THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 9, Number 3, September 2001

CONTENT

DETAILS

On Weak Fuzzy Convexity Spaces

M.V.Rosa

Department of Mathematics,Bharata Mata collage Kochi 682 021,India

Abstract: In this paper we introduce the notion of a weak fuzzy convexity space which is analogous to the definition of F.W.Levi[2] in (crisp) convexity theory.In[6],we introduced the concept of associated-fuzzy convexity in a given(crisp) convexity space according to the definition of R.E.Jamison[1] .On the other hand,given a weak fuzzy convexity space,we can associate a (crisp) convexity;this is discussed in this paper. Also we study separation axioms in weak fuzzy convexity spaces and study certain concepts related to this.

Keywords: Fuzzy convexity, fuzzy subspace, fuzzy convexity space, weak fuzzy convexity space.

Fuzzy Mixed VVR Models with An Application to Banking

Y.Uemura

Faculty of Education. Mie University, 1515 Kamihama, Tsu, 514, Japa E-mail:ueinura@edu.mie-u.ac.jp

Abstract: The evaluation of efficiency for DMUs (Decision Making Units) in some company is very important. In this view point, the study of evaluation of efficiency is very active, on the basis of the formulation for the production function. Recently, DEA (Data Envelopment Analysis) is focused on the evaluation of efficiency. We have the representation model in DEA as CCR Model and BCC Model. Generally, BCC efficiency is bigger than CCR efficiency. This means that BCC analyzes DMUs most optimistically, and CCR model is the most pessimistic analysis. In this paper, first, we formulate Fuzzy Mixed CCR Model by introducing a fuzzy goal by BCC model into CCR model. On the other side, DEA model for outputs has been proposed. Second, we fuze DEA model for inputs and one for outputs by introduced a fuzzy goal from DEA model for outputs into that for inputs.

Keywords: CCR Model, BCC Model, Fuzzy Goal.

Fuzzy Mixed CCR Model Fuzzy Topology on Fuzzy Sets:Functions with Fuzzy Closed Graphs and Strong Fuzzy Closed Graphs

M.A.Fath Alla and F.S.Mahmoud Department of Mathematics, Faculty of Science, Sohag-(82524), Egypt

Abstract: In this paper, we introduce and study new notions of functions which have fuzzy (strong fuzzy) closed graphs, using the recent notion of a fuzzy proper function which was introduced in [2] . Also, we introduce some new separation axioms in fuzzy topology on fuzzy sets [2]. We establish some of their fundamental properties and discuss relations between these concepts.

Keywords: Fuzzy proper function, Fuzzy closed graph and strong fuzzy closed graph.

Intuitionistic Fuzzy Closed Ideals in BCH-algebras

Young Bea Jun

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

Wieslaw A.Dudek Institute of Mathematics, Technical University Wybrzezc Wyspianskiego 27, 50-370 Wroclaw, Poland E-mail:dudek@im.pwr.wroc.pl

Abstract: We consider the intuitionistic fuzzification of subalgebras and closed ideals in BCH-algebras, and investigate some of their properties. We establish the relation between an intuitionistic fuzzy subalgebra and an intuitionistic fuzzy closed ideal. We state a condition for an intuitionistic fuzzy subalgebra to be an intuitionistic fuzzy closed ideal. We also give characterizations of intuitionistic fuzzy closed ideals.

Keywords: BCH-algebra, (intuitionistic fuzzy ) subalgebra, (intuitionistic fuzzy) closed ideal.

Extended Operations on Normal Interval-valued Fuzzy Sets Space

Li Xiaoping and Wang Guijun

Department of Mathematics, Tonghua Teachers' College Tonghua, Jilin, 134002, P.R.China

Abstract: In this paper, on the normal interval-valued fuzzy sets space, we first give the definitions of their extension operations and orders by introducing the operations of interval numbers and t-norms operator,and then discuss basic properties with respect to their operations. Consequently, we obtain some basic results for this kind of speial interval-valued fuzzy numbers.

Keywords: Interval-valued fuzzy sets, normal interval-valued fuzzy sets, t-norms, extension operations, interval-valued fuzzy numbers.

Stability Behaviour of The Solutionsof Second Order Fuzzy Differential Equation

P.C.Nayak

Department of Mathematics M.P.C.College Baripada Mayurbhanj Orissa, India.

Abstract: In this paper we deal with a fuzzy differential equation.

Keywords: Stability behaviour.

Intuitionistic Fuzzy Rough Sets and Rough Intuitionistic Fuzzy Sets

S.K.Samanta and Tapas Kumar Mondal

Department of Mathematics, Visva-Bharati University Santiniketan-731235, W.Bengal, INDIA E-mail:syamal@vbharat.ernet.in

Abstract: In this paper the definitions of intuitionistic fuzzy rough sets and rough intuitionistic fuzzy sets are introduced . Some fundamental algebraic and functional properties are studied in both these settings.

Keywords: Fuzzy topology, intuitionistic fuzzy set, rough set, fuzzy rough set, intuitionistic fuzzy rough set, rough intuitionistic fuzzy set.

On Prime Filters of Lattice H Implication Algebras

Yang Xu, Keyun Qin

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

Eun Hwan Roh

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

Abstract: We prove that A(a) is the filter generated by a in a lattice H implication algebra. We define the subset in a lattice implication algebra and prove that is a filter in a lattice H implication algebra. By using these results, we give an equivalent condition of a prime filter in a lattice H implication algebra. Finally, we prove that the notions of prime filters and ultrafilters coincide in a lattice H implication algebra.

Keywords: Lattice implication algebra, lattice H implication algebra, (prime, ultra) filter.

Fuzzy Soft Sets

Pabitra Kumar Maji, Ranjit Biswas and Akhil Ranjan Roy*

Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, West Bengal, India

Abstract: In this paper we define fuzzy-soft-sets and establish some results on them.

Keywords: Soft set, fuzzy-soft-set.

On Lacunary Statistical and p-Cesaro Summability of Fuzzy Numbers

Joong Sung Kwon

Department of Mathematics, Sun Moon University Asan, Chungnam (337-840), KOREA E-mail:jskwon@email.sumoon.ac.kr

Soo Hak Sung

Department of Applied Mathematics, Pai Chai University Doma-2-Dong, Seo-Gu, Taejon 302-735, Korea E-mail:sungsh@www.paichai.ac.kr

Abstract: In this paper, the concept of Lacunary strongly p-Cesaro summability of a sequence of fuzzy number is introduced. The relationship between Lacunary statistical convergence and Lacunary strongly p-Cesaro suitability is discussed.

Keywords: Fuzzy number, Statistical convergence, Strong p-Cesaro summability.

On Quotient Lattice Implication Algebras Induced by Fuzzy Filters

Yang Xu and Keyun Qin

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

Eun Hwan Roh

Department of Mathematics Education Chinju National University of Aducation, Chinju 660-756, Korea E-mail:ehrohlacue,ac,kr

Abstract: We define a congruence relation on lattice implication algebras induced by fuzzy filters and we prove the Fuzzy Homomorphism Fundamental Theorem. As an application of the Fuzzy Homomorphism Fundamental Theorem, we can prove the Homomorphism Fundamental Theorem of lattice implication algebras.

Keywords: Lattice implication algebra, lattice homomorphism D-kernel, (fuzzy) filter.

On -convex L-processes

Marian Matloka

Department of Mathematics, University of Economics, al.Niepodleglosci 10,60-967 Poznan, Poland

Abstract: In this paper a concept of L-processes is introduced. First the definition of -convex L-process is presented and next its properties are considered.

Keywords: -convex set, L-multifunction, -convex L-process.

Interval-valued Fuzzifications of Subalgebras in BCH-algebras

Young Bae Jun and Sung Ming Hong

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

Abstract: The purpose of this paper is to define the notion of an interval-valued fuzzy subalgebra (briefly, an i-v fuzzy subalgebra) of a BCH-algebra. Necessary and sufficient conditions for an i-v fuzzy set to be an i-v fuzzy subalgebra are stated. A way to make a new i-v fuzzy subalgebra from old one is given. The images and inverse images of i-v fuzzy subalgebras axe defined, and how the images or inverse images of i-v fuzzy subalgebras become i-v fuzzy subalgebras is studied. Using a collection of subalgebras with some conditions, an i-v fuzzy subalgebra is constructed.

Keywords: Refined minimum, i-v fuzzy subalgebra, i-v level subalgebra.

Strato-closed Operator and L-fuzzy Paracompactness*

Meng Guangwu, Yao Zhongping

Department of mathematics and Systems Scienc Liaocheng Teachers University, Shandong 252059, P.R.China

Chen Shuili

Department of mathematics, Jimei University Xiamen, Fujian 361021, PR.China

Abstract: In L-fuzzy topological spaces, strato-closed operator is introduced, and stratiform L-topologies are presented. Based on this ,some charavterizations for III type strong fuzzy paracompactness are given.

Keywords: Fuzzy topology, strato-closed operator, fuzzy paracompactness, stratiform L-fuzzy topology.

The Characterization and Independence of Algebras

Pei Daowu

Institute of Mathematics, Sichuan University, Chengdu 610064, Sichuan, P.R.China

Department of Mathematics, Yancheng Teachers College, Yancheng 224002, Jiangsu, P.R.China

Abstract: algebras have important applications in fuzzy logic and fuzzy reasoning. In this paper, algebras are further studied. Some characterization theorems of algebras are obtained, and the independence of axiom systems of algebras also are showed.

Keywords: Fuzzy logic, algebra, weak algenbra, implication lattice, variety, independence.

Study On Fuzzy Differential Game

Ebrahim A.Youness

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

Abd EI-Moneim A.Megahed

Department of Basic Science, Faculty of Computers and Informatics Suez Canal University, Ismaelia, Egypt.

Abstract: In this paper we study fuzzy differential game problem, in which the information obtained by any player may contain some sort of uncertainties, which are usually difficult to characterize either deterministically or stochastically. A necessary condition for optimal strategy of an open loop Nash-equilibrium solution for fuzzy differential game is derived an illustrative example is presented to clarify the developed result.

Keywords: Differential game, fuzzy Differential game, Nash-equilibrium solution.

Fuzzy Space Geometry I: Points, Lines and Planes

F.Nemat and E.Eslami

Department of Mathematics Shahid Bahonar University of Kerman, Kerman, Iran

J.J.Buckley

Department of Mathematics, University of Alabama at Birmingham Birmingham, Alabama 35294, USA

Abstract: We extend the definition of a fuzzy point in the plane to the three dimensional space. Using a direction vector we define fuzzy lines in space in two ways: a parametric form and a symmetric form. The relation between these two forms, basic and general properties of fuzzy lines are studied. Then we define fuzzy planes in space and discuss their general properties. Intersecting fuzzy planes are studied. A characterization theorem of fuzzy planes is also proved.

Keywords: Fuzzy point, fuzzy line, fuzzy plane, three dimensional fuzzy spaces

Intuitionistic Fuzzy Soft Sets

Pabitra Kumar Maji, Ranjit Biswas and Akhil Ranjan Roy*

Department of Mathematics, Indian Institute of Technology. Kharagpur-721302, West Bengal, INDIA.

Abstract: In this paper we define intuitionistic fuzzy soft sets and establish some result on them.

Keywords: Soft set, intuitionistic fuzzy soft set.

Fuzzy Space Geometry II: Subpoints and Sublines

F.Nemat

Payam-e-Noor University, Kerman, Iran

E.Eslami

Department of Mathematics,Shahid Bahonar University of Kerman, Kerman, Iran.

J.J.Buckley

Department of Mathematics, University of Alabama at Birmingham Birmingham, Alabama U.S.A

Abstract: This paper is a continuation of our studies in Fuzzy Space geometry. Here we show that we may have not a fuzzy line passing through two fuzzy points and two intersecting fuzzy lines do not necessarily determine a fuzzy plane. There motivates us to define new notions as subpoints and sublines and prove some related theorems.

Keywords: Fuzzy spacegeometry, subpoint, subline.

On A Fuzzy Trigonometric Approximation Theorem of Weierstrass-type

George A.Anastassiou

Department of Mathematics Sciences University of Memphis, Memphis, TN 38152, USA E-mail:ganastss@memphis.edu

Sorin G.Gal*

Department of Mathematics, University of Oradea Str.Armatei Romane 53700 Oradea, Romania E-mail:galso@math.uoradea.ro

Abstract: In this paper we prove that any -periodic fuzzy continuous function form R to the fuzzy number space , can be uniformly approximated by some fuzzy trigonometric polynomials.

Keywords: Fuzzy number, fuzzy continuous function, fuzzy trigonometric polynomials.

A Note to the Entropy of Fuzzy T-dynamical Systems

Radko Mesiar* and Doretta Vivona**

*STU, Radlinske'ho 11,81368 Bratislava, Slovakia. and UTIA AVCR18208 Prague 8, Czech Republic E-mail:mesiar@vox.svf.stuba.sk

**Dipartimento MeMoMat, University di Roma "La Sapienza" Via A.Scarpa, 16, 00161 Roma, Italy E-mail:vivona@dmmm.uniromal.it

Abstract: Recently, Ban [2] introduced an entropy of fuzzy partitions and fuzzy dynamical systems based on some special t-norm T. Supposing the continuity of T, we give an essentially shorter proof of all his results based on the structure of involved fuzzy operations.

Keywords: Entropy, t-norm, fuzzy T-partition, fuzzy T-dynamical system.

Dissimilarity Between Fuzzy Sets: An Application to Transport Economics*

Henri Gwet

Departement of Computer Sciences Nationale Polytechnic Institute, P.O Box 8390 Yaounde.Cameroon E-mail:hgwet@polytech uninet.cm

Abstract: In this paper, we have introduced a new notion of logic equivalence based on a parametric family of fuzzy operators. This equivalence operator has helped us to define a new dissimilarity index for fuzzy sets. Our index is the fuzzy counterpart of a series of distances commonly uses in Data Analysis and in particular the cardinal distance of the symmetric difference. From what follows, we used this dissimilarity to define a new efficiency indicator for a transport system. This has been made possible with the use of fuzzy uncoupling and its interpretation in terms of fuzzy logic connectives. We used these new tools on the data from an investigation that we carried out concerning the transportation of food stuff in Cameroon.

Keywords: Indicators, transportation, fuzzy connectives, fuzzy coding.

Fuzzy Dot Ideals of BCK-algebras

Young Bae Jun

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

Abstract: The notion of fuzzy dot ideals in BCK-algebras is introduced, and its several properties are investigated.

Keywords: Ideal, fuzzy (dot) ideal, homomorphism, sup property.

The Application of Comprehensive Fuzzy Judgment in The Interpretation of Water-flooded Reservoirs

Shui-Li Chen

Department of mathematics, Teachers' College Jimei University, Xiamen, Fujian 36102, P R.China

Abstract: The comprehensive fuzzy judgement and mathematical statistical theory are used in this paper to establish a qualitative model for the interpretation of water-flooded reservoirs in the area for the purpose of studying H fault in some oil field, which is on the base of analysing in a general way on the data of well logging, geology and welltesting. Data from 8 wells analyzed and manipulated. The coincidence rate is 85%.

Keywords: Comprehensive, fuzzy judgement, water-flooded reservoir, interpretation model.

Fast Extracting Fuzzy Rules and System Simulation Based on Radial Basis Function Neural Networks

Xi Lin

Basic Course Department Jimei University, Xiamen 361021, P.R.China

Yee Leung

Centre for Environmental Studies The Chinese University of Hong Kong, Shatin, Hong Kong

Abstract: In this paper, a new method for extracting fuzzy rules from data is proposed based on a king of new radial basis function networks. Not only fast and effective the method is, but also the extracted rules are clear. The fuzzy neural networks constructed by this method may be used to approach nonlinear functions.

Keywords: Radial basis function, RBF network, extracting fuzzy rules, system simulation