The Journal of Fuzzy Mathematics
Volume 5 Number 1, March 1997
CONTENT
DETAILS
Pointwise Fuzzy Lattice
Zhi-jian Xu
Financial Department,Luo Jia Den 122
Wuhan,430035 P.R.China
Abstract: In this paper, We investigate the algebraic properties of a pointwise fuzzy lattice at the base of [1],[2]. First, we give the definitions of PO, P-PO, A-PO, M-PO, and some examples and properties of the Pos; then we define a pointwise fuzzy lattice and find out the sufficiency and necessary of a fuzzy set become a pointwise fuzzy lattice . Finally, we discuss the properties of complement and same value complenment.
Keywords: PO, P-PO, A-PO, B-PO, M-PO, complenment.
Fuzzy Transversal and Fuzzy Matroid
Mo Zhi Wen
Department of Mathematics, Sichuan Normal University
Chengdu, 610066 P.R. China
Wang Xian Qing
Department of Mathematics, Jin Zhou Teacher¡¯s College
Hubei 434104 P.R. China
Abstract: In this paper, first fuzzy transversal and partial transversal are defined, a sufficient and necessary condition on existence of fuzzy transversal is obtained, and the relation between partial fuzzy transversal and fuzzy matroid is set up .Second, some substructures of fuzzy matroid are induced ,we verify that they are really fuzzy matroid respectively, we discuss the properties of substructure, such as rank function, base, circuit, and -operator.
Keywords: Fuzzy matroid, matroid, fuzzy rank function, fuzzy basis, fuzzy circuit, transversal, fuzzy transversal.
On Fuzzy Finite State Machines
Pratyayananda Das
Department of Mathematics, Burdwan University
Burdwan,West Bengal, India
Abstract: Given a fuzzy finite state machine ( ), is extended to , a fuzzy subset of with the help of ¡®V¡¯ and product where is the set of all words of finite length with elements from . The validity of results, analogous to those obtained by Malik, Mordeson and Sen [2] are examined.
Keywords: Fuzzy algebra, fuzzy finite state machine, semigroup, admissible relation, fuzzy transformation semigroup.
LP-fuzzy Normal Subgrophs and Fuzzy Quotient Groups
Zhou Jun
Department of Basic Sciences, Liaoning Institute of Technology
Jinzhou, Liaoning 121001, P.R. China
Li Su-Yan
Department of Mathematics, Jilin Institute of Education
Changchun, Jilin 130022, P.R. China
Li Shu-You
Department of Basic Sciences, Liaoning Institute of Technology
Jinzhou, Liaoning 121001, P.R. China
Abstract: 1. In this paper, we give the definitions of the homomorphism of LP-fuzzy groups, the normal LP-fuzzy subgroup, LP-fuzzy quotient group, and so on, and their fundamental qualities are studied. 2. The two sufficient and necessary conditions of the normal LP-fuzzy subgroup are proposed. 3. We prove the basic homomorphic theorem of the LP-fuzzy group.
Keywords: LP-fuzzy group, homomorphism, isomorphism, normal LP-fuzzy group, LP-fuzzy quotient group.
On the Finite Union Preserving Property of the Derived Operator in L-fuzzy Topological Spaces
Zhou Wu-neng
Mathematics Department of Jinzhou Normal College,
Jinzhou Hubei, 434100, China
Abstract: In this paper, the open problem whether the derived operator preserves finite union in LFT -topological spaces is solved by a counter example we constructed. Furthermore, two sufficient conditions about finite union preserving are given and the results that the finite union preserving property of the derived operator is hereditary and preserves image under weakly homeomorphic mapping are obtained.
Keywords: LF-topological space, derived set, hereditary,weakly homeomorphic mapping.
Design and Application Fuzzy Contrller in Mulitivariable Coupled System
Moxi Zhu
Department of Mechanical and Electrical Engineering
Shandong Institute of Light Industry
Jinan, 250100, P.R. China
Abstract: This paper discusses the design of fuzzy controller in a multivariable coupled system and its application to control basis weight and moisture of paperboard.
Keywords: Fuzzy controller, control decision table, multivariable, coupled.
Design and Application of Fuzzy PID Controller
Moxi Zhu
Department of Mechanical and Electrical Engineering
Shandong Institute of Light Industry
Jinan, 250100, P.R. China
Abstract: In this paper a new kind of fuzzy PID controller based on digital PID controller and with variable PID parameters has been introduced by using fuzzy set theory. The emphasis is put on the introduction of the structure, principle and design method of this controller. The practical results indicate that compared with digital PID controller, fuzzy PID controller has better dynamic characteristics and wider adaptability.
Keywords: Fuzzy sets, parameters of PID controller, fuzzy PID controller.
Based on Grey-fuzzy Relational Grade Model and Its Application in High Voltage
Kun-Li Wen and John W.Wu
Department of Mechanical Engineering£¬National Central University
P.O. Box 9-20, Chung-Li, Taiwan
Abstract:
In this paper, we define a new concept, ¡°grey-fuzzy relational grade¡± which derived from the combination of the grey relational coefficient and the degree of fuzziness. An application in the prediction of the breakdown in gas is also given.
This paper can be divided into three parts. First, the concept of new fuzziness is developed, and a new approaching degree is also derived. Second, an example of prediction in probability of the breakdown in gas is simulated by C language and emulated by practical experiment.
Finally, we come to a conclusion that our method is a new method in the prediction of the breakdown in gas.
Keywords: Grey-fuzzy relation grade, grey relational coefficient, degree of fuzziness, breakdown in gas.
Coincidence Point Theorems for Fuzzy Mappings
J.S. Jung
Department of Mathematics£¬Dong-A University
Pusan 604-714, Korea
S.S. Chang
Department of Mathematics£¬Sichuan University
Chengdu, Sichuan 610064, P.R. China
B.S. Lee
Department of Mathematics£¬Kyungsung University
Pusan, 608-736, Korea
Y.J. Cho and S.M. Kang
Department of Mathematics£¬Gyeongsang National University
Chinju 660-701, Korea
Abstract: In this paper, we establish coincidence point theorems for fuzzy mappings in generating spaces of quasi-metric family. As consequences, we obtain coincidence points and fixed points for fuzzy mappings in fuzzy metric spaces and probabilistic metric spaces. Results on the existence of coincidence points and fixed points for set-valued mappings defined on the same spaces are presented.
Keywords: Coincidence points, generating spaces of quasi-metric family, fixed points, fuzzy mappings, fuzzy metric spaces, probabilistic metric spaces.
Fuzzy Programming Approch to Multi-objective Trans-shipment Problems
Rakesh Verma, M.P. Biswal, A. Biswas
Department of Mathematics
Indian Institute of Technology
Kharagpur-72302, India
Abstract: In this paper a solution procedure to a multi-objective trans-shipment problem is presented. The trans-shipment problem is converted to an equivalent transportation problem. Then the fuzzy programming approach is applied to solve the problem. A numerical example is included to illustrate the methodology. Finally the solution is compared with the solution obtained by weighting method by setting equal weights to the different objective.
Keywords: Multi-objective decision making, trans-shipment problem, fuzzy linear programming, membership function, weighting method.
Covering Dimension in Fuzzy Topological Spaces
Eduardo Cuchillo-Ibanez
U.D. Matematicas, E.T.S.I. Montes,
Universidad Politecnica, 28040 Madrid, Spain
Juan Tarres
Dep. Geometriay Topologia,
Facultad de CC. Matematicas, Universidad Complutense,
28040 Madrid, Spain
Abstract: We introduce and study a definition for the fuzzy covering dimension which is a ¡®good extension¡¯ of the topological covering dimension.
Keywords: Fuzzy topology, fuzzy subspace, fuzzy covering dimension.
Bases of Completely Distributive Lattices
Zhao dongsheng
Division of mathematics, School of Science
Nanyang Technological University, Singapore
Abstract: In this paper , we define and discuss bases of completely distributive lattices.
The main result is that the set of all coprime elements of L is the smallest basis of L closed under up directed joins.
Keywords: Completely distributive lattices, coprime elements, bases, set system.
Finite Valued Fuzzy Ideals in BCK-algebras
Y.B.Jun
Department of Mathematics Education
Gyeongsang National University, Chinju 660-701, Korea
E-mail: ybjun@nongae.gsnu.ac.kr
Abstract: In this short note, we find a characterization of finite valued fuzzy ideals. We also prove every fuzzy ideal of a Noetherian BCK-algebra is finite valued.
Keywords: Finite valued fuzzy ideals, Noetherian BCK-algebra.
Unfuzzy Non Dominated Solutions in the Linear Programming Problem with Fuzzy Coefficients in the Objective Functions
Stefan Chanas
Institute of Industrival Engineering and Management(1-23)
Technical University of Wroclaw.
Wzbryeze Wyspianskiego 27,
50-370 Wroclaw, Poland
Pawel Zielinski
Department of Mathematics
Higer Engineering School Opole, Poland
Abstract: In the paper the linear programming problem with fuzzy coefficients in the objective function is analyzed. It is assumed that the solution of the problem is the set of non dominated solutions, according to the concept of Orlovsky, with respect to a preference relation defined on the set of fuzzy numbers. The main result of the paper is a characterization, useful from the practical point of view, of the set of unfuzzy non dominated solutions with respect to six different fuzzy preference relations. In each case, it has been shown that the unfuzzy non dominated solutions coincide either with the feasible solutions of a linear inequalities system or with the optimal solutions of classical linear programming problem. They can thus be determined by means of classical linear programming methods.
Moreover, in the paper several properties of the considered relations are given. They are needed in the proofs of the main theorems of the paper, but are interesting per se and can be used also for other purposes.
Keywords: Linear programming, fuzzy programming, fuzzy preference relation, non dominated solution.
L-fuzzy Topological Vector Spaces
Fang Jin-xuan
Department of Mathematics, Nanjing Normal University
Nanjing, Jiangsu, 210097, China
Yan Cong-hua
Department of Mathematics, Huaiyin Teachers College
Huaiyin, Jiangsu, 223001, China
Abstract: In this paper, we introduce the concept of L-fuzzy topological vector spaces, and study some of their basic properties. Also, we give a characterization of such spaces in terms of the corresponding R-neighborhood bases of .
Keywords: Fuzzy lattice, L-fuzzy topological vector spaces, R-neighborhood base.
FRA-modules and FRA -modules Categories
Zhzo Jianli
Department of Mathematics, Liaocheng Teacher¡¯s college,
Shandong, 252000,China
Abstract: Based on [1], in this paper we discuss fuzzy modules over fuzzy rings (FRA -modules) further, obtain a characteristic description and a kind of representation of the fuzzy modules over fuzzy rings. The paper also introduces the concepts of categories of FRA -modules, discusses the concrete structures and some properties of product and coproduct of categories of FRA -modules.
Keywords: FRA-module, homomorphism of FRA-module, categoriy of FRA-modules, product of category, coproduct of category.
Fuzzy Net-theoretic Approach and Lowen¡¯s Category
Ratna Dev Sarma
Department of Mathematics, Rajdhani College
University of Delhi, India
Pradeep Kumar Jha
Department of Mathematics
University of Delhi, India
Abstract: The category of fuzzy topological spaces, introduced by Lowen, can also be obtained by adopting fuzzy net-theoretic approach. The fuzzy nets used for this purpose are -nets, a generalization of -nets introduced by Wang Guojun. Fuzzy closure operator and the convergence classes generating the fuzzy topological spaces of this category are also discussed.
Keywords: Fuzzy point, fuzzy net, -nets, -nbd.
Fuzzy Ideals,Fuzzy Local Functions and *-fuzzy Topology
R.A. Mahmoud
Department of Mathematics, Faculty of Science,
Menoufia University, Egypt
Abstract: Fuzziness is one of the important and useful concepts in the modern scientific studies. This is because the fact that since 1965, when Zadeh had first presented the notion of fuzzy sets in his classical paper, immediate applications of this idea are investigated by a great staff of authors. Throughout the development of several theories based on fuzzy sets, many interesting phenomena have been observed. Therefore, this paper is devoted to define the class of fuzzy ideals which is considered as a generalization of ideal studies which known early, specially in topological studies also it helps to present the concept of fuzzy local function of any A X, where (X, ) is a fuzzy topological spaces due to Chang. Depending on these previous new concepts, the class *-fuzzy topology has been constracted as a generalization of the fuzzy topology. Moreover, several properties of all investigated new notions are discussed.
Keywords and phrases: Fuzzy set, fuzzy topological spaces, fuzzy point, fuzzy neighborhood, fuzzy ideal, fuzzy filter, fuzzy local function, fuzzy closure operator, *-fuzzy topology and -fuzzy closed set.
Successor and Source Functions
Nobuaki Kuroki
Department of Mathematics
Joetsu University of Education
Joetsu-shi, Niigate-ken, Japan 943
John N.Mordeson
Department of Mathematics/Computer Science
Creighton University
Omaha,Nebraska 68178
U.S.A.
Abstract: Similarities between finite state machines and directed graphs can be seen from the natural way a directed graph can be associated with a finite machine to describe the state transition of the finite state machine. Likewise, there are similarities between fuzzy finite state machines and fuzzy directed graphs. All four of these concepts and others this similarity, namely that of the notion of successor and source. This paper continues an axiomatic treatment of the notion of successor and source previously started. In particular, the connection between successor and source is examined to determine structure properties of the spaces which come under this approach.
Keywords: Finite state machines, directed graphs, fuzzy finite state machines, fuzzy directed graphs, successor, source, retrievable, strongly connected, separated subspace, and primary subspace.
Structure of Rough Sets and Rough Groups
Nobuaki Kuroki
Department of Mathematics, Joetsu University of Education
Joetsu-shi, Niigate-ken, 943 Japan
John N.Mordeson
Department of Mathematics/Computer Science, Creighton University
Omaha,Nebraska 6817, U.S.A.
Abstract: We examine the notion of the upper approximation of a set in an axiomatic manner. This allows us to bring to bear on rough sets both crisp and fuzzy techniques, results, and points of view from abstract algebra, automata theory, and graph theory. In particular, we show that we can treat the upper approximation E of a set V in such a way that it defines a ¡°space¡±. Hence we show that has a basis and that the cardinality of a basis is unique. The axiomatic approach also allows us to show that each satisfies certain retrievability and connectedness properties similar to those defined in automata theory, graph theory, and information retrieval systems.
Keywords: Rough set, rough groups, finite state machines, directed graphs, fuzzy finite state machines, fuzzy directed graphs, successor, source, retrievable, strongly connected, connected, separated subspace, and primary subspace.
On L-fuzzy N-Accumulation Point
Zhou Wu-neng
Mathematics Department of Jinzhou Normal College,
Jinzhou Hubei, China , 434104,
Chen Shui-Li
Mathematics Department of Jianghan Petroleum Institute,
Jinzhou Hubei, China , 434102,
Abstract: In this paper ,the concept of L-fuzzy N-accumulation point is introduced in L-fuzzy topological spaces, which is a proper generalization of the concept of L-fuzzy accumulation point. Moreover, we investigate systematically its properties.
Keywords: L-fuzzy topology, nearly N-compact closed set, N-accumulation point, L-fuzzy net, L-fuzzy ideals.
Properties of Lattice-limit of a Sequence on X-lattice
Guangquan Zhang
Department of Mathematics, Hebei University
Baoding, Hebei 071002, P.R. China
Yanchuan Zhang Jie Lu
Department of Mathematics & Computing
University of Southern Queensland
Toowoomba, Queensland 4350, Australia
Abstract: The concepts of lattice-valued distance and lattice-limit of elements of a lattice and X-lattice are introduced by Liu and Zhang [1], but the properties of above mentioned concepts are not discussed. In this paper, some elementary properties and some similar to those of limit of a sequence of real-numbers are obtained.
Keywords: Fuzzy number, fuzzy limit, fuzzy analysis, convergence, lattice.
Complete Extension of Non-additive Lattice Valued Measure on the Lattice
Guangquan Zhang
Department of Mathematics, Hebei University
Baoding, Hebei 071002, P.R. China
Jie Lu and Yanchuan Zhang
Department of Mathematics & Computing
University of Southern Queensland
Toowoomba, Queensland 4350, Australia
Abstract: In this paper, we give a complete extension of non-additive lattice-valued measure, and prove the above-mentioned complete extension with inheritance.
Keywords: Fuzzy measure, non-additive measure, lattice, complete extension.
Logic Foundations of Fuzzy Modus Ponens and Fuzzy Modus Tollens
Guo-Jun Wang
Institute of Mathematics, Shaanxi Normal University
Xian 710062, P.R. China
Abstract: The aim of this paper is try to establish logic foundations for fuzzy modus ponens and fuzzy modus tollens.
Keywords: Q-system, fuzzy modus ponens, fuzzy modus tollens, ¦Á-tautology, sustentation degree, similarity degree. |