THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 14, Number 2, June 2006

CONTENT

DETAILS

-topological Vector Spaces Generated by -norm

T. Tamizh Chelvam

Department of Mathematics, Manonmaniam Sundaranar University Tirunelveli 627012, Tsmilnadu, Indla E-mail: tamche_59@yahoo.co.in

A.Singadurai

Department of Mathematics, TDMNS College, T.Kallikulam 627113 Tamilnadu, Indla

Abstract: In this paper we define -normed space and contruct -topological vector spaces ftom a given -normed space ( , , )

Keywords: -norm, -topological vector spaces.

Contractive Conditions and Common Fixed Points in Fuzzy metric Space

Vyomesh Pant

Department of Mathematics Kumaon University, D. S. B. Campus Nainital-263002 INDIA FF(HC) FF Division, MHA 1st Floor, Lok Nayak Bhavan, Khan Market New Delhi-110003. INDIA E-mail: vyomeshpant@yahii.co.in

Abstract: This paper is aimed at obtaining common fixed point theorems in fuzzy metric space under contractive condition using the notion of noncompatibility.

Keywords: Fuzzy metric space, Compatible maps, Noncompatibility, Common fixed point, -weak commutativity.

Fuzzy Inner Product Space-A New Approach

Binimol Punnoose and Sunny Kuriakose, A.

Department of mathematics, U. C. College, Aluva, 683102 Kerala, India.

Abstract: In this paper we introduce a new version of fuzzy inner product on a fuzzy vector space over the set of fuzzy real number, which enables us to introduce the concept of fuzzy orthogonality. Some immediate results are also proved.

Keywords: Fuzzy number, Fuzzy vector subspaces, Fuzzy norm, Fuzzy inner product spaces and fuzzy orthogonal set.

The Fuzzy Integrated Judgment of The Market-oriented Grade

Yuanyuan Lin

Finance College Jimei university, Xiamen Fujian 361021, P R..China

Abstract: It is very important meaning for enterprises to manage with market-oriented rank. At the present day, the studies of the market-oriented principle primarily adopt qualitative analysis. This paper constructs the model of judgment of market-oriented rank with the theories and ways of fuzzy, and discusses the problems of check and evaluation of market-oriented rank. The outcomes of studies show that the quantitative analysis of market-oriented rank can handle this model.

Keywords: Market orientation Fuzzy matrix Integrated judgment

Circulant and Min Circulant Fuzzy Matrices

E. G. Emam

Department of Mathematics, faculty of Science , Zagazig University , Zagazig ,Egypt.

Abstract: In the paper we study and investigate some results on circulant fuzzy matrices . The first row of the coirculant fuzzy matrices play an important role in this studing. We introduce the concept of min Circulant fuzzy matrices and prove some results concerning it.

Keywords: Fuzzy matrices, circulant fuzzy matrices and min circulant fuzzy matrices.

On Two Types of Fuzzy Closed Sets

G. Elsalamony

Department of Mathematics, Faculty of Sciences, Benha university, Benha , Egypt

Abstract: Various concept related to the category of fuzzy closure spaces have been introduced, and relations among them are studied by several author [4-8]. In the paper , we introduce the weak fuzzy closure operators which need not be closed under unions, showing that many concepts and properties of closure space(FCS) can be proved without additional hypothesis. Initial structures of weak fuzzy closure spaces are obtained. Two notions of closed fuzzy sets, one in terms of fuzzy sets, the other in terms of fuzzy points, are introduced. The interrelations between these two notions are studied, provided with some counterexamples.

Keywords: Fuzzy closure spaces, weak fuzzy closure spaces, fuzzy adherent points, topological category.

Circuits of A discrete Fuzzy Matroid

N. Sriddharan Alagappa University, Karaaikudi-630003, India N. Chandrasekaran St.Joseph¡¯s College, Trichy-620002, India

Abstract: In this paper, we introduce discrete fuzzy matroids and show that a discrete fuzzy matroid can be developed by circuit axioms.

Keywords: Matroids-fuzzy sets-discrete fuzzy matroids-circuits.

Necessary and Sufficient Conditions for Oscillations of First-order Neutral Difference equations

M.A.El-Attar and E.M.El-Abd

Department of Mathematics, Faculty of Science Tanta University, Egypt

Abstract: In this paper we shall establish necessary conditions for the oscillations of the various solutions of a first order neutral difference equation. An explicit condition for the non existence of positive solutions for the following equation is derived.

Keywords: Oscillations, delay difference equation

New Methods of Ranking Fuzzy Numbers

Xingfang Zhang, Han Meng and Guangwu Meng

School of Mathematics Science, Liaocheng University, Liaocheng, Shandong 252059, P. R. China

Abstract: Two methods of ranking fuzzy numbers, layer ranking and right ranking, are built.

Keywords: Fuzzy number, layer ranking, right ranking.

Fuzzy Filters Redefined in Lattice Implication Algebras

Y. B. Jun,

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

Y. Xu and K. Y. Qin

Department of Applied Mathematics, Southwest Jiao-tong University, Chengdu 610031, Sichuan, P. R. china E-mail address: xuyang@home.swjtu.edu.cn

Abstract: Using the belongs to relation and quasi-coincidence with relation between fuzzy points and fuzzy sets, the concept of -fuzzy filters where , are any two of with is introduced , and related properties are discussed. Relations between -fuzzy filters and -fuzzy filters are investigated, and conditions for an -fuzzy filter to be an -fuzzy filter are provided. Characterizations of -fuzzy filters are given, and conditions for a fuzzy set to be a -fuzzy filter are provided.

Keywords: Lattice implication algebra, belong to, quasi-coincident with, -fuzzy filter, -fuzzy filter, -fuzzy filter.

Some Properties of Implication Operators

Yong Chan Kim and Jung Mi Ko

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

Abstract: In this paper, we introduce the -norms, -conorms and implications induced by the product -norm. We investigate the relations among implication operators, Archimedean -conorm ( -norm) and strictly decreasing (increasing) continuous functions.

Keywords: Implication operators, -norms, -conorms, fuzzy negations

The Number of Distinct Equivalence Classes of Fuzzy Subgroups of a Finite Abelian Group

Li Ying and Zhao Jianli

College of Mathematics Science, Liaocheng University, Shangdong, China, 252059

Abstract: In this paper, we study equivalence classes of fuzzy subgroups under a given equivalence relation and find out the formula the number of distinct equivalence classes of maximal fuzzy subgroup and fuzzy group of a finite abelian group.

Kewords: Maximal fuzzy subgroup, -dimensional divisor vector chain, maximal -dimensional divisor vector chain, quotient vector chain

Normal Fuzzy Filter in Lattice Implication Algebras

Shuwei Chen, Jun Ma and Yang Xu

Department of Mathematics, Southwest Jiaotong University Chengdu 610031, Sichuan, P.R. China E-mail: chensw915@163.com

Abstract: In this paper we introduce the concept of maximal fuzzy filters and completely normal fuzzy filters in lattice implication algebras. We show that every maximal fuzzy filter of a lattice implication algebra is a completely normal.

Keywords: Normal fuzzy filters, Maximal fuzzy filters, completely normal fuzzy filters, lattice implication algebras

Intuitionistic Fuzzy filters in Lattice Implication Algebras

Shuwei Chen, Yang Xu

Department of Mathematics, Southwest Jiaotong University Chengdu 610031, Sichuan, P.R. China E-mail: chensw915@163.com, xuyang@ swjtu.edu.cn

Yong Bae Jun

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

Abstract: Based on Atanassov¡¯s idea, we consider the intuitionistic fuzzification of filters of a lattice implication algebra, called intuitionistic fuzzy filters. We also discuss the intuitionistic fuzzification of dual ideals of lattice, called intuitionistic fuzzy lattice dual ideals, and study the relations between intuitionistic fuzzy filters and intuitionistic fuzzy lattice dual ideals. We establish some characterizations of intuitionistic fuzzy filters.

Keywords: Intuitionistic fuzzy filters, Lattice Implication Algebras, Intuitionistic Fuzzy Lattice Dual Ideals

Intuitionistic Fuzzifications of -closed Sets in Lattice Implication algebras

Y. B. Jun

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

S.W. Chen and J.Ma

Department of Mathematics, Southwest Jiaotong University ,Chengdu ,Sichuan 610031, China E-mail address: chensw915@163.com(S.W. Chen) mj99032@263.net(J.Ma)

Abstract: Using the notion of intuitionistic fuzzy sets which are generalization of fuzzy sets, the notion of intuitionistic fuzzy -closed sets in lattice implication algebras in introduced, and related properties are investigated. We generalize the concept of fuzzy topological -closed sets, initiated by Roh, Kim and Jun [6], to the case of intuitionistic fuzzy sets.

Keywords and phrases: Intuitionistic fuzzy -closed sets, Lattice implication algebra, intuitionistic fuzzy topological -closed set, -homomorphism.

A Comparison between Intuitionistic Fuzzy Sets and Generalized Intuitionsitic Fuzzy Sets

M. Panigrahi and S. Nanda

Department of Mathematics, India Institute of Technoligy, Kharagpur-721302, West Bengal, INDIA E-mail: motilal.panigrahi@gmail.com, snanda@maths.iitkgp.ernet.in

Abstract: In this paper we have shown that some opweations that are valid for intuitionsitic fuzzy sets are not valid for generalized intuitionsitic fuzzy sets. Also we have found that some results which appeared in the paper by Krassimir Atanassov are not correct and we have presented the correct version of the results. We have further introduced some new operations cver generalized intuitionsitic fuzzy sets.

Keywords: Fuzzy subsets, intuitionistic fuzzy sets, generalized intuitionsitic fuzzy sets, operations on GIFSs.

The Folding of Fuzzy Immersed Submanifolds

A.E. El-Ahmady

Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt.

H. M. Shamara

Mathematics Department, Faculty of Science, Tanta University, Kafr El-sheikh, Egypt.

Abstract: In the article we will introduce the general fuzzy system of fuzzy hyperspaces and fuzzy hyperspheres and gives the concept of the fuzzy folding of fuzzy immersed submanifolds.

Keywords: Folding, Fuzzy manifold.

Properties of Weak Topos on The Category of Real Valued Functions

Xue-hai Yuan

Department of Applied Mathematics, Dalian University of technology, Dalian 116024, P R China Department of Mathematics, Liaoning Normal University, Dalian 116029, P r China

Zun-quan Xia

Department of Applied Mathematics, Dalian University of technology, Dalian 116024, P R China

Abstract: In this paper, a category RVF of real valued functions is presented. Topos properties of the category RVF are studied. It is proved that the category RVF satisfies all properties of a topos except one, for it has no subobject classifier. It is pointed that although the category RVF is not a topos, RVF has a middle object and consequently RVF is a weak topos. By the use of weak topos RVF, power object of a real valued function in the category RVF is described.

Keywords: Category, topos , middle object, weak topos, power object.

Regression Analysis Models with Type-( ,c) Fuzzy Variables

Cao Bing-yuan

Mathematics and Information Science School, Guangzhou University, Guangdong, ZIP 510006, P. R. China E-mail: bycao@gzhu.edu.cn

Abstract: In this paper, first, type-( ,c) fuzzy variables is induced into regression and self-regression models after more extensively used models with type-( ,c) fuzzy variables are built. And then a way is developed to model determination under a cone index . Meanwhile the relation is proved between such models and other models with -fuzzy variables, flat (or trapezoidal) fuzzy variables, so that the former is applied to the state with flat fuzzy variables . And finally, methods are given to type-( ,c) fuzzy data.

Keywords: Type-( ,c) fuzzy variables (or data), fuzzy regression and self-regression model, non-fuzzyfication.

Oscillations of The solutions of Retarded differential Equations

M. A. El-attar, E. M. El-Abd and E. E. Al-Adad

Department of Mathematics, Faculty of Science, Tanta University, Egypt.

Abstract: We shall study in this paper the oscillatory solutions behavior to the equation where , , and are positive functions, in particular, it is shown that if: where, , is odd real number, all solutions oscillate about origin 0.

Keywords: Oscillations retarded differential equations.

Fuzzy Assessment Procedure for Estimating The Scaling Constants of Multiattribute Quasi-additive Utility Function

Samir A. Abass

Department of Mathematics and Theoretical Physics, Nuclear Research Center, Atomic Energy Authority, B. O. Box 13759, Egypt, E-mail: samir_001us@yahoo.com

Abstract: There are several forms for the utility function: additive form, multiplicative form, and quasi-additive form. This paper introduces an assessment procedure for estimating the scaling constants of quasi-additive utility function under fuzzy environment by using the Kuhn-Tucker necessary optimality conditions. An illustrative numerical example is given to clarify the developed procedure.

Keywords: quasi-additive utility function, -level set, Fuzzy parameters, Scaling constants.

Common Fixed Point in Fuzzy Metric Space

Ireneuse Kubiaczyk

Faculty of Mathematics and Computer Science Adam Mickiewicz University Ul. Umultowska 8761-614 Poznan, Poland

Sushil Sharma

Department of Mathematics Madhav Vigyan Mahavidyalaya Vikram University Ujjain-456010, India E-mail: sksharma2005@yahoo.com

Abstract: The purpose of this paper is to obtain some common fixed point theorems for multivalued mappings in fuzzy metric space. Our results extend, generalize and fuzzify several fixed point theorems on metric spaces, probabilistic metric spaces, uniform spaces and fuzzy metric spaces.

Keywords: Fuzzy metric space, sequence, common fixed point.

On L-fuzzy Order-preserving Operator -spaces

Shui-Li Chen

Department of Mathematics, School of Science, Jimei University, Xiamen, Fujian 361021, P. R. China

Abstract: In this paper, the concepts of an -fuzzy order-preserving operator -space having universal significance and including -fuzzy topological space, -neighborhood, -closure, -interior, -closed set and -open set are first introduced. Some foundational properties are obtained. Secondly, the notions of -subspace, -base and -subbase of an -fuzzy order-preserving operator -space are presented and discussed. Finally, the conceptions of -continuity, -openness, -closeness and -homeomorphism of -fuzzy mapping from an -fuzzy order-preserving operator -space into another -fuzzy order-preserving operator -space are recommended. Their characterizations and some interesting properties are given. Almost all the existing types of -fuzzy continuous mapping and its various weaker forms between -fuzzy topological spaces and many result concerning them are regarded as special cases of our corresponding notions and results.

Keywords: Fuzzy Lattice; -fuzzy order-preserving operator -space; -fuzzy mapping; -closure; -base; -neighborhood; -interior; -closed set; -open set

Stability of Multiple Knapsack Problems under Fuzzy Environment

Samir Abdou Abass

Department of Mathematics and Theoretical physics, Nuclear Research Center Atomic Energy Authority, B. O. Box, 13759, Egypt

Abstract: This paper deals with multiple knapsack problems with fuzzy parameters in the constraints (FMKP). This problem is to assign a subset of items to knapsacks with maximize the total profit of the selected items. The existing results concerning the qualitative and quantitative analysis of basis notions in parametric fuzzy multiple knapsack problems. These notions are the set of feasible parameters, the solvability set and the stability set of the first kind,

Keywords: Knapsack problem, fuzzy parameters, stability, integer programming.