The Journal of Fuzzy Mathematics
Volume 7£¬Number 4, December 1999
CONTENT
DETAILS
Fuzzy Uniform Space-Covering Approach
G.K.Chandrika
Department of Mathematics
Avinashilingam Deemed University, Coimbatore-641043, India
K.N. Meenakshi
Department of Mathematics
Avinashilingam Deemed University, Coimbatore-641043, India
Abstract: In the classical theory of uniform spaces there are three important different approaches to the definition of uniform spaces. The first approach is in terms of entourages, the second in terms of collection of pseudo-metrics and the third in terms of coverings. The entourage approach and the pseudo-metric approach have been generalized to fuzzy situation by Lowen [6] and Hohle [1] respectively. The study presented in this paper is a generalization of the covering approach by Isbell, in his classic work ¡°Uniform spaces¡±[3]
. Keywords: F-star function, F-star refinement, fuzzy uniform structure.
Scott Topology and Fuzzy Sets
D.N.Georgiou
University of Thessaly, Faculty of Technological Sciences
Department of Planning and Regional Development,
Department of Civil Engineering, 383 34 Volos, Greece.
B.K. Papadopoulos
Democriyus University of Thrace,
Department of Mathematics, 67100 Xanthi, Greece.
Abstract: The importance of the Scott topology in a complete lattice is well known(see [G-¡]). Motivated by this fact we introduce the Scott topology in the set of fuzzy open sets of a fuzzy topological spaces and we also study some useful generalizations of this topology. Finally we introduce and study the fuzzy Scott topology on a fuzzy topological space.
Keywords: Fuzzy sets, Scott and strong Scott topology.
Algebraic Properties of Fuzzy Subsetsof A Fuzzy Partial Algebra Nistala V. E. S. Murthy
MIG-B-171, Sagarnagar Visakhapatnam-530043
A.P.State, India
Abstract: The aim of this paper is to show that for any fuzzy -partial algebra, the fuzzy subsets of the underlying fuzzy set of the fuzzy -partial algebra and power set on the fuzzy-point-set of the underlying fuzzy set can be naturally algebraised in such a way that they partially ordered -sub algebra of the s-closed subsets of the fuzzy-point-set.
Keywords: Partial algebra, fuzzy subset.
On The Solution of Fuzzy Multiobjective Integer Nonlinear Programming Problems With A Parametric Study
Omar M. Saad
Department of Mathematics, Faculty of Science,
Helwan University, Cairo, Egypt
Abstract: In this paper, we focus on multiobjective integer nonlinear programming problems having fuzzy parameters in the constraints. The set of -Pareto optimal solutions is determined for the problem under consideration together with the corresponding stability set of the first kind (SSkl). In addition, an algorithm is described to solve the formulated model. This algorithm is based on the -constraint method together with the branch-and-bound technilque. The approach presented in this paper is demonstrated with a numerical simple example.
Keywords: Fuzzy multiobjective nonlinear problems, Mixed-integer problems, Fuzzy parameters, Fuzzy numbers, -Constraint method, Branch and. ¨CBound method, Stability.
The Products in Category of Fuzyy R-Modules
Zhao Jianli and Wangwensheng
Department of Mathematics, Liaocheng Teachers College
Shandong 252059, P. R. China
Abstract: In this paper, we introduces the concepts of product in category of fuzzy modules, and discuss the structures and some properties of product in category of fuzzy modules.
Keywords: L-fuzzy module, F-homomorphism, category of L-fuzzy modules, product.
Extended Quasi-linear Weighted Means
T.Calvo, G.Mayor and M.Carbonell
Department of Mathematics and Computer Science, University of The Balearic Islands
Ctra.de Valldemossa, Km 7.5 07071 Palma de Mallorca, Spain
Abstract: In this work, the concept of an Extended Quasi-Iinear Weighted Mean (EQLWM) is introduced. Furthermore, Extended Quasi-linear Weighted Mean that are Extended Aggregation Functions (EAF) are characterized by means of left descending probabilistic triangles. Moraever, we study the self identity property for these means, so a new characterization is shown by left balancing probabilistic triangles which are generated by the sequence , . After that, conditions to obtain an EQLWM as well as its reverse function which are EAF and satisfy the self identity property are given. Finally, in the last section two inequalities close to the self identity related with EQLWM are analyzed. In this case, two characterizations are obtained when the generator of EQLWM is an increasinging function.
Keywords: Extended aggregation function, extended quasi-iinear weighted mean, N-dual function, reverse function, self identity, descending and balancing probabilistic triangle, super-self identity, sub-self identity.
Fuzzy Constrained Matrix Games with Fuzzy Payoffs
Li Dengfeng
Department of Basics, Dalian Naval Academy
Dalian 11 6018,P.R.China
Abstract: Game problems in fuzzy enviroment have been investigated. Models of the fuzzy contrained matrix game with a payoff matrix of fuzzy numbers are established and a corresponding effective solution method based on the fuzzy linear programming is proposed. Comparison and analysis are illustrated with the help of a numerical example.
Keywords: Game theory,fuzzy systems,fuzzy number,fuzzy mathematical programming.
Characterization of Cardinal Power Fuzzy Lattice
Jia Wu, Li Wenlong
Department Of Mathematics, Wuhan Economics College
Luo Jia Dun 122©|, Wuhan, 430035, P.R.China
Zhu Degao
Dept.of Math. Huazhong Normal University
Wuhan, 430072.P.Rchina
Liu Weiping
Dept.of Math.Tongji Medical University
Wuhan, 430072.P.Rchina
Abstract: In this paper, we make researches on fuzzy lattices in two ways. Firstly, we get that is a fuzzy lattice iff X is a fuzzy poset by discussing the relation the relation between the finite poset X and cardinal power . Secondly, we present the important characterization theorem of the general fuzzy lattice by the E-nonempiness property of .
Keywords: Fuzzy poset, minimal element, E-nonempiness, infinite intersection property.
On -Continuous, -Open and -Closed Order Homomorphisms
Cheng Ji-Shu
Qinghai Junior Teacher¡¯S College
Xining 810007, Qinghai, P.R. China
Abstract:In this paper, the properties of -closure and -interior of an L-fuzzy set are obtained. The concepts of -open, -closed and -continuous order homomorphisms are introduced and studied. We give the characterizations of these order homomorphisms by using the notions of -closure and L-nets in L ¨Cfuzzy topological spaces.
Keywords:
Fuzzy topology, -closure, -interior, -continuity, order homomorphism.
Grey Model Selections Based on Fuzzy Trend Prediction
Yen-Tseng Hsu, Chan-Ben Lin and Hau-Chian Cheng
Department of Electrical Engineering.
National Taiwan University Of Science And Technology
Taipei, Taiwan
Abstract: This paper utilizes the fuzzy inference to predict future trend, which extends from fuzzy prediction. Because the original data of different systems vary significantly, we have to take the appropriate prediction models for a long ¨Cterm forecasting. According to the characteristics of the original data , we have separated it into two kinds of typical sequence in this paper, such as monotone sequence and central symmetry sequence. On the basis of the grey system theory, this paper uses the results of fuzzy trend prediction to decide the appropriate grey model which has the less prediction error. The proposed method has been applied to model a non-linear system, Mackey-Glass chaotic time series, and compared with GM(1,1), grey Verhulst model and Wang-mendel approach. The simulation results show that this novel method is more accurate than the other approach.
Keywords: Fuzzy prediction,Grey system GM(1,1).
A Fuzzy Multiobjective ProgrammingApproach to Solve Fuzzy Matrix Games
Li Dengfeng
Department of Basics, Dalian Naval Academy
Dalian 11 6018,P.R.China
Abstract: The value of the fuzzy matrix game with fuzzy numbers(FMG) has been considered as a fuzzy number in this paper. Fuzzy multiobjective linear programming models for each player are established and corrresponding effective solution methods are proposed. Effectiveness is illustrated with the help of a numerical example.
Keywords: Fuzzy matrix game, fuzzy numbers, fuzzy multiobjective programming.
Forecasting Model of Neural Network with Fuzzy Pattern Recognitionand Evolutionary Simplex Method
Chen Shouyu and Nie Xiangtian
School of Civil Engineering and Architecture.
Dalian University of Technology. Dalian 116024,P.R.China
Abstract: A forecast model of fuzzy recognition with neural network is developed in this paper. This makes a break through to the topologic structure of neural network. The Fuzzy Recognition Model developed by Chen Shouyu is used as the stimulation function. An Evolutionary Simplex Method is proposed for model learning. An example is given at last.
Keywords: Fuzzy recognition model, neural network, stimulation function, evolutionary simplex method.
The Pointwise Compactness on TML
Liu Xiaoshi
Department of Mathematics
Sichuan University, Sichuan, P. R. China
Abstract: It is known that topological molecular lattice(TWL) is a generalization of L-fuzzy topological space . In the various investigation on the properties of TWL, since TWL does not possess the structure of stratification, the investigation on the covering property of TWL, such as compactness, has not been well developed. In this paper, we take a idea of pointwise compactness on TWI, it is not only a extension of crisp compactness, but also is a good extension or fuzzy N- compactness to some extent.
Keywords: pointwise compactness, subbase theory, cartesian product.
-Closedness and -Compactness on Fuzzy Topological Spaces
A.M. Zahran
Department of Mathematics, Faculty Of Science,
All Azhar University, Assiut 7151 1.Egypt
Abstract: The concepts of fuzzy -closedness and fuzzy compactness for fuzzy topological spaces were introduced by A.A. Allam and A.M. Zahran[2,3]. Y.B. Park, etal [9], introduced the concept of RS-compact on fuzzy topological spaces. In this paper we characterize these spaces in terms of the concepts of fuzzy -filterbasis and fuzzy semi-preopen sets. Some properties of these spaces are established using the concepts of fuzzy semi -cluster point, fuzzy semi -cluster point, fuzzy emi-pre -cluster point and fuzzy regular semi -cluster point. Finally, we show that some results in [9] are special cases from some results in this paper and our paper [3].
Keywords: Fuzzy semi-preopen set, fuzzy semipen set, fuzzy regular semipen set, fuzzy -closed space, fuzzy compact space, fuzzy -filterbasis.
The Join in The Lattice of Fuzzy (Left, Right) Ideals of A Ring*
Qingde Zhang
Department of Computer, Liaocheng Teachers College
Shandong 252059, P.R. China
Shuili Chen
Department of Mathematics, Jianghan Petroleum Institute
Jiangling, Hubei 434102, P.R. China
Guangwu Meng
Shuili Chen
Department of Mathematics, Liaocheng Teachers College
Shandong 252059, P.R. China
Abstract: In this paper, we use the technique of strong cut to investigate the lattice of fuzzy (left, right) ideals with the same tip ¡°t¡±;(2) the lattice of all fuzzy ideals of a ring is not distributive, thus the main theorem ( is distributive) in [1] is erroneous;(3) The Lattice of all fuzzy (left, right) ideals with same tip ¡°t¡± of a ring R is modular, this generalizes the main theorem in [2].
Keywords: Lattice; fuzzy subring, uzzy (left, right) ideal, strong cut, distributive, modularity
Fuzzy Valued Functions Approximated Arbitrarily Close by A Class or Regular
Fuzzy Neural Networks
Liu Puyin
Department of System Engineering And Mathematics
National University Of Defense Technology
Changsha, Hunan 410073, China
Abstract: In the paper, we introduce the pagoda-shaped fuzzy valued ftinctions, whose some properties are obtained. A few of equivalent conditions which the continuous fuzzy neural networks with sigmoid units on the hidden layer are showed. Our proofs are constructive. The conclusions obtained here generalize the results in [2].
Keywords: Pagoda-Shaped fuzzy valued ftinctions, subtractive fuzzy valued ftinctions, regular fuzzy neural networks.
Sharpening Operators and Extended Fuzzy Relations
Leon Gonzalez* and Angel Marin
Department of Automatics and Computation. Public University of Navarra.
Compus Arrosadia. 31006 Pamplona Spain.
e-mail£ºamarinldsz¡±.upna.es
Abstract: Here it is dealt with contrast intensification hedging processes, and it is analyzed their effects on structral properties of second order fuzzy relations, which are otained from elementary ones by aggregated extension. Among these properties there are the ones involved in structures of order and classification.
Keywords: Fuzzy relations, hedges, entropy.
A Kind of Paracompactness Defined on Topological Molecular Lattices
Liu Xiaoshi
Department of Mathematics, Sichuan University,
Chengdu 610064,Sichuan, P. R. China
Abstract: Topological molecular lattice (TML) is a kind on generalized topological space, which plays an important role in topology on lattice. Since TML does not possess the structure of stratification, the investigation on the covering properties of TML, such as compactness, paracompactness, etc, has not been well developed in the investigation on the properties of TML. In this paper, based on pointwise . compactness [3] on TML, a kind takes pointwise compactness on TML as a special case. Some representations of this kind of paracompactness on TML and the relations between it and some separations such as regularity, normality are discussed here.
Keywords: Pointwise paracompactness, -locally finite, inverse element.
SU-Separation Axioms in Topological Molecular Lattices*
Shui-Li Chen
Department ofmathematics, Jianghan Petroleum Institute
Jingzhou, Hubei 434102, P.R. China
Wu-Neng Zhou
Department ofmathematics, Jingzhou Normal College
Jingzhou, Hubei 434104, P.R. China
Abstract: In this paper, we introduce the concepts of SU-regular and SU-normal separation axioms in topological molecular lattices, systematically discuss their properties and mutual relationships between them and £¬SU-regular and SU-normal separation axioms, and prove that the , SU-regular and SU-normal separation properties are semi-topological invariant.
Keywords: Topological molecular lattice; separation axiom; generalized order-homomorphism; -convergence; homomorphism
Fuzzy LI-Ideals in Lattices Implication Algebras
Young.Bae Jun
Department of Mathematics Education
Gyeongsang Nationaluniversity, Cianju660-701,Korea
e-mail: vb un (Onongae.gsnu.ac.kr
Yang Xu
Department of Applied Mathematics,Southwest Jiaotong University
Chengdu, Sichuan 610031, P.R. China
e-mail: yxu(Dcenter2.swjtu.edu.cn
Abstract: In this paper we consider the fuzzification of LI-ideals in lattice implication algebras, called a fuzzy LI-ideals. We also mention the fuzzification of lattice ideals in lattice, called a fuzzy lattice ideal, and discuss relationships between fuzzy LI-ideals and fuzzy lattice ideals.
Keywords: Lattice(H) implication algebras, (fuzzy) LI-ideal, (fuzzy) lattice ideal.
Fuzzy Homological Theory in (¢ó)*
Zhao Jianli and Wang Baoming
Department of Mathematics, Liaocheng Teachers College
Shandong 252059, P.R. China
Abstract: In this paper, we introduce the concepts of F-flat module- and morita equivalence of fuzzy subring. In this process we study the important properties of F-tensor products , F-flat modules- and morita of fuzzy subring.
Keywords: - module, module- , F-homomorphism, F-tensor product, F-flat module- , - module category, fuzzy able groups category, morita equivalence of fuzzy subring.
Quotient Lattice Implication Algebras Induces by Fuzzy LI-ideals*
Young Bae Jun
Department of Mathematics Education
Gyeongsang Nationaluniversity, Cianju660-701,Korea
e-mail: ybjun@nongae.gsnu.ac.kr
Yang Xu and Jun Liu
Department of Applied Mathematics
Southwest Jiaotong University , Chengdu, Sichuan 610031, China
e-mail: yxu(Dcenter2.swjtu.edu.cn
Abstract: We define quotient lattice implication algebras induced by fuzzy LI-ideals and study the relation bteween quotient structures and fuzzy LI-ideals.
Keywords: Lattice(H) implication algebras, (fuzzy) LI-ideal, implication homomorphism, quotient lattice implication algebra.
Compactness: Probabilistic Convergence Versus Fuzzy Convergence
J. Minkler, G. Minkler and G. Richardson
Department of Mathematics, University Of Central Florida,
Orlando, Fl 32816-1364, Usa
e-mail: garyr@pegasus.cc.ucf edu
Abstract: The category of probabilistic convergence spaces can be viewed as generating a nice sub category of fuzzy convergence spaces. This relationship is exploited to give com-pactness results for fuzzy convergence spaces.
Keywords: probabilistic convergence, fuzzy topology, fuzzy convergence, fuzzy compactness, fuzzy compactifications.
On Convexity of Fuzzy Syntopogenous Spaces
Mo Zhi Wen
Department of Mathematics, Sichuan Normal University,
Sichuan Chengdu, 610066, P. R. China
Abstract: In this paper, we combine fuzzy syntopogenous structures with algebraic structures on X, and research their correspongding structures and typical properties. First, the -increasing and -decreasing spaces have been studied. Second, two general types of convexity on L-fuzzy syntopogenous structures have been defined and their relationship has been investigated. Third, the equivalent depictions of convexity have been given; Finally, a sequence of important properties of convexity have been obtained.
Keywords: Fuzzy topology, order, convexity.
Normal Fuzzy LI-ideals of Lattice Implication Algebras*
Young Bae Jun
Department of Mathematics Education
Gyeongsang Nationaluniversity, Cianju660-701,Korea
e-mail: ybjun@nongae.gsnu.ac.kr
Yang Xu and Keyun Qin
Department of Applied Mathematics
Southwest Jiaotong University , Chengdu, Sichuan 610031, China
e-mail: yxu(Dcenter2.swjtu.edu.cn
Abstract: In this paper we introduce the notion of normal fuzzy LI-ideals. maximal fuzzvLI-ideals and completely normal fuzzy LI-ideals in lattice implication algebras. We showthat every maximal fuzzy LI-ideals of a lattice implication algebra is completely normal.
Keywords: Lattice implication algebras, (fuzzy) LI-ideal, (completely) normal fuzzy LI-ideal, maximal fuzzy LI-ideal.
A Note on B-preinvex Fuzzy Mappings
Yu-Ru Syau
Abstract: In this paper, we introduce and study two kinds of convergent series of fuzzy numbers by using a metric defined as the supremum of the Hausdorff distances of a -level sets of fuzzy numbers, and levelwise convergence, and then series of B-vex fuzzy mappings and B-preinvex fuzzy mappings are defined and their properties are studied. In addition some basic properties of compositions of fuzzy mappings are presented.
Keywords: Fuzzy numbers, series of fuzzy numbers, convex fuzzy mappings, B-vex fuzzy mappings, B-preinvex fuzzy mappings. |