THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 13, Number 1, March 2005

CONTENT

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Entropy Function for Infinite Fuzzy Partitions

M.Ebrahimi and A.R.Poihassani

Department of Mathematics, Vail-Asr University, Rafsanjan, Iran E-mail:ebrahimil2000us@yahoo.com E-mail:apouhassani@hotmail.com

Abstract: One of the importance concepts in physics and mathematics is ¡°entropy¡± and a part of dynamical systems and ergodic theory¡¯s studding is about this paper the concept in the area of finite partitions and fuzzy finite partitions [11,12]. In this paper the concept of entropy will be extended to the infinite fuzzy partitions and some of properties of them will be studied.

Blocks in Fuzzy Graphs

M.S.Sunitha

Department of Mathematics, National Institute of Technology Calicut-673 601, India . (sunitha@nitc.ac.in)

A.Vijayakumar

Department of Mathematics, Cochin University of Science & Technology, Cochin-682 022 India (vijay@cusat.ac.in)

Abstract: Some properties of fuzzy bridges and fuzzy cutnodes are discussed and a characterization of blocks in fuzzy graphs is obtained.

Keywords: Fuzzy bridge, fuzzy cut node,fuzzy tree, block.

Fuzzy Hahn-Banach Theorem-A New Approach-¢ò

Binimol Punnoose and Sunny Kuriakose.A

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

Abstract: We have proved the fuzzy version of the Hahn-Banach theorem on a fuzzy vector space over the set of fuzzy vector real numbers [1]. Here in this paper, we discuss some applications of the theorem.

Keywords: Fuzzy number, fuzzy vector subspace, fuzzy linear functional, fuzzy Hahn-Banach theorem, fuzzy topological vector space, fuzzy norm.

 

 

Hong Wang

College of Science, Southwest University of Science and Technology, Mianyang 621000£¬Sichuan , P.R.China

Abstract: In this paper, first image and inverse image of refinement of semi-topogenous order on L have been defined by GOH. Second, the image and inverse image of refinement of syntopogenous structure on L have been researched. Some important properties have been obtained.

Keywords: Syntopogenous structure, ref , GOH, image and inverse image

Encryption of Fuzzy Recognition with t-order Iteration

Changjing Luxury

Department of Computer Sciences, Sanming College Sanming 365004£¬P. R. China

Kaiquan Shi

School of Mathematics and System Sciences, Shandong University Jinan,250100£¬China, P. R. China

Abstract: Using researches given in [1], the paper puts forward encryption of fuzzy recognition with t-order iteration; we gives the structure of encryption-decryption with t-order and false t-order on elliptical curve; we presents generation theorem of false plaintext and uniqueness theorem of cryptograph; on the basis of these researches, the paper gives the applications for encryption of fuzzy recognition with t-order iteration and encryption of fuzzy recognition with false t-order iteration. This paper is a continuance of [1].

Keywords: Fuzzy recognition, elliptical curve, t-order iteration, false generation theorem, application

Correlation and Entropy of Interval-valued Fuzzy Sets

Nishi Kanta Jana and Madhumanggal Pal

Department of Applied Mathematics with Oceanology and Computer Programming , Vidyasagar University ,Midnapore-721 102£¬INDIA

Abstract: In this paper, we study the concept of correlation on interval-valued fuzzy sets. In the mean time, some properties are presented on covariance and correlation coefficient. Then we define the degree of fuzzyness i.e.,entropy using Hamming distance of interval valued fuzzy sets. Also we studied some properties of entropy.

Keywords: Interval-valued fuzzy set, covariance, correlation coefficient, Hamming distance, entropy

A Fuzzy Interactive Approach for Solving Possibilistic Multiobjective Programming Problems

M.H.Rasmy, Sang M.Lee, Waicl F.Abd El-wahed, Ali M.Ragab, M.M.El-Sherbiny

Faculty of Computer and Information, Cairo University , Egypt Management Depar, University of Nebraska-Lincoln, USA Operations Research Department, Faculty of Computers and Information El-Menoufia University, Shiben El-Kom, Egypt Institute of Statistical Studies and Research (ISSR), Cairo University, Egypt Dept. of Computer and Information Sciences, (ISSR), Cairo University, Egypt

Abstract: This article presents a fuzzy interactive estimating approach (FIEA) for Solingen the multiobjective possibility programming problems. FIEA uses a set of decision-making rules to obtain a solution to the problem under qualitative information conditions. To solve such a problem, an interactive approach is proposed . Potential applications of FIEA are shown Through an illustrative problrm.

Keywords: Multiobjective decision making, Fuzzy variable, Linguistic variable, Fuzzy Inference, Linguistic approximation, Fuzzy expert system .

Similarity Measures between Intuitionistic Fuzzy Sets and between Elements and Application to Pattern Recognitions

Liu Huawen

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

Abstract: Recently, Li and Cheng [2] proposed several new similarity measures between intuitionistic fuzzy sets (IFSs), and presented some examples to illustrate the application of the said measures in handing pattern recognition problems. In this paper, we showed by examples that the similarity measures proposed by linguistic and Cheng do not fit well in some cases, and proposed a set of modified measures proposed by Li and Cheng do not fit well in some cases, and proposed a set of modified measures and discussed their some properties. Comparing the similarity degree of each measure, the modified similarity measures turned to be more reasonable in more general cases than previous one. We also proposed the similarity measure between elements and discussed its properties. Finally, the modified similarity measures between IFSs were applied to pattern recognitions.

Keywords: Fuzzy sets, Intuitionistic fuzzy sets, Similarity measures, Pattern recognition

Fixed Points of Expanding Fuzzy Multifunctions

Abdelkader Stouti

Department of Mathematics, Faculty of Sciences and Techniques University Cadi Ayyad, P. O.Box 523. Beni-Mellal 23000, Morocco e-mail:stouti@yahoo.com

Abstract: In this paper, we first prove the existence of a fixed point of expanding fuzzy multifunctions in ¦Á-fuzzy preordered sets. After this, we establish the existence of greatest and maximal fixed points of expanding fuzzy multifunctions in ¦Á-fuzzy ordered sets.

Keywords: Fuzzy set, ¦Á-fuzzy preorder relation, ¦Á-fuzzy order relation, expanding fuzzy multifunction, fixed point.

Fuzzifying Convex Sets Based on Continuous-valued Logic

Zhang Guang-ji, Zouk kai-qi and Zhang Cheng

In formation Engineering College, Dalian University, Datian 116622£¬China

Abstract: In this paper, we used a semantic method of continuous-valued logic to develop fuzzy convex set from a completely different direction and thereby have established elementary fuzzifying convex set which is dual to the existing fuzzy convex set, and given the algebraic properties and the topological properties of fuzzifying convex set.

Keywords: Continuous-valued logic, fuzzifying convex set, topological linear space

Extremally Disconnectedness in Ordered Fuzzy Toplogical Spaces

M.K.Uma

Department of Mathematics, Sri Sarada College for women, Salem -636 016£¬Tamil Nadu

G.Balasubramanian

Department of Mathematics, Periyar University, Salem-636 011,Tamil Nadu, India

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

Keywords: Ordered fuzzy extremally disconnected space, fuzzy normally ordered space and ordered fuzzy continuous mapping.

The Measurability and (K) Integrability About Fuzzy n-cell Number Value Mappings

Wang Guixiang

Information and Telecommunication Engineeing School Harbin Engineering University, Harbin , 150001£¬P.R.China

Department of information and Mathematics Science, Hanhzhou institute of Electronice Engineering, Hangzou, 310018£¬ P.R.China

Zhao Chunhui

Information and Telecommunication Engineeing School Harbin Engineering University, Harbin , 150001£¬P.R.China

Abstract: In this paper, we consider the characterization of measurability and integrability about fuzzy n-cell number value mapping by using the concrete structure into which we embed the fuzzy n-cell number metric space . Several necessary and sufficient conditions are given on measureability and integrability of fuzzy n-cell number value mappings.

Keywords: Fuzzy number, fuzzy n-cell number, fuzzy n-cell number value mapping, embedding theorem, measurability, integral

T-congruence Permutable of Algebra

F.I.Sidky Mathematics

Department, Faculty of Science, Zagzig University, Zagazig, Egypt M.M.Atallah Mathematics Department, Faculty of Science, Tanta University, Tanta , Egypt

Abstract: The permutability of the two T-congruence relations of algebra is given and we prove that a fuzzy congruence permutable implies that a fuzzy congruence modular, an application of group is given.

Keywords: Algebra, congruence cermutable, T-congruence relation.

Fuzzy Factor Semigroup of semigroups on Strong Semilattices

AL.Narayanan and T.Manikantan

Department of Mathematics, Annamalai University ,Annamalainagar-608 002£¬Tamilnadu, India e-mail:alagappan_cdm@rediffmail.com

Abstract: In this paper, we further extend the work of Shuk Yee Lee and K.P.Shum [10]. In fact, we exhibit the fuzzy factor semigroup to the semigroups on strong semilattices. Further, we extend some more fuzzy algebraic properties from a local semigroup to a global one on a strong semilattice Y.

Keywords: Strong semilattice of semigroups, Fuzzy factor semigroup, Fuzzy complete innerunitary subsemigroup, Fuzzy semiprime

Fuzzy Setting of Ideals in BZ-algebras

Y.B.Jun

Department of Mathematics Education, Gyeongsang National University, Chinju (jinju) 660-701£¬ Korea e-mail:ybjun@gsnu.ac.Kr

X.H.Zhang

The Faculty of Science, Ningbo University, Ningbo 315211£¬ Zhejiang Province, P.R.China e-mail:zxhonghz@263.net

Abstract: The fuzzification of T-ideals in BZ-algebras is considered. Relationship between a fuzyy BZ-ideal and a fuzzy T-ideal are investigated. Conditions for a fuzzy BZ-ideal to be a fuzzy T-ideal are given. Using the notion of level sets, a characterization of a fuzzy T-ideal is provided. Extension property for s fuzzy T-ideal is established. Using an increasing sequence of T-ideals, a fuzzy T-ideal is built. Using level subsets of a BZ-ideal with respect to a fuzzy set in , a new fuzzy T-ideal is constructed.

Keywords: (fuzzy) BZ-ideal, (fuzzy) T-ideal

Characterization of Fuzzy Substructures of A Near-ring and A Near-ring Group

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: Our attemot is on to characterize fuzzy completely prime ideals of a near-ring N in terms of fuzzy points and investigate some properties of such ideals. In this paper, the notion of fuzzy annihilator of a fuzzy subset of a near-ring group is introduced. It is proved that fuzzy annihilator of a fuzzy subset of an N-group is a fuzzy left ideal of N. the concept of fuzzy annihilator leads using to a structure that is termed as fuzzy prime N-subgroup. Certain properties Involving fuzzy prime N-subgroup are established. Finally, it is shown that the factor N-group induced by a fuzzy ideal is a fuzzy prime N-group if and only if the fuzzy ideal is a prime ideal of N.

Keywords: Near-ring, near-ring group, fuzzy ideal, fuzzy prime ideal, fuzzy annihilator, fuzzy prime N-subgroup

Remoted Neighbourhoods and Separation Axioms in Fuzzy Bitopological Spaces

G.A.Gameel

Mathematics Department, Faculty of Education in Port Said, Suez Canal University, Egypt

Abstract: In this paper we give and study different typeset of separation axioms using the remoted neighbourhoods of a fuzzy point and a fuzzy set in the fuzzy supratopological space which is generated by the fuzzy bitopological space . Several characterizations, Properties on these separation axioms are investigated.

Keywords: Remoted neighborhoods, fuzzy bitopology, supratopology, separation axioms, fuzzy filter, Q-neighbourhood.

Almost Automorphic Fuzzy-number-valued Functions

Sorin G.Gal

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

Gaston M.N¡¯ Guerekata

Department of Mathematics Morgan State University Baltimore, MD21251, USA e-mail:gnguerek@jewe;.morgan.edu

Abstract: In [2] a theory of almost periodic functions of real variable and with values in The space of fuzzy real numbers has been considered. The purpose of the present paper is to generalize this theory to the case of almost automorphic fuzzy-number-valued functions. Although the class of fuzzy real numbers does noyes form a linear normed space, the majority of main properties of almost automorphic functions with values in Banach spaceship are extended to this case. The applicability of the theory is considerably enlarged by considering almost automorphic functions with values in new spaces (of functions or sequences) constructed with the class of fuzzy numbers. Applications to dynamical systems and fuzzy differential equations are given.

Keywords: Fuzzy numbers, almost automorphic functions, fuzzy-number-valued functions, semigroups of linear operators, mild solutions of fuzzy differential equations, dynamical systems.

Quotient BH-algebras Via Fuzzy Translation BH-ideals

Qun Zhang

Department of Mathematics, Education Affairs of South-Central, University for Nationalities, Wuhan 430073£¬P. R. China

Eun Hwang ROh

Department of Mathematics Education Chinju National University of Education Chinju 660-756,Korea

Young Bae Jun

Department of Mathematics Education, Gyeongsang National University, Chinju (jinju) 660-701£¬ Korea e-mail:ybjun@gsnu.ac.kr

Abstract: We discuss quotient BH-algebras induced by fuzzy translation BH-ideals, and establish the fuzzy fundamental homomorphism theorem for some BH-algebras.

Keywords: (Fuzzy) BH-ideal, (fuzzy) translation BH-ideal, quotient BH-algebra

The Structures of Power Lattices

Pinghua Ming

Department of Computer, Xianning Teachers College, Hubei 437005£¬P. R. China

Chongyou Zheng

Department of mathematics, Capital Normal University, Beijing 100037£¬ P. R. China

Abstract: In this paper, the concept of power lattice on a lattice is given, two sufficient and necessary conditions of power lattice on the lattice are obtained, relation between regular power lattice and quotient lattice on the lattice and that between relative power lattice and quotient lattice are discussed.

Keywords: Lattice, Distributive lattice, Power lattice, Power set lattice, Quotient lattice, Regular lattice, relative lattice

-fuzzy Topology, R-fuzzy Topology and -fuzzy Topology

Xuehai Yuan D

epartment of Applied Mathematics, Dalian University of Technology, Dalian 116024£¬ P.R. China School of Mathematics, Liaoning Normal University, Dalian 116029£¬ P. R. China

Zunquan Xia

Department of Applied Mathematics, Dalian University of Technology, Dalian 116024£¬ P.R. China

Feng Liu

Department of Basement, Dalian Navy Academy, Dalian 116600, P. R. China

Abstract: By the use of the relationship between fuzzy points and fuzzy sets and implication operators of fuzzy logic, definitions of -fuzzy topology and R-fuzzy topology are given. Two new fuzzy topologies called -fuzzy topology and -fuzzy topology are obtained, Relationship between -fuzzy topology and R-fuzzy topology are discussed. In the end, concept of -fuzzy topology is given. -fuzzy topology generalizes fuzzifying topology, -fuzzy topology and -fuzzy topology.

Keywords: Fuzzy topology, fuzzy point, implication operators, -fuzzy topology, -fuzzy topology, R-fuzzy topology, fuzzifying topology, -fuzzy topology.

Weakly PS-compact L-subsets

Bai Shi-Zhong D

epartment of Mathematics, Wuyi University, Jiangmen Guangdong 529020£¬ P. R. China

Abstract: In this paper, the weak PS-compactness in L-topological spaces is introduced. It is a kind of compactness between fuzzy compactness and PS-compactness in L-topological spaces, and is defined for any L-subset. And some good results are obtained.

Keywords: L-topological spaces, remote-neighborhhod, -net, -filter, weak PS-compactness.