The Journal of Fuzzy Mathematics
Volume 2, Number 1, March 1994
CONTENT
DETAILS
Evaluation Functions on Fuzzy Convexity Paces and Completely FS3 Spaces
M. V. Rosa
Department of Mathematics Mata College
Thrikkakara Cochin 682021,India
Abstract: In this paper we introduce the concept of evalutionfuntions in a given fuzzy convexity space and study certain concepts related to this.We also introduce completely FS3 Spaces as a continuation of the study of separation axioms in fuzzy convexity spaces in [3] and study subspace and product in this context.
Keywords: Fuzzy convexity, fuzzy convexity spaces, fuzzysubspace, fuzzy topology fuzzy convexity spaces.
Fuzzy Ordering and Completeness of Fuzzy Metric Spaces
Ismat Beg
Department of Mathematics ,
Lahore University of Management Science,547292-Lahore,Pakistan
E-mail:ibeg@lums.Edu.PK.
Abstract: We proved a fuzzy variational principle and as application obtained a charaterzation of complete fuzzy metric spaces in terms of existence of fixed points in fuzzy metric spaces.
Keywords:
fuzzy order,fuzzy metric space,completeness,fixed point, fuzzy variational principle.
Variation of Interval-Valued and Fuzzy Functional
Cao Bing Yuan
Department and Institute of Mathematics
Shantou University ,Guangdong,ZIP 515063, China
E-mail:bycao@Stu.edu.cn
Abstract: Having put forward the conception of variation for the first time,the author discusses some properties and extremely valued condition for interval-valued and fuzzy functional, which lays a foundation in the application of physics and approximate calculation for interval-valued and fuzzy calculus variation.
Keywords: Interval-valued and fuzzy functional,variation, operation property,extreme value.
Common Fixed Points for Noncompatible Mapping in Fuzzy Metric Spaces#
S. Muralisankar and P. Balasubramainam
Department of MathematicsGandhigram Rural Institute-Deemed University
Gandhigram-624302, Tamil Nadu,India
Jong Yeoul Park
Department of Mathematics Pusan National University
Pusan,609-735,Korea
E-mail:jyepark@hyowon.pusam.ac.kr
Abstract: In this present paper, we prove a common fixed point theorem for a pair of noncompatible fuzzy mapping in fuzzy metric space without assuming completeness of the space or continuity of the mappings involved. We also study this problem for a pair of mappings and establish a situation in which the common fixed point is a point of discontinuity.
keywords: Fuzzy set, fuzzy metric space, noncompatible maps, common fixed points.
Fuzzy Games
AL. Narayanan and AR. Meenakshi
Department of Mathematics, Annamalai University
Annamalai Nagar-608002,TamilNadu,India
A.M. S.Ramasamy
Department of Mathematics, Pondicherry University
Pondicherry-605014,India
Abstract: The existing theory of crisp game theory has certain serious limitations. The purpose of this paper is to obviate such difficulties. It is shown in this paper how a crisp game can be fuzzifed.The following schemes are providein this paper for agame,possibility approach for a crisp game and possibility
approach for a fuzzy interval game.
Keywords:
crisp game, interval valued pay-off matrix, fuzzy interval game.
Static Fuzzy Topological Spaces
Sunil C. Mathew
Department of Mathematics, St.Thomas College Pala
Kottayam(Dt.), Kerala,India-686574
T. P. Johnson
Cochin University College of Engineering Kuttanadu,Pulincunnu P.O.
Alleppey(Dt.),Kerala,India-688504
Abstract: In this paper, we introduce the concept of static fuzzy topological space and study some of its properties. Certain aspects of static fuzzy topological space in relation with subspaces, sums, products, quotients and the concept of strong fuzzy points are also investigated. Consequently we introduce the notion of D-fuzzy topological space and establish its interrelations with static fuzzy topological space.
Keywords:Static fts, gem, power, D-fts, strong fuzzy point, nearly crisp.
Generalized Intuitionistic Fuzzy Sets
Tapas Kumar Mondal and S.K. Samamta
Department of Mathematics£¬Visva-Bharati
Santiniketan-731235,W.Bengal.India
E-mail:syamal@vbharat.ernet.in
Abstract:
In this paper, we introduce definitions of generalized intutionistic fuzzy sets,generalized intutionistic fuzzy relation,generalized intutionistic fuzzy topology and study some of their properties.
Keywords:
Fuzzy subset, intutionistic fuzzy set,generalized intutionistic fuzzy set,fuzzy relation,intutionistic fuzzy family,generalizedintutionistic fuzzy topology.
Fuzzy Finite Switchboard State Machines
Yasuhiro Sato
Joint Graduate School(Ph. D. Progra) in the Sciences of School Education
Hyogo University of Teacher Education
(Joetsu University of Education Joetsu-shi,Niigata-ken,943-8512,Japan)
Nobuaki Kuroki
Department of Mathematics Joetsu University of Education
Joetsu-shi,Niigata-ken,943-8512,Japan
Abstract: we introduce the concept of fuzzy finite switchboard state machines and fuzzy switchboard transformation semigroups. The idea of switching homomorphism is introduced, and some properties which are analogous to those obtained by Malik, Mordeson and Sen [4] are examined.
Keywords: Fuzzy finite state machine, fuzzy finite switchboard state machine, fuzzytransformation semigroup,
switching homomorphism.
Fuzzy Vector Analysis
F. Khosropour
Department of Mathematics,University of Alabama at Birmingham
Birmingham, Alabama,35294
E. Eslami
Department of Mathematics,ShahidBahonar University of Kerman
Kerman.Iran
J. J. Buckley
Payam-e-Noor University,Kerman.Iran
Abstract: We introduce a comperehensive study of fuzzy vector analysis in this paper by first defining a fuzzy vector and a fuzzy vector space.
Keywords:
Fuzzy vector, fuzzy vector space.
Fuzzy Ideal Generated by a Fuzzy Subset in Semigroups
Bingxue Yao, Yong Li and Kaiquan Shi
School of Mathematics and System Science, Shandong University
Jinan 25100, P. R. China
Abstract:
Based on the concepts of various generated fuzzy ideals given by N. Kuroki and Mo and Wang, the concepts of a fuzzy subsemigroup and a fuzzy left ideal (fuzzy right ideal, fuzzy ideal, fuzzy bi-ideal)
generated by a fuzzy subset in semigroup are characterized by means of supremum and infimum. Some properties of various generated fuzzy ideals are discussed.
Keywords: Fuzzy subsemigroup, fuzzy left ideal, .fuzzy right ideal, fuzzy ideal, fuzzy bi-ideal
On Fuzzy Implicative Filters of Lattice Implication Algebras
Young Bae Jun
Department of Mathematics Education, Gyeongang National University
Chiju 660-701, Korea
E-mail:ybjun@nongae.gsnu.ac.kr
SeokZun Song
Department of Mathematics , Cheju National University
Cheju 690-756, Korea
E-mail:szsong@cheju.ac.kr
Abstract:
In connection with fuzzy (implicative) filters in lattice implication algebras, further basic properties are investigated. Characterizations of fuzzy (implicative) filters are given. Extension property for fuzzy implicative filters is established.
Keywords: (Implicative) filter, fuzzy (implicative) filter.
Mixed Quasi variational Inequalities with Fuzzy Mappings
Jong Yeoul Park
Department of Mathematics , Pusan National University
Pusan 669-735, South Korea
Jae UgJeong
Department of Mathematics , Dong Eui University
Pusan 614-714, South Korea
Abstract: In this paper, we introduce and study a new class of variational inequalities, which is called the mixed quasi variational inequalities with fuzzy mappings. The resolvent operator technique is used to establish the equivalence among mixed quasi variational inequalities, fixed point problems and the set-valued implicit resolvent equations with fuzzy mappings. This equivalence is used to study the existence of a solutions of mixed quasi variational inequalities with fuzzy mappings and to suggest a number of iterative algorithms for solving mixed quasi variational inequalities with fuzzy mappings. The results proved in this paper represent a significant refinement and improvement of the previously known results in this area.
Keywords: Quasi variational inequalities, fuzzy mappings.
On Intuitionistic Fuzzy Topological Lattice Implication Algebras
Young Bae Jun
Department of Mathematics Education, Gyeongang National University
Chiju 660-701, Korea
SeokZun Song
Department of Mathematics , Cheju National University
Cheju 690-756, Korea
Abstract: We generalize the concept of fuzzy topological lattice implication algebras, initiated by the first author et al. [4], to the case of intuitionistic fuzzy sets which aer generalization of fuzzy sets.
Keywords:
Intuitionistic fuzzy topological lattice implication algebra.
A New Lattice-valued Propositional Logic System Lvp*
Jun Ma, Keyun Qin and Yang Xu
Department of AppliedMathematic,SouthwestJiaotong University,
Chengdu, 610031,Sichuan, P.R.China
E-mail:mj99032@263.net
Abstract: Nowadays, non-classical logic plays an important role in the study of artificial intelligence and uncertainty reasoning. In order to establish a logical system eith truth value in a relatively general lattice, we present a lattice-valued propositional logical system Lvp system with truth value in lattice implication algebra. Modus Ponensis selected as the unique reasoning rule and seven axioms are given as the starting point of our discussion. The syntax and semantics of this logic systm is presented. The definitions of semanic consequence, semantic consistency and syntactical consistency are introduced and the weak deduction theorem, the soundness thorem are proved. At the end of this paper we discuss the relation between Lvpand the classical logical system.
On Semantics of L-valued Modal Propositional Logic LMP(X)
WenJiang Li and Yang Xu
Department of AppliedMathematic,SouthwestJiaotong University,
Chengdu, 610031,Sichuan, P.R.China
E-mail:wjl_73@263.net
Abstract: In this paper,modal words ¡°necessary¡±and¡°possible¡± are introduced into lattice-valued propositional logical system, then the semantics problems of lattice-valued propositional logic include-satisfi
-ability,-satisfiability,-imply and -imply are discussed. Besides some results different from lattice-valued propositional logic are given.
Keywords: Lattice-valued modal propositional logic, -satisfiability,-imply.
Fuzzy Reasoning Based on the L-valued Logic Lvpl
Ping Zhou, Keyun Qin and Yang Xu\
Dept. of Applied Math.Southwest Jiaotong University,
610031,Sichuan, P.R.China
Eun Hwan
Dep.t of Math.Education , Cheju National University of Education
Cheju 660-756, Korea
Abstract: In thispaper, fuzzy reasoning based on the L-vaued logic Lvptare discussed. The fuzzy reasoning of modus ponens, modus tollens and hypothetical syllogism are proved.
Keywords: L-vaued logic Lvpt, modus ponens, modus tollens, fuzzy hypothetical syllogism.
The Simplification of Addition and Subtraction Operations of Fuzzy Numbers*
XingFang Zhang* and Guang Wu Meng
Department of Mathematics and System Science,Liaocheng University,
Shangdong 252059, P. R. China
Abstract: In this paper, the new concept of generalized fuzzy numbers is put by removing the ¡°normality¡± on the definition of fuzzy numbers. It is introduced that the notions of isosceles triangle fuzzy number, triangle fuzzy number and partial fuzzy numbers,and a series results are proved so that the computation is simplified for addition and subtraction on fuzzy numbers.
Keywords:
fuzzy number, addition and subtraction operation on fuzzy numbers.
On Fuzzy Filters of MTL-algbras
Kyung Ho Kim
Department of Mathematics, Chungju National University
Chunju 380-702,Korea
E-mail:ghkim@gukwon.chungju.ac.kr
Qun Zhang
Department of Mathematics, South-Central University for Ethnic Communities,
Wuhan 430074, China
E-mail:qzhang@scuec.edu.cn
Young Bae Jun
Department of Mathematics Education, Gyeongang National University
Chiju (Jinju) 660-701, Korea
E-mail:ybjun@nongae.gsnu.ac.kr
Abstract:
Fuzzification of a filter in a MTL-algebra is considered,and some related properties are investigated.
Keywords:
MTL-algebra, (fuzzy) filter, level filter.
On Uniqueness and Completeness Theorems for the Root Functions Expansion of the Nonlocal Sturm-Liouville Integro-Differential Operator
E.M.El-Abd, M. A. El-Attar and Sh. El-Bendary
Department of Mathematics, Faculty of Science,
Tanta University, Egypt
Abstract: In this paper we investigate the spectrum and root functions expansion of integrodifferential operator and to find a necessary and sufficient condition for recovering functions in L1[0,a] by means of its coefficients in this root function expansion,We give sufficient conditions imposed on the functional
Such that the root functions to be complete in LP[0,a], , As well as the expansion to be summable by Riesz means in L1[0,a]. If we give also sufficient conditions for uniform convergence of the root function expansion.
Keywords: Nonlocal sturm-liouvilleoperater-root functions expansion.\
The Upper Approximation with Respsct to the Least Group Congruence on anInverse Semigroup
Nobuaki Kuroki
Department of Mathematics, Joetsu University of Education
Joestu-shi,Niigate-ken, Japan 943
John N.Mordeson* and Shih Chuan Cheng
Department of Mathematics and Computer Science, Creighton University,
Omaha,Nebraska 68178,U. S. A
Abstract: In this paper, we give some properties of the upper approximation of the semilattice of idempotens E of an inverse semigroup S with respect to the least group congruence on S. We introduce the concept of the upper normal inverse subsemigroup and we give some properties of such a subsemigroup.
Keywords:
Upper approximation, inverse semigroup, group congruence, upper normal inverse subsemigroup.
Fuzzy Integra Equations
James J. Buckly*
University of Alabama at Birmingham,Department of Mathematices,
Birmingham, Alabama,35294,USA
buckley@math.uab.edu
Thomas Feuring
University of Siegen,Department of Electrical Engineering and Computer Science,
Holderlinstr.357068 Siegen,Germany
feuring@informatik.uni-siegen.de
Abstract: We present two new solution methods for fuzzy integral equations.Both solution methods are applied to two procedure for solving the crisp problem: (1) the resolvent kernel method,and (2) special solution methods for symmetric kernels. Numerous examples are given.
Generating Sets for T-fuzzy Subspaces
John N. Mordeson
Department of Mathematics, Creighton University,
Omaha,Nebraska 68178,U. S. A
E-mail:mordes@creighton.edu
Abstract: It is known that a fuzzy subspace of a finitely generated vector space need not be finitely generated if the fuzzy subspace is defined in terms of t-norm other than min. In this paper, we develop a theory concerning the generating of such a fuzzy subspace of a certain type, We find a minimal generating set of such a fuzzy subspace and show that this generating set uniquely determines it.
Keywords:
Fuzzy subspace, minimal generating set, vector space, Abelian group, field extension. |