THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 14, Number 4, December 2006

CONTENT

DETAILS

Some Structures of -fuzzy Topology

M.A.Abdel-Satar

Department of Mathematics, Faculty of Science, Cairo University, Beni-Suef, Egvpt.

Abstract: In this paper, we introduce a concept of -fuzzy neighborhoos system of a fuzzy point and we establish their properties. We study the concept of -fuzzy filter and their convergence.

Keywords: -fuzzy topology, fuzzy point, -fuzzy filter, fuzzy neighborhood system.

Fuzzy ¨Cseparation Axioms in Fuzzifying Topology

O.R.Sayed

Department of Mathematics, Faculty of Science, Assiut University,71516 Egypt E-mail: o_r_sayed@yahoo.com

Abstract: In the present paper we introduce and study -, -, -, -, -, -, - strong - and strong -separation axioms in fuzzifying topology and give some of their characterizations as well as the relations of these axioms and other separation axioms in fuzzifying topology introduced by Shen, Fuzzy Sets and Systems, 57(1993), 111-123.

Keywords: Fuzzy logic, fuzzifying topology, Fuzzyifying -open sets, Fuzzifying separation axioms.

-compactness in Fuzzifying Topology

O.R.Sayed

Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 EGYPT E-mail: o_r_sayed@yahoo.com

Abstract: In this paper the concepts of fuzzifying -irresolute functions and fuzzifying -compact spaces were characterized in terms of fuzzifying -open sets and some of their properties are discussed.

Keywords: Lukasiewicz logic; fuzzifying topology ; fuzzifying -open set; fuzzifying compactness. (1991) Mathematics Subject Classification: 54A40

Smooth Group Induced by Group and Its Fuzzy Normal Subgroup

Jianli Zhao

Department of Mathematics ,East China Normal University, Shanghai, P. R .China 200062 Liaocheng University,School of Mathematics Science,Laocheng,P.R.China 252059

Zhenming Ma

Department of Mathematics,Linyi Normal University,Linyi,P.R.China 276005

Abstract: In paper [6], Jianli Zhao and Zhenming Ma induced a group by smooth group based on fuzzy equality, which relates the smooth group to group. As an adverse problem, in this paper, we are to obtain a kind of smooth group by group and a fuzzy equality, which we define it by the fuzzy normal subgroup of group. And we investigate the properties of this kind of smooth group, by discussion, we find the close relationship between smooth group and crisp group; Inparticular, we get some perfect example of smooth group which are more suitable than M. Demicri¡¯s in paper [4].At the last of this paper, we study the classification of this kind of smooth groups.

Keywords: Fuzzy equality; fuzzy normal subgroup; smooth group; fuzzy congruence.

L ¨Cfuzzy Uniform Spaces

Y.C.Kim

Department of mathematics,Kangnung National University, Gangneung,Gangwondo,210-702,Korea

A.A.Ramadan and M.A.Usama

Department of Mathematics, Faculty of Science, Al-Qasseem University, P. O. Box 237,Burieda 81999,Saudi Arabia

Abstract: In this paper, we introduce the notion of L-fuzzy uniform spaces as a view point of the entourage approach in a strictly two-sided, commutative quantale. We define the subspaces of L-fuzzy uniform spaces. We study the several (L,¡Ñ,¡Ä) ¨Cfuzzy topologies induced by an L-fuzzy uniform spaces.

Keywords: L-fuzzy uniform spaces, LF-uniformly continuous functions, (L,¡Ñ,¡Ä) ¨Cfuzzy topological spaces, LF-uniformly continuous functions.

Metatheorem and Fuzzy Quasiideals in Semigroups

Anand Swaroop Prajapati

Department of Mathematics, A.R.S.D.College, University of Delhi, Dhaula kuan, New Delhi-110021,India E-mail:prajapati_anand@yahoo.co.in

Ravi Srivastava

Department of Mathematics,Swami Shraddhanand College, University of Delhi,Alipur,Delhi-110036,India E-mail: ravi hritik20002000@yahoo.co.in

Abstract: In the area of fuzzy algebraic structures, the year 1995 is marked by the development of metatheorem, which was formulated by Prof. Tom Head [3] in order to obtain fuzzy versions of classical results. In this paper we provide various applications of metatheorem by obtaining fuzzy analogs of results pertaining to the notions of semiprime ideals,quasiideals and biideals of a semigroup. Following this approach we establish several characterizations of a semigroups. Moreover,we provide a necessary and sufficient condition of a semigroup to be a semilattice of group. We also introduce pointwise definition of a fuzzy quasiideal and a specific construcation of a fuzzy quasiideal and a specific construction of a fuzzy quasiideal generated by a fuzzy set is provided.

Keywords: Semigroup; fuzzy biideals; fuzzy semiprime ideals; level subsets; strong level subsets.

Equivalence Class Representation of Fuzzy Numbers Application to Evidence Theory and Decision Analysis

Gigi George

Mar Thoma College for Women,Perumbavoor,Kerala,India Sunny Kuriakose A. Union Christian College ,Alwaye,Kerala ,India

Abstract: In this,paper equivalence classes of closed intervals inRand fuzzy numbers inR,where R is the set of real numbers,are analyzed. The collection of equivalence classes of closed intervals in R and R are proved equivalent. Also,a fuzzy valued basic probability assignment is introduced using equivalence class representation of fuzzy numbers and it is applied to statistical fuzzy decision problems,which involve fuzzy valued basic probability assignments and fuzzy utilities.

Keywords: Equivalence classes of closed intervals,equivalence classes of fuzzy numbers,fuzzy valued basic probability assignment funcation,fuzzy valued belief measure,fuzzy valued plausibility measure.

A Fuzzy Multicriteria Approach for Inverse Radiotherapy Planning Problem

Samir A.Abass

Department of Mathematics and Theoretical Physics,Nuclear Research Center, Atomic Energy Authority,P.O.Box 13759,Cairo,Egypt E-mali:samir 001us@yahoo.com

Eman M.A.Massoud

Department of Protection,National Center for Nulear Safety,Atomic Energe Authority

Abstract: The aim of radiotherapy of local disease is to achieve a high dose to the planning target volume simultaneously keeping the dose to the organs at risk as low as possible. Modern radiation treatment techniques and particularly is called intensity modulated radiotherapy (IMRT). IMRT design is the process of choosing low beams of radiation will travel through a cancer patient to treat the disease. The increased technology found in modern treatment facilities makes the use of optimization paramount in the design of successful treatment plans. In this paper, we formulate the inverse radiotherapy planning problem as a multicriteria problem with conflicting objectives incorporates the fuzziness. We propose a solution algorithm to solve the problem of concern.

Keywords: Radiotherapy-fuzzy concept-multicriteria

On Prime, Semiprime, Completely Prime, Completely Semiprime Fuzzy Ideals in Semirings

Chen Gui-ying

Mathematics and Science College,Liaocheng university,Shandong 252059, China E-mail:chengguiying@eyou.com.cn

Abstract: The concept of fuzzy ideal generated by fuzzy point in a semiring was introduced and its properties were studied,by this concept new characterizations of prime,semiprime,completelyprime,completely semiprime fuzzy ideals in a semiring were given and their relation was studied finally.

Keywords: Fuzzy Semiring; Fuzzy Ideal Generated by Fuzzy point in a Semiring; Fuzzy Ideals; Prime Fuzzy Ideals; Semiprime Fuzzy Ideals; Completely Prime Fuzzy Iderals; Completely Semiprime Fuzzy Ideals.

Fuzzy Bitopology on Fuzzy Sets: Fuzzy Pairwise ¦Ã Continuity and Fuzzy Pairwise ¦Ã Retract

I.M.Hanafy

Department of Mathematics, Faculty of Education, Suez Canal University ,El-Arish, Egupt.

F.S.Mahmoud and M.M.Khalaf

Department of Mathematics, Faculty of Science (82524) Sohag-Egypt

Abstract: The concept of a fuzzy topology in a fuzzy set was introduced by Chakrabarty and Ahsanullah in 1992. The concept of a fuzzy retract was introduced by Rodabaugh in 1981 and this concept has been extended to the fuzzy bitopological setting in 2001. The concept of a fuzzy retract in a fuzzy topology on a fuzzy set has been introduced in 2003. The aim of this paper is to introduce Fuzzy Pairwise ¦Ã Continuity and Fuzzy Pairwise ¦Ã Retract and establish some of their properties. Also,the relations between these new concepts and others are discussed.

On (T-) Fuzzy k-ideals/subalgebras of B-algebras

M.Akram

Punjab University College of Information Technology University of the Punjab Lahore£¬pakistan E-mail£ºm.akram@pucit.edu.pk

Hee Sik Kim

Department of mathematics hanyang university seoul 133-791£¬korea E-mail£ºheekim@hanyang.ac.kr

Abstract: In this paper we introduce the notion of a£¨£¨T-£©fuzzy£©k-ideal in B-algebras,and show that the notions of a£¨fuzzy£©subalgebra,a£¨fuzzy£©normal subalgebra and a£¨fuzzy£©k-ideal are equivalent in 0-commutative B-algebras,and discuss T-fuzzy subalgebras/k-ideals in B-algebras.

Key words and phrases: £¨T-£© fuzzy £¨k-ideal£¬subalgebra£¬normal£©,B-algebras,imaginable,t-norm,0-commutative.

Max-Product Fuzzy Relation Geometric Programming

Jihui Yang

Department of Mathematics,Shantou University,Shantou, Guangdong,515063,China P.R

Bingyuan Cao

School of Math,And Inf.Sci.,,Guangzhou University, Guangdong Guangdong,510006,chinaP.G.

Abstract: An optimization model is presented with a posynomial objective function subject to max-product fuzzy relation equations.Then the structure of solution set and its solving method are related about max-product fuzzy relation equations.Next the optimum solution is discussed,based on exponent of monomial among objective function,then a solution procedure is proposed.And finally,two practical examples are given for illustration purpose.

Keyword: Geometric programming,max-product fuzzy relation equations;discriminate matrix;simplification matrix;

Intuitionistic M-fuzzy h-ideals in M-hemirings

Jianming zhan

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

K£®P£®Shum

Faculty of Science£¬The Chinese University of Hong Kong, Shatin, Hong Kong£¨SAR,£©P.R.China E-mail£ºkpshum@math.Cuhk.edu.hk

Abstract: The concept of intuitionistic fuzzy sets which is a kind of generalized fuzzy sets was first introduced by Atanassov in 1986.In this paper, we define the intuitionistic M-fuzzy h-ideals of a M-hemiring on intuitionistic fuzzy sets and study their properties. Some recent result of fuzzy left h-ideals in hemirings obtained by Jun,Ozturk ,Song and also by Zhan, Davvaz and others are extended and generalized.

Keywords: M-hemirings;£¨Intuitionistic£©M-fuzzy left h-ideals;Left M-h-ideals;Equivalence relations;M-normal intuitionistic M-fuzzy left h-ideals.

(L,¡Ñ)-quasi-uniform Spaces and(L,¨’)-quasi-couniform Spaces

Yong Chan Kim and Jung Mi Ko

Department of mathematics,kangnung national university, Cangneung,angwondo,210-702,korea

Abstract: In this paper,we introduce the notion of L-closure(L-interior)spaces and (L,¡Ñ)-quasi-uniform (L,¨’)-quasi-couniform spaces as a view point of the entourage approach in a strictly two-sided,commutative quantale. Moreover,we investigate the properties of them.

Keyword: L-closure£¨L-interior£©spaces ,(L,¡Ñ)-quasi-uniform ((L,¨’)-quasi-couniform£©spaces

Difference Sequence Spaces of Fuzzy Numbers

Ekrem Savas

Yuzuncu Yil University,Faculty of Arts and Science,

Department of Mathematics,zeve campus,Van-TURKEy E-mail address:ekremsavas@yahoo.com

Abstract: Quite recently E.savas [5] defined and ,the set of all convergent and bounded difference sequences of fuzzy numbers and proved that and are complete metric spaces. In this paper we generalize the spaces and by using Orlicz function. we also establish some inclusion theorems.

Keywords: Sequence spaces,Fuzzy numbers,Orlicz Function.

Fuzzy Natural Function Spaces

Gerhard Preuss

A paper in honor of Darrell c.kent I.Mathematics Institut Freie Universitat,Berlin Arnimallee 3 D-14195 Berlin,Germany E-mail£ºpreuss@math.fu-berlin.de

Abstract£º Fuzzy preuniform convergence spaces are presented,where the concept of a fuzzy filter w.r.t. a frame L with different least element 0 and greatest element 1 in the sense of P. Eklund and w.Gahler is used It turns out that the construct FPUConv of fuzzy preuniform convergence spaces is Cartesian closed£¨i.e. it has natural function spaces£©,and topological which implies that initial and final structures exist .the main discovery results in the fact that from the natural function spaces structure in FPUConv other natural function space structures can be derived, e.g.the structure of fuzzy continuous convergence as well as the fuzzy analogue of the uniformly continuous SUConv-structure and the Cauchy continuous Fil-structure known from convenient topology.Furthermore,in case L={0,1},i.e.in the non-fuzzy case,all concepts may be identified with the usual ones.

Keywords£º Fuzzy preuniform convergence spaces,fuzzy semiuniform convergence spaces,fuzzy filter spaces£¬fuzzy Cauchy spaces£¬fuzzy generalized convergence spaces£¬fuzzy kent convergence spaces,fuzzy limit spaces£¬,bireflectiongs and bicoreflections,cartesian closedness.

Interval-valued Fuzzy Subalgebra of BCK-algebra

Young Bae Jun

Department of mathematics education Gyeongsang National University Chinju 660-710,Korea E-mail£ºybjun@nongae.gsnu.ac.kr

Kyung ho kim

Department of Mathematics Chungju National University Chungju 380-702,Korea E-mail£ºghkim@gukwon.Chungiu.ac.kr

Abstract: We introduce the notion of interval-valued fuzzy subalgebras with respect to the interval Min-norm Min £¨briefly, Min-fuzzy subalgebras£©in BCK-algebras,and investigate some of the properties. Using upper level set, we give a characterization of Min-fuzzy Subalgebras. we also show that every subalgebra of a BCK¨Calgebra X can be realized as an upper level subalgebra of a Min-fuzzy subalgebra of X. Finally, we establish the theorems of the homomorphic image and the inverse image.

Keywords: Interval number, interval Min-norm, Min-fuzzy subalgebra, BCK-algebra, (fuzzy)subalgebra, homomorphism. The first author was supported by Korea Research Foundation Grant£¨KRF-99-005-D00003£©.