THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 11, Number 3, September 2003

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On The Root Function Expansion of A Non-local Sturm-Liouville Operator

E.M.El-Abd

Department of Mathematics,Faculty of Science Tanta University,Egypt

Abstract: In this paper we consider the root function expansion of the non-local Strum-Liouville problem Where and are continuous linear functional in C[0,a].By certain assumptions imposed on this functional,theorems for completeness and basis property of the root functions of this problem are proved.

Parametric Study of Multi Objective Nonlinear Fractional Programming Problems without Differentiability

E.E.Ammar and M.A.Kassem

Dept.of Math.Faculty of Science, Tanta University,Egypt

Abstract: Different basic notions like to feasibility,the solvability,the stabilitysets of the smooth fuzzy parametric multi objective NLPprograms have been discussed in several papers.In this paper,these notions have been defined and qualitatively analyzed for a general class of non smooth multi objective,nonlinear,fractional,programming problems with fuzzy parameters in both the objective and constraints functions under the concept of -pareto optimality.

Keywords: Multi objective nonlinear fractional programming non smooth functions,parametric approach,fuzzy parameters, -pareto optimality,stability.

On the Cartesian Product of Intuitionistic Fuzzy Sets

Glad Deschrijver and Etienne Kerre

Department of Applied Mathematics and Computer Science Ghent University, Krijgslaan 281,S9,B-9000Ghent,Belgium E-mail:Glad.Deschrijver@rug.ac.be and Etienne.Kerre@rug.ac.be

Abstract: Cartesian products of intuitionistic fuzzy sets have been defined using the min-max and the product-probabilistic sum operations.In this paper we introduce and analyz the properties of a generalized Caresian product of intuitionistic fuzzy sets using a general triangular norm and conorm.In particular we investigate the emptiness ,the commutativety ,the distributivity,the interaction with respect to generalized unions and intersections,the distributivity with respect to the difference,the monotonicity and the cutting in terms of level-sets.

Keyword: Intuitionistic fuzzy set,generalized Cartesian product

About Two Probability Representations of Fuzzy Measures on A Finite Set

G.Sirbiladze and N.Zaporozhets

Chair of Random Processes Theory Department of Applied Mathematics and Computer Science Tbilisi State University,Georgia

Abstract: In this paper,we consider two probability representations of fuzzy measures on a finite set:L.M.Campos,M.J.Bolanos[1]representation(CBR) and T.Murofushi,M.Sugeno[2]representation(MSR).Analogously CBR for MSR we prove theorems of existence of Choquet¡¯s second order capacities.We introduce a definition of a distance between fuzzy measure for MSR,which is similar to the definition of a distance for CBR in terms of associated probabilities[3].Some properties of monotone expectation[1] in relation to MSR are also obtained.

Keyword: Fuzzy measure, Choquet¡¯s capacities of order two, associated probabilities, probability representation of fuzzy measure, distance, monotone expectation.

On Fuzzy N-Subgroups and Fuzzy Ideals of Near-Rings and Near-Ring groups

Helen K. Saikia

Department of Mathematics,Gauhati University Guwahati, 781014, India E-mail:hsaikia@yahoo.com

Lila.K.Barthakur

Department of Mathematics, Marigaon College Marigaon, 782105, India

Abstract: In this paper we investigate some characteristics of fuzzy N-subgroups and fuzzy ideals of a near-ring. The notions of fuzzy near-ring subgroups and fuzzy ideals of a near-ring group are introduced. The factory N-group induce by a fuzzy ideal is also defined. Finally some characterizations of strongly near-ring are given in terms of fuzzy ideals.

Keywords: Fuzzy N-subgroup, fuzzy ideal, fuzzy factor N-group, near-ring, near-ring group.

On and Separation Axioms in Intuitionistic Fuzzy Topological Spaces

Sadik Bayhan

Hacettepe University, Department of Mathematics 06532 Beytepe-Ankara/TURKEY E-mail:bayhan@hacettepe.edu.tr

Dogan Coker

Akdeniz University, Department of Mathematics 07058-Antalya/TURKEY E-mail:coker@pascal.sci.akdeniz.edu.tr

Abstract: The purpose of this paper is to investigate several types of separation properties in intuitionistic fuzzy topological spaces,developed by Coker[7]. After giving some characterizations of and separation axioms and some counterexamples in intuitionistic fuzzy topological spaces,we also investigate the interrelation between several types of separation axioms and some preservation properties.

Keywords: Intuitionistic fuzzy set, intuitionistic fuzzy topological spaces, intuitionistics fuzzy pair, intuitionistic fuzzy point, vanishing intuitionistic fuzzy point, fuzzy separation.

General Strongly Nonlinear Variational Inequalities for Fuzzy Mappings *

JiHui Zhang

School of Mathematics and Computer Science, Normal University Nanjing 210097, People¡¯s Republic of China E-mail:jihuiz@jlonline.com

Abstract: In this paper, we investigate a new classes of variational inequality and quasivariational inequalities for fuzzy mappings which include , as a special case, some known results in this field. A projection method is used to suggest an iterative algorithm for finding the approximate solution of this class.

Keywords: Variational inequality, fuzzy mappings, projection method, iterative algorithm.

Region Extraction Using Fuzzy Similarity Measures

Tamalika

Chaira Electronics and Electrical Engineering Department,India Institute of Technoplogy Kharagpur, India E-mail:tamalika@ece.iitkgp.ernet.in

A.K.Ray

B.Electronics and Electrical Engineering Department,India Institute of Technoplogy Kharagpur, India E-mail:akray@ece.iitkgp.ernet.in

Abstract: Region extraction algorithm is presented here to identify a textured region similar to the query image from an image database, containing images with different types of teatures. The matching process is based on several fuzzy similarity measures between the query image and the images in the database.

Index terms: Fuzzy similarity measure, histogram.

Boundedness in L-Fuzzy Topological Spaces

Ali Ahmed Nouh

Mathematic Department, Faculty of Science Mansoura University, 35516,Egypt

Abstract: In this paper,we introduce the concept of N-boundedness on arbitrary L-fuzzy sets in L-fuzzy topological spaces. Several characterizations of N-boundedness in terms of convergence theory of -ideals are obtained. We prove that the concept is good extension, productive and topologically invariant.

Keywords: Molecules, R-neighborhoods, L-fuzzy topology, -nets, deals, limits and cluster point, N-compact and N-bounded sets.

Homological Algebraic Structure of Fuzzy Modules

FuZheng Pan

Institute of Mathematics and Computer Science, Hubei University Wuhan 430062, P.R.China E-mail:panfz@hubu.edu.cn

Abstract: This paper presents a summary to fuzzy modular category by means of homological algebra. After introducing the exact sequence and fuzzy split in fuzzy linear maps(or:fuzzy modular maps). We construct the exact homomorphism functors hom( ,) and hom (, ). Then we define the tensor product for two fuzzy modules and and construct the exact tensor functors and . Finally the weak isomorphism relations between Hom functors and Tensor functora in fuzzy modular category are given.

Keywords: Fuzzy modular category, exact sequence of fuzzy linear, fuzzy split, hom functor,tensor functor.

Fuzzy Quick Ideals in BCK/BCI-Algebras

Sun Shin Ahn

Department of Mathematics Education Dongguk University Seoul 100-715, Korea E-mail:sunshine@dgu.ac.kr

Young Bae Jun

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

Hee Sik Kim

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

Abstract: The fuzzification of quick ideals in BCK/BCI-algebras are considered, and some related properties are investigated. We also discuss the product of fuzzy quick ideals and the projections of fuzzy quick ideals.

Keywords: Fuzzy ideals, fuzzy quick ideals, fuzzy subalgebra, level subalgebra.

Fuzzy Function Spaces with F@-Generated Fuzzy Topologies

M.E.El-Shafei

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

A.I.Aggour

Mathematics Department, Faculty of Science, Al-Azhar University Nasr City (11884), Cairo, Egypt

Abstract: In this paper,we define some fuzzy topologies on the set of all fuzzy continuous maps of a fuzzy topological space (fts) X into another Y in order to satisfy, by using the F@-generated F@t-topologies for defined in (Abd-Allah and Aggour, 1994), the exponential law of maps. In fact, one of the aim of this paper is to introduce the notion of the F@-generated fuzzy topology on FC(X,Y) which plays an important role in this study.

A Note on the Continuity of Triangular Norms

GaiMei Guo

Dept. of Basic Science, Changchun Universuty Changchun, jilin 130022, P.R.China

DeLi Zhang

Dept. of Math, Jilin Prove. Inst. Of Education Changchun, Jilin 130022, P.R.China

Abstract: In the short note,an equivalent theorem on continuity of triangular norms is shown.

Keywords: Triangular norm,continuity

Fuzzy Congruence Pairs on A Regular Semigroup *

Yonghua Li and Chengxian Chen 1.

Department of Mathematics South China Normal University Guangzhou 516031, P.R.China E-mail:liyh@scnu.edu.cn 2.School of Science Xi¡¯an Jiaotong university g~ Xi¡¯an 710049, P.R.China

Abstract: In this paper, we show that each fuzzy congruence on a regular semigroup is determined by its fuzzy congruence pair. It is obtained that there exists a non-one correspondence between fuzzy congruence paris and fuzzy congruence on a regular semigroup.

Keywords: Fuzzy congruence pair, fuzzy kernel, fuzzy trace, Green¡¯s equivalence relations, regular semigroup.

Discontinuity and Weakcompatibility in Fixed Point Consideation on Noncomplete Fuzzy Metric Space

Sushil Sharma

Department of Mathematics Madhav Science College Ujjain (M.P.),India E-mail:sksharma2005@yahoo.com

Bhavana Deshpande

Department of Mathematics Govt Arts and Science P.G. College Ratlam (M.P.),India E-mail:bhavnadeshpande@yahoo.com

Abstract: The aim of this paper is to prove some common fixed point theorem in fuzzy metric spaces by removing the assumption of continuity, relaxing the condition of compatibility or compatibility of type ( ) or compatibility of type ( ) to weak compatibility and replacing the completeness of the spaces with a set of alternative conditions.

Keywords: Fuzzy metric spaces, coincidence point, common fixed point, compatible maps, weakly compatible maps.

Finite Dimensional Fuzzy Normed Linear Spaces

T Bag and S.K.Samanta*

Department of Mathematics, Visva-Bharati Santiniketan 731235 , West Bengal, India *E-mail:syamal-132@yahoo.cn

Abstract: Following the concept of fuzzy norm introduced by S.C.Cheng and J.N.Mordeson, a definition of fuzzy norm is given on a liner space. A decomposition theorem of the fuzzy norm is established. Properties of finite dimendional fuzzy normed linear are studied.

Keywords: Fuzzy norm, fuzzy normed linear space.

Fuzzy Ideals in -Near-Rings

G.L.Booth

University of Port Elizabeth Prot Elizabeth 6000, South Africa

Abstract: It is shown that if M is a -near-ring with a strong left unity and left operator near-ring L, then there exists a one-to-one correspondence between the sets of fuzzy right (two-sided) ideals of L and M. One-to-onecorrespondences are also established between the sets of level sets of certain fuzzy right (two-sided) ideals in L and M. Equiprime fuzzy ideals are defined, and similar correspondences are shown without any assumption concerning the existence of unities.

Keywords: -near-ring, left operator near-ring, fuzzy ideal, level-set, equiprime.

Common Fixed Point for Three Operators

Dr . A. Tamilarasi and P. Thangaraj

Department of Mathematics, Kongu Engineering College, Perundurai Erode-638052, Tamilnadu E-mail:a_tamilarasi@yahoo.com

Abstract: In this paper we establish a unique common fixed point for three operators of a complete fuzzy metric space.

On Somewhat Fuzzy Continuous Function

G. Thangaraj and G. Balasubramanian

Department of Mathematics, Periyar University Salem-636011, Tamil Nadu, India

Abstract: In this paper the concept of somewhat fuzzy continuous functions, somewhat fuzzy open functions and weakly somewhat fuzzy open functions are introduced and some intersecting properties of these functions are investigated besides giving some characterization of these functions.

Keywords: Somewhat fuzzy continuous, somewhat fuzzy open, weakly somewhat fuzzy open, dense fuzzy set, somewhat fuzzy homeomorphism, separable fuzzy topological space, fuzzy irresolvable space.

Extremal Disconnectedness in L-Topological Spaces

Ratna Dev Sarma

Department of Mathematics, Rajdhani College University of Delhi, Delhi-110015, India

Debajit Hazarika

Department of Mathematics Science, School of Science an Techbology Tezpur University, Napaam-784028, India E-mail:debajit@tezu.crnet.in

A. Sharfuddin

Department of Mathematics Faculty of Nature Sciences Jamia Millia Islamia, New Delhi-110025, India

Abstract: The notion of extremal disconnectedness is examined for L-topological space. Two notins namely extremal disconnectedness and E-disconnectedness are introduced and their propertiers are discussed. Both extremal disconnectedness and E-disconnectedness in L-topological spaces are found to be open hereditary and are preserved under sum spaces besides having other properties similar to its general topological counterpart. Various relationships between E-disconnectedness and zero-dimensional space, regular space, semi L-continuity and weak L-continuity have been established.

Keywords: Extremely disconnectedness, E-disconnectedness, zero-dimensional space, weakly L-continuity, semi L-continuity, regular space.

On Semigroups which are Groups*

Niovi Kehayopulu and Michael Tsingelis

University of Athens, Department of Mathematics Panepistimiopolis, Athens 15784, Greece E-mail:nkehayop@nikias.cc.uoa.gr

Abstrsct: We give the solution of the following open problem in[1](cf.page 74): If every fuzzy (1,2)-ideal of a semigroup S is a constant function then is S a group? The answer is positive: The semigroups for which the (1,2)-ideals are constant functions, are groups. As a consequence, a semigroup S is a group if and only if each (1,2)-ideal of S is a constant function. We also answer the second open problem in [1,p.74]: Let be a fuzzy bi-ideal of a semigroup S. Is a fuzzy (1,2)-ideal of S a fuzzy left (or right) ideal of for all , ? The answer is: It is not, in general.

Some Sequence Space of Fuzzy Numbers Generated by Infinite Matrices

Metin Basarir

Department of Mathematics,Sakarya University Sakarya-54100, Turkey E-mail:basarir@sakarya.edu.tr

Mursaleen

Department of Mathematics, Aligarh M. University Aligarh-202002, India E-mail:mursaleen@postmark.net

Abstract: In this paper, we define some new sequence spaces of fuzzy numbers by using the A-transforms. We study some topological properties and relations for these new sequence spaces.

Keywords: Fuzzy numbers, sequence space, infinite matrix, paranorm.