THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 13, Number 3, September 2005

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On Fuzzy Power Algebra

Zhang Chengyi

Department of Mathematics, Hainan Normal University, 571158, Hainan, Haikou, P.R.China

Abstract: In this Paper, we develop a general theory of fuzzy power algebraic systems, the cardinality of the element in a fuzzy power algebraic systems is discussed. It is pointed that this kind of fuzzy power algebraic systems is not the fuzzy quotient algebraic systems and it can be represented by a classical algebraic systems. For example, a regular representation of a fuzzy power group on a finite group is given.

Keywords: Fuzzy power algebraic system, Fuzzy power group, fuzzy power ring, representation.

Common Fixed Points of Expansive Mapping on Fuzzy Ordered Set

Ismat Beg

Department of Mathematics, School of Arts and Sciences Lahore University of management Sciences 54792-Lahore, PAKISTAN E-mail: IBEG@LUMS.EDU.PK

Abstract: We proved the existence of common fixed points of two expansive mappings defined on fuzzy ordered set.

Keywords: Fuzzy ordered set, common fixed point, expansive mapping.

The Continuity and Boundedness of Fuzzy Linear Operators in Fuzzy Normed Space

Jialu Zhang

Department of Mathematics, Xiangnan University, Chenzhou, Hunan,423000, China E-mail: zj10735@163.com

Abstract: This paper defines the concept of norm on fuzzy linear space. In the fuzzy nomed space, the continuity and boundedness of fuzzy linear operators and the convergence of basic fuzzy linear operators.

Keywords: Basic fuzzy point; Fuzzy linear operator; norm of bounded fuzzy linear operator

Prime and Semiprime ideals: redefined

A.K.Ray

Department of mathematics Dibrugarh University Dibrugarh-786004, Assam,India.

Abstract: We propose to introduce a new definition of Prime ideal and semiprime ideal of a ring.

Keywords: ideal; Prime ideal; Semiprime ideal; Maximal ideal

Product Fuzzy Normed Linear Spaces

T. Bag and S. K. Samanta

Department of Mathematics Visva-Bharati Santiniketan 731235, West Bengal, INDIA E-mail: syamal_123@yahoo.co.in

Abstract: In this paper, some results on observations on the conditions (N6) and (N7) have been established. The concept of three types of product fuzzy norms are defined and the completeness of the product fuzzy normed linear spaces is studied.

Keywords: Fuzzy norm, Product fuzzy norm.

Multi-objective Fuzzy Economic Production Quantity Model with Spaces Constraint: A Geometric Programming Approach

Sahidul Islam and Tapan Kumar Roy*

Department of Mathematics Bengal Engineering College (D. U.), Howrah-711103,West Bengal, India.

Abstract: A multi-item multi-obiective Economic Production Quantity (EPQ) model with reliablility consideration of production Process and demand dependent unit production cost under storage space constraint has been formulated. In most of the real world situations, the constraint goal is imprecise in nature. Hence the constraint is imposed here in fuzzy environment. This model has been solved by geometric programming method. The model is illustrated with numerical example.

Keywords: Inventory; Geometric programming method; Multi-objective; Multi-item; Fuzzy storage space

Compactness in Intuitionistic Gradation of Openness

A. A. Rammadan

Department of Mathematics, King Saud University, Kingdom of Saudi Arabia

Y. C.Kim

Department of Mathematics, Kangnung National University, Korea

S. E. Abbas

Department of Mathematics, Faculty of Science, Sohag, Egypt

Abstract: In this paper, we intuoduce the concepts of intuitionistic (weakly) continuity, intuitionistic (weakly) open and intuitionistic (weakly) open and intuitionistic (weakly) closed functions in intuitionistic fuzzy topological spaces. Also, the concepts of intuitionistic compactness, intuitionistic almostand near compactness are introduces and studies in intuitionistic fuzzy topological spaces.

Keywords: Intuitionistic gradation of openness, intuitionistic fuzzy topological spaces, intuitionistic (weakly) continuity, intuitionistic (almost, near) compactness

On generalized Closed Fuzzy Sets

M. E. EL-Shafei

Mathematical Department, Faculty of Science, Mansoura University, Egypt

A. Zakari

Girls College of Education in Gazan, Kingdom of Saudi Arabia

Abstract: In this paper we intuoduce the concepts of generalized closed fuzzy sets and generalized fuzzy sets in fuzzy topological spaces. Furthermore, generalized fuzzy sets are extended to generalized fuzzy sets. Also, we introduce the concepts of fuzzy generalized continuous and fuzzy generalized irresolute mappings.

Keywords: Fuzzy topology, generalized closed fuzzy sets, generalized fuzzy sers, generalized closed fuzzy sets, fuzzy generalized continuous mappings, fuzzy generalized irresolute mappings.

Knowledge Filter and Its Dependent reasoning Discovery*

Changjing Lu

Department of Computer Science, SanMing College, Sanming, Fujian 365004, P. R. China School of Mathematics and System Science, Shandong University Jinan 250100, P. R. China

Kaiquan Shi

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

Abstract: The paper presents the concept of knowledge filter, and gives numerical degree of knowledge filter and the principle of knowledge griddle. By the concept of knowledge filter, it gives reasoning structure of knowledge in dependent reasoning, numberical relation of dependent reasoning and its application in knowledge discovery. It is a novel approsch for knowledge discovery research to combine knowledge discovery. It is a novel approach for knowledge discovery research to combine knowledge filter with dependent reasoning.

Keywords: Rough set, knowledge filter, dependent reasoning, principle of knowledge griddle , knowledge discovery, application.

Fuzzy Congruence Relations on Hyper algebras

R. A. Borzooei

Department of Mathematics Sistan and Baluchestan Uinversity, Zahedan, Iran E-mail: borzzooei@hamoon.usb.ac.ir,

M. Bakhshi

Department of Mathematics Sistan and Baluchestan Uinversity; Zahedan; Iran E-mail: bakhshi@parsimail.com

Young Bae Jun*

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

Abstract: In this manuscript, first we define the notion of fuzzy congruence relation on a hyper algebra. Then, under suitable conditions we obtain a bijection correspondence between the set of all fuzzy congruence relations and the set of all fuzzy reflexive hyper ideals.

Keywords: (quasi, alternate) hyper algebra, positive implictive hyper algebra,(fuzzy reflexive) hyper ideal, fuzzy (congruence) relation.

Paracompactness in fuzzy Topological Spaces

M. E. EI-Shafei

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

Abstract: In this paper, we introduce and study three kinds of paracompactness on fuzzy Topological spaces. Each of them is a good extension of its classical topological counterpart. They are invariant of various types of mappings.

Keywords: fuzzy semi-paracompactness, fuzzy almost paracompactness, fuzzy paras-closedness, irresolute.

Semigroups of Operators on Spaces of Fuzzy-number-valued Functions with Applications to Fuzzy Differential Equations

Ciprian S. Gal

The University of Memplis Department of Mathematical Sciences Memphis, TN, 38152,U. S. A. E-mail: cgal@memphis.edu

Sorin G. Gal

Department of Mathematics University of Oradea, Romania 3700 Oradea, Romania E-mail: galso@uoradea.ro

Abstract: In this paper we introduce and study semigroups of operators on spaces of Fuzzy-number-valued functions and various applications to fuzzy differential equations are presented.

Keywords: Fuzzy numbers, Fuzzy-number-valued functions, semigroups of operators, fuzzy differential equations.

Fuzzy Comprehensive Evaluation of Investment Environment of Foreign Direct Investment

YunLiu

School of Management, Huazhong Science and Technology University, Wuhan, Hubei, 430074, China School of Business Administration, Jimei University, Xiamen, Fujian, 361021, China

Shui-Li Chen

Department of Mathematics, Jimei University, Xiamen, Fujian, 361021,China Zi-Gang Zhang School of Management, Huazhong Science and Technology University, Wuhan, Hubei, 430074, China

Abstract: According to this paper, a model of investment environment of the mainland was established basing on fuzzy comprehensive evaluation (FCE). First, the target system of FCE is set up. Second, a model of environment evaluation is built on the base of FCE and given target system. Finally, an example is taken to explain use of the model. It is significant for the mainland to carry on the self-evaluation of investment environment to attract TNC, which will clarify the advantages and disadvantages of the districts, therefore effective steps will be taken to improve investment environment, and the district superiority of attracting investment will be created and cultivated.

Keywords: Transnational corporation; investment environment; target system; FCE

fuzzy Normal Subgroups and fuzzy Quotient Subgroups

Bingxue Yao

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

Abstract: Based on the definition of fuzzy subgroup introduced by Yuan we introduce the concepts of fuzzy normal subgroups and fuzzy quotient subgroups which can be regarded as a generalization of Rosenfeld¡¯s and Bhakat and Das¡¯correspondence concepts. We also discuss some properties of fuzzy subgroups and fuzzy normal subgroups and give the relations between fuzzy subgroups fuzzy subgroups ( fuzzy norm subgroups) under a group homomorphism.

Keywords: fuzzy subgroup, fuzzy norm subgroups, fuzzy quotient group, fuzzy quotient subgroup

Fuzzy Uniformities in Fuzzy Box Products

D. Susha

Department of Mathematics Catholicate College Pathanamthitta Kerala, India E-mail: sushasivam@yahoo.com

Abstract: In this paper we introduce fuzzy uniformities in fuzzy box products as a continuation of the study of fuzzy box products introduced in [5].

Keywords: Fuzzy filter, Fuzzy uniformity, Fuzzy uniformizable space, Cauchy fuzzy filter, Fuzzy topologically complete space.

Ranking Fuzzy Numbers with the Best Approximation Interval

Liu Hua-wen, Shi Kai-quan

School of Mathematics and System Sciences, Shandong University. Jinan, Shandong 250100,China

Abstract: The aim of this paper is to rank fuzzy numbers with the best approximation interval of fuzzy numbers. First, we define a new and more reasonable distance between interval numbers and then, on the basis of this ,introduce a new distance between fuzzy numbers. Then, the best approximation interval of a fuzzy number is obtained by solving a nonlinear programming problem. We also point out that the expected interval of a fuzzy number is a special best approximation interval. Furthermore, a ranking function for fuzzy numbers is proposed. Finally, the discussion indicates that the Ranking function introduced in this paper is a generalization of the other same type methodsand is more convenient and reasonable in applications.

Keywords: Fuzzy number; Ranking; Interval number; Approximation interval; Distance

A Fixed Point Result for A Sequence of Mutually Contractive Self-mappings on Fuzzy Metric Sraces

Binayak S. Choudhury and P. N. Dutta

Department of Mathematics Bengal Engineering and Science University, Shibpur, Howrah-711103, India

Abstract: We define mutually contractive mappings on a completes fuzzy metric space in the sense of George and Veeramani and establish a unique common fixed point theorem in such spaces.

Keywords: Mutually contractive mappings, complete fuzzy metric space, fixed point.

Operations on Equivalent Fuzzy Subgroups

V. Murali

Department of Mathematics (Pure Applied) Rhodes University Grahamstoum 6140 South Africa

B. B. Makamba

Department of Mathematics University of Fort Hare Alice 5700 South Africa

Abstract: In this paper, we introduce and study the operations of union, intersection and sum of fuzzy subgroups of a finite group under an equivalence. In order to facilitate the study of equivalence, we introduce the notion of a pinned-flag on .First we establish a one-to-one correspondence between equivalence classes fuzzy subgroups and pinned-flag on . We determine the pinned-flags of intersection and sum of two fuzzy subgroups. Further we investigate the images and pre-images of fuzzy subgroups under a homomorphism with regard to equivalence. Whenever the equivalences are not preserved, we haveprovided suitable counter-examples.

Keywords: Equivalence, Fuzzy subgroup, Sum, Keychain, Pinned-flag.

Inclusion Degree and Support Degree of Fuzzy Sets

Baoqing Jiang

Intelligence Control Development Center, Southwest Jiaotong University Chengdu, Sichuan 610031,China E-mail address: jbq@henu.edu.cn School of Computer and Information Engineering, Henan University Kaifeng, Henan 475001, China

Jun Ma and Xuefang Wang

Intelligence Control Development Center, Southwest Jiaotong University Chengdu, Sichuan 610031, China

Abstract: The concepts of ¡°inclusion degree¡± and ¡°support degree¡± play a very important role in measuring the degree of inclusion for two fuzzy sets. In this paper, one instance of inclusion degree is presented and its properties are discussed. Also, an instance of support degree is given, and its properties and the relation with inclusion degree are investigated.

Keywords: Fuzzy sets; Inclusion degree; support degree