THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 13, Number 4, December 2005

CONTENT

DETAILS

Fuzzy Eigenvalues

James J. Buckley*

University of Alabama at Birmingham, Department of Mathematics Birmingham, Alabama, 35294, USA buckley@math.uab.eduThomas Feuring University of Siegen, Department of Electrical Engineering and Computer Science H lderlinstr. 3, 57068 Siegen, Germany feuring@informatik.uni-siegen.de

Yoichi Hayashi

Meiji University Department of Computer Science Tama-ku, Kawasaki 214-8571, Japan hayashiy@cs.meiji.ac.jp

Abstract: We first consider various methods of defining and computing fuzzy eigenvalues and fuzzy eigenvectors. We argue against all but one of the proposed methods. The procedure selected is then used on two examples, a and a symmetric fuzzy matrix, to compute fuzzy eigenvalues and eigenvectors.

Keywords: Fuzzy algebra.

Fuzzy Based Image Thresholding

Tamalika Chaira and A. K. Ray

Department of Electronics and Electrical Communication Engineering Indian Institute of Technolog, Kharamgpur, India E-mail: tamalika@ace.iitkgp.ernet.in akray@ace.iitkgp.ernet.in

Abstract: Thresholding plays an important role in image processing. To select a suitable threshold requires some criteria on which to base the selection. A new image thresholding method using fuzzy divergence, linear index of fuzziness and quadratic index of fuzziness has been proposed here. Fuzzy divergence finds the separation between the ideally and experimentally segmented images. The threshold is selected by minimizing the measures of fuzziness of an image. A comparative study of three fuzzy measures for the images has been carried out and promising results are obtained.

Keywords: Exponential entropy, divergence, and index of fuzziness and membership function.

Broad Fuzzy Extention of Certain Fuzzy Ideals of Semigroups on Strong Semilattices

Shuk Yee Lee and K. P. Shum*

Faculty of Science, The Chinese University of Hong Kong Shatin, N. T. Hong Kong, China (SAR) e-mail: suelee@pacific.net. hk, kpshum@math.cuhk.edu.hk

Wu Congxin

Department of Mathematics, Harbin Institute of Technology Harbin, China

Abstract: We consider the fuzzy extension form each semigroup component of a strong semilattice of semigroups to the whole semigroup. A new concept ¡°broad fuzzy extension¡± is introduced so that most properties of fuzzy ideals can be preserved under such kind of fuzzy extention. This approach provides the best possible way to construct fuzzy semigroups from some small ones to a larger one.

Keywords: Broad fuzzy extension; Strong semilattice of semigroups; Fuzzy semigroups; Fuzzy ideas

Product and Extension Operations of the Intuitionistic Fuzzy Normal Subgroups*

Li Xiaoping

School of Management, Tianjin Normal University Tianjin, 300074, P. R. China

Abstract: In this paper, on the basis of the concept of the intuitionistic fuzzy set introduced by K. Atanassov, we first give the definition of the product and extension principle, study the structures and characterizations of the product for intuitionistic fuzzy normal subgroups. Second, on the conditions that homomorphism and isomorphism between two classical groups, applying the extension principle, we will discuss the extension products of general intuitionistic fuzzy sets and the extension operation of the intuitionistic fuzzy normal subgroups.

Keywords: Intuitionistic fuzzy sets; product; extension principle; intuitionistic fuzzy normal subgroups.

On Genuine Topological Space

I.M.Hanafy

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

Abstract: Using first order genuine sets [3], we introduce and study several basic results related to the product of functions, continuous functions, open functions and almost continuous functions in genuine topological spaces.

Keywords: Genuine sets, Genuine topological spaces, Genuine continuous functions, Genuine open functions, Genuine regular open sets, Genuine almost continuous functions.

Some Aspects of connectedness in topological Spaces

Ratna Dev Sarma

Eritrea Institute of Technology, Minefe Asmara, Eritrea E-mail: ratna_sarma@yahoo.com

Debajit Hazarika

Department of Mathematical Sciences, School of Science and Technology Tezpur University, Napaam-784028(India)

A.Sharfuddin

Department of Mathematics, Faculty of Natural Sciences Jamia Milia Islamia, New Delhi-110025(India)

Abstract: connectedness is further studied for topological Spaces. Components are defined using equivalence relations and their properties are investigated. Further, local connectedness is introduced and its important properties are discussed. Interrelationship between component and local connectedness is also investigated.

Keywords: topological, connectedness, continuity, quasi-components, components.

Extensions of Fuzzy Syntopogenous Spaces

O. A. El-Tantawy

Department of Mathematiecs, Faculty of Science, Zagazig University, Zagazig, Egypt.

Abstract: Some extension of fuzzy syntopogenous spaces are introduced and studied.

Keywords: Fuzzy syntopogenous structures, extensions of syntopogenous spaces, fuzzy filter.

Quotient Ring of A Ring Generated by An Ideal and A Fuzzy Subset

T.Ali* and A.K.Ray

Department of Mathematics Dibrugarh University, Dibrugarh-786004, Assam,India

Abstract: In this paper we have introduced the concept of cosets of an ideal in a ring gengerated by an element of the ring and a translational invariant fuzzy subset of the ring. We have proved some results analogous to certain basic results of the classical ring theory. Finally we have defined the quotient ring of generated by an ideal and .

Keywords: Cosets, Translational invariant fuzzy subset, Quotient ring.

Joint Root Function Expansion of The Nolocal Partial Integro-differential Operators of First Order

E.M.El-Abd

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

Abstract: The paper deals with the convolutional structure of a system of the nonlocal partial integro-differential operators of first order, whose integral part is of Volterra type, as well as with the convolutional structure and uniqueness theorem for their expansion on joint root functions(joint eigen and associated functions). Sufficient conditions for completeness of the joint root functions of these operators in the spaces are considered as well.

Keywords: Convolution, joint root function expansion

Components in Lattice Implication Algebra

Yi Liangzhong

Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan

Department of computer science and Engineering Xihua University Chengdu 610039, Sichuan

Xu Yang

Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan

Qin Keyun

Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan

Abstract: In this paper, Proposition 1 in [1] is generalized. Components in a lattice implication algebra are discussed and some necessary and sufficient conditions that b is one component of a in a lattice implication algebra are obtained.

Keywords: Modular lattice, Order-reversing involution, Implication operator, Lattice implication algebra, Component.

On Generalizing Fuzzy Semi-open Set*

H.Harada

Department of Mathematics, Seiryo High School 6-1 Betsuin, Mojiku, Kitakyushu, 800-0035 Japan

M.Kojima

Department of Mathematics, Seiryo High School aza-Hiroisi oaza-Jurokucho, Nishi-ku, Fukuoka 811-1347 Japan

F.Tamari and T.Fukutake

Department of Information Sciences, Fukuoka University of Education 1-1 Akamabunkyoumachi, Munakata, Fukuoka 811-4192 Japan

H.Maki

Department of Mathematics, Faculty of Culture and Education Saga University, saga 840-8502 Japan

Abstract: The aim of this paper is to generalize the notion of semi-open sets and semi-closures [5] into a fuzzy system where is a non-empty set and are two subfamilies of fuzzy sets on . And we have a formula of the semi-closure in a fuzzy system (cf. Theorem 3.2). Moreover, we construct two groups corresponding to a fuzzy system (cf. Theorem4.9).

Keywords: Topology, fuzzy semi-open sets, fuzzy preopen sets fuzzy semi-open sets, fuzzy semi-closures, fuzzy irresolute functions, fuzzy semi-homeomorphisms, fuzzy homeomorphisms.

Perturbed Proximal Point Algorithms of General Quasivariational-like Inclusions for FuzzyMappings

Jae Ug Jeong

Department of Mathematics Dong Eui University Pusan 614-714,South Korea

Abstract: In this paper, we introduce and study a class of general quasi-variational-like inclusions and develop some new perturbed proximal point algorithms of Mann and Ishikawa type for finding the approximant solutions of the general quasi-variational-like invlusions for fuzzy mappings. The convergence criteria of the sequences of approximate solutions generated by these new algorithms are also discussed. Our algorithms and results improve and generalize many known results of qusi-variational inequalities (inclusions) for fuzzy mappings.

Keywords: Variational inclusions; proximal mapping; Fuzzy mapping.

The Properties of Implication Operator in Lattice Implication Algebra

Yi Liangzhong

Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031,Sichuan Department of computer science and Engineering Xihua University, Chengdu 610039,Sichuan

Xu yang

Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031,Sichuan

Abstract: The article discusses the properties of implication operator in lattice implication algebra, and gives the method to set up lattice implication algebra with an order-reversing involution be difined implication operator, finally studies the union operation, intersection operation, inverse operation and composition operation of implication operator in lattice implication algebra.

Keywords: Implication operator, Order-reversing involution, Lattice, Lattice implication algebra.

On Multiplicative Fuzzy algebras

Wieslaw.A.Dudek

Institue of Mathematics, Technical University of Wroclaw, Wybrzeze Wyspiazskiego 27,50-370 Wroclaw,Poland E-mail address: dudek@im.pwr.wroc.pl

Young Bae Jun*

Department of Mathematics Education, Gyeongsang National University,Chinju660-701,Korea E-mail address: ybjun@gsnu.ac.kr

Abstract: The notion of multiplicative fuzzy algebras is introduced, and some of their properties are investigated. Multiplicative fuzzy topological algebras are also discussed.

Keywords: Fuzzy algebras, multiplicative fuzzy (topological) algebras.

On Fuzzifying Topological Spaces

A.K.Katsaras and C.G.Petalas

Department of Mathematics, University of Ioannina, Greece

Abstract: Some of the properties of fuzzifying topologies are investigated. Sequential fuzzifying Topologies and connectedness in fuzzifying topological spaces are introduced and several of the theorems on classical topologies follow from the results obtained in the paper.1991A.M.S.Subject Classification: 54A40

Keywords: Fuzzifying topology, convergence of nets, sequential continuity, connectedness.

Fixed Points, Attractors and Weak Fuzzy Contractive Mappings in A Fuzzy Metric Space*

Cristina Di Bari+, Calogero Vetro

Dipartimento di Matematica ed Applicazioni Via Archirafi 3490123 Palermo(Italy) E-mail: dibari@math.unipa.it

Abstract: In this paper we give a result regarding the link between the fuzzy metric notion of contractivity, in Gregori and Sapena¡¯s sense, and topological notion of attractor. Also we prove a result of fixed point for weak fuzzy contractive mappings.

Keywords: Fuzzy metric spaces, Fuzzy contractive and weak fuzzy contractive mappings, Fixed points.

Free fuzzy Subgroups

K.R.Bhutani

Department of Mathematics The Catholic University of America Washington D.C.20064,USA

R.L.Crist

Department of Mathematics and Computer Science Corresponding author E-mail: mordes@creighton.edu

J.N.Mordeson

Department of Mathematics and Computer Science Creighton University Omaha, Nebraska 68178, USA In Honor of Azreel Rosenfeld

Abstract: We extend the notion of an fuzzy subgroup of a group G to a more general situation. It is known that is an fuzzy subgroup of G if and only if We define a quasi-fuzzy subgroup of G by use of a fuzzy complement which has an equilibrium . We show that is a quasi-fuzzy subgroup of G if and only if If is the standard fuzzy complement defined by then .we also study the notion of an fuzzy Subgroups. This notion is more general then that of a quasi-fuzzy subgroup.The latter can be obtained by letting . The notion of a free fuzzy Subgroups is developed.

Keywords: fuzzy subgroup, quasi-fuzzy subgroup, fuzzy Subgroups

Extended norms and Its Applications in Portfolio Selection Model

Bablu Samanta and Tapan Kumar Roy*

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

Abstract: In this paper, we convert binary norms into extended ary norms and their Some limiting cases are calculated. Next consider a multi-objective Portfolio Selection model in fuzzy environment and finally norm based fuzzy optimization programming technique is used to solve the problem. The model is illustrated with numerical examples.

Keywords: Portfolio selection model, multi-objective optimization, norm.