munakata-gun, 811-32 Japan

Abstract: The aim of this paper is to extend the notion of generalized closed subsets [13] in a topological space into a Chang¡¯s fuzzy topological spaces [5]. In the contex of works due to A.P. Shostak [14] we introduce and investigate a certain number called as a fuzzy generalized closedness degree corresponging to a fuzzy subset. The fuzzy generalized closedness degree corresponding to a fuzzy subset.The fuzzy generalized closedness of fuzzy subsets is characterized completely by the degree. Also the concept of fuzzy §ä1/2spaces is investigated.

Keywords: Fuzzy g-closed set, degree of fuzzy sets,fuzzy-§ä1/2space.

On ¦¸-fuzzy Ideales of BCK/BCI-algebras

Young Bae Jun

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

Kyung Ho Kim

Department of Mathematics Chungju National University, Chungju 380-702, Korea E-mail: ghkim@gukwon.chungju.ac.kr

Qun Zhang

Department of Mathematics ,Education Affairs of South-Central University for Nationalities,Wuhan 430073,P.R.China E-mail: qzhang@scuec.edu.cn

Abstract: Given a set ¦¸,the notion of ¦¸-fuzzy ideals of BCK/BCI-algebras is introduced, and some related properties are investigated. Relations between ¦¸-fuzzy ideals and ¦¸-fuzzy subalgebras in BCK/BCI-algebras are given . We prove that every ¦¸-fuzzy ideal is an ¦¸-fuzzy subalgebra in a finite BCI-algebra, and that in a p-semisimple BCI-algebra, every ¦¸-fuzzy subalgebra is an ¦¸-fuzzy ideal.

Keywords: p-semisimple BCI-algebra, ¦¸-fuzzy set, ¦¸-fuzzy subalgebra,(closed) ¦¸-fuzzy ideal

Characterization of Fuzzy Ordered Filters in Negatively Partially Ordered Monoid

S.W.Kuresh

Department of Mathematics Xinjiang Normal University, Urumqi, China 830053

John N.Mordeson and S.C.Cheng

Department of Mathematics and Computer Science Creighton University, Omaha, Nebraska, USA 68178

Abstract: In this paper, we further investigate some structure¡¯s properties of fuzzy ordered filters in negatively partially ordered monoid.

Keywords: Fuzzy ordered filter, negatively partially ordered monoid.

Normal Fuzzy Ordered Filters in Negatively Partially Ordered Monoid

S.W.Kuresh

Department of Mathematics Xinjiang Normal University Urumqi,China 830053

John N.Mordeson and S.C.Cheng

Department of Mathematics and Computer Science Creighton University Omaha,Nebrasa, USA 68178

Abstract: In [6] and [7] Kuresh et al. fuzzified the concept of ordered filters of a negatively partially ordered monoid and investigated its properties. In this paper, we introduce the notion of normal fuzzy ordered filters and maximal fuzzy ordered filters in a negatively partially ordered monoid S. We prove that every maximal fuzzy ordered filters of S is normal and if ¦Ìis a maximal fuzzy ordered filter of S ,then S¦Ì={X¡ÊS|¦Ì(X)=¦Ì(I)}is a maximal ordered filter of S.

Keywords: Fuzzy ordered filter, negatively partially ordered monoid, normal,maximal.

Relations between Fuzzy Implication Algebra and MV Algsbra*

Zhiwei Li and Chongyou Zhang

Department of Mathematics, CapitalNormalUniversity, Beijing 100037,P.R.China

Abstract: Fuzzy implication algebra(FIA for short)is a kind of algebraic Abstraction of implicative connective of logic system which takes values in[0,1].In this paper, the concept of distributive FIA is given, then the relations among regular FIA, commutative FIA and distributive FIA are established and the relations between these FIAs and MV algebra are obtained.

Keywords: Fuzzy Implication Algebra; Regular FIA; Distributive FIA;MV Algebra.

Fuzzy Pairwise Retract and Fuzzy Pairwise Strong Retract

F.S.Mahmoud and A.A.Ellatif

Mathematics Department,Faculty of Science,Sohag,Egypt

Abstract: The notion of a fuzzy retract was introduced by Rodabaugh in[17],in another paper[5]S.Dang added some new properties of fuzzy retraction. Inthis paper,we define the notions of fuzzy pairwise retract, fuzzy pairwise n.b.d retract, pairwise t-retract, pairwise strong retract and pairwise ultra retract.Moreover the relations between thess new concepts are discussed.

Keywords: Fuzzy bitoplogical spaces, fuzzy pairwise retract, pairwise strong continuous mapping, pairwise strong retract.

Product Operations of Fuzzy Pointwise Metric Spaces

Fu-Gui Shi

Department of Mathematics,Beijing In of Technology Beijing,100081,P.R.Chine

Abstract: In this paper a pointwise metric function is constructed on the product space of countablely many fuzzy pointwise metric spaces. Hence it is proved that countable product of pointwise metric spaces is pointwise metrizable.

Keywords: Fuzzy topology, pointwise pseudo-metric,pointwise metric,product space

Fuzzy Membership and Topological System*

Yixiang Chen

Department of Mathematics,ShanghaiNormalUniversity Shanghai 200234,P.R.China Email:ychen@shtu.edu.cn

Abstract: Since the birth of fuzzy topology,the fuzzy membership between fuzzy point and fuzzy subset has been drawn attention, and various fuzzy memberships has been introduced,e.g.Pu and Liu¡¯s quasicoincidence,Wang¡¯sremote-neighborhood, and Johnston¡¯s locale-wise. In this paper, the author will show that those fuzzy memberships above could be unified into the model-relation in Vicker¡¯s topological system.The suthor¡¯s aim is to introduce an approach to study fuzzy topology.

Keywords: Fuzzy topology, fuzzy membership, topology system, Tychonoff product theorem, compactness.

On Lattice-valued Functions I:Simple Functions on Lattice

Guangquan Zhang and Yong-Hong Wu

School of Mathematics and Statistics,CurtinUniversity of Technology GPO Box U1987,Perth,Western Australia,6845, Australia {zhangg,yhwu}@cs.cuitin.edu.au

Abstract: In this paper, lattice-valued simple functions are introduced.Two kinds of order-relations of lattice-valued simple functions are preseted and a number of propositions characterizing their properties are developed.

Keywords: Non-additive measure,fuzzy measure, lattice-valued simple function,order-relation

On Fuzzy Syntopogenous Structure and Algebraic Structure

Wang Hong

Department of mathematics,Mianyang teacher¡¯s collage, Mianyyang 621000,Sichuan,P.R.China

Abstract: In this paper we combine fuzzy topological structure on X with algebraic structure on X and investigate their corresponding structures and their properties.First,we research the preorder relation generated by an L-fuzzy syntopogenous structures. Conversely,we study the L-fuzzy syntopogenous structure defined by a preorder relation.Second,we define*-increasing(*-Decreasing) L-fuzzy syntopogenous spaces with preorder and study some properties of them.Finally, we give an important example of*-increasing L-fuzzy syntopogenous space.

Keywords: Fuzzy topology, fuzzy syntopogenous structure,order,algebra.