The Journal of Fuzzy Mathematics
Volume 7,Number 1,March 1999
CONTENT
DETAILS
Stable Fuzzy Indirect Adaptive Control for a Class of Decentralized Nonlinear Systems*
Tong Shaocheng
Department of basic mathematics,Liaoning Institute of Technology,Jinzhou,Liaoning,121001.China
Wang Leizhen
Department of basic mathematics,Hebei Institute of archectrue Engineering,Zhang Jiakou,Hebei,
075024. China
Chai Tianyou
Automatic Research Center of Northeastern University Shenyang,Liaoning,110006. China
Abstract: In this paper,a stable fuzzy indirect control scheme is presented for a class of interconnected nonlinear systems for which an explicit linear parameterization of the uncertainty is either unknown or impossible.In the control algorithm,fuzzy logic systems are employed to approximate the optimal controllers,which are designed on the assumption that all dynamics for each subsystems are known,then the fuzzy controllers and adaptation mechanisms for each subsystems depend only upon local measurements to procide asymptotic tracking of a reference trajectory.In addition,fuzzy sliding mode controller is developed to compensate for the fuzzy approximating errors and attenuate the interactions between subsystems.Global asymptotic stability is established in the Lyapunov sense,with the tracking errors converging to a neighborhood of zero.In order to verify the effectiveness of the proposed algorithm,we apply it to a two-inverted pendulum system.
Keywords: Fuzzy control,adaptive control,fuzzy sliding mode,nonlinear systems,stability.
Some Sufficient Conditions for A Family of OWA Bag Mappings Having Identities
Hou Jian
Department of Basic Courses,Shanxi Finance and Economical College,Taiyuan,030012,China
Abstract: In this paper,we first discuss when OWA bag mappings have a fixed identity,and give a sufficient and necessary condition for OWA bag mappings Having fixed-identity.Moreover,we give some sufficient conditions for OCWA bag mappings and NCWA bag mappings having fixed-identity and self-identity.
Keywords: Bag,fuzzy bag,bag mapping,value functional,fixed-identity,OWA,OCWA,NCWA.
Fuzzy Programming Approach for A Class of Multiple Objective Linear Fractional Programming Problem
Sandipan Gupta and M.Chakraborty
Department of Applied Mathematics,Indian School of Mines Dhanbad,826004 India
Abstract: The present paper deals with the development of methodology for a restricted class of Multi-objective linear fractional programming problems in the sense that there exist some values of decision variables for which the numerator is positive and the denominator is positive for all values of decision variables in the feasible region.A fuzzy approach has been used to solve the problem by defining suitable membership functions.Using the proposed methodology numerical examples have been presented.
Keywords: Multi-objective,fractional programming,fuzzy,restricted class,membership function.
Stability In Possibilistic Fuzzy Multiobjective Programming Problems
F.S.Abd El-Ghaffar
Department of Mathematics,Faculty of Education,Kafr El-sheikh,Egypt
Abstract: Throughout this paper,we focus on possibilistic fuzzy multiobjctive problems.The definition of ¦Á-stability set is presented using the definition of ¦Á-possibily efficient solution,and the determination of fuzzy ¦Á-stability set is discussed.Also an illustrative example is given to clarify the developed result.
Keywords: Multiobjective programming,possibilistic variables,stability set,fuzzy parameters.
On Fuzzy Approaches to Solve The Vector Optimization Problems
Elsaid Ibrarim Ammar
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
Abstract: In this paper, we give two fuzzy approaches to solve the nonlinear vector optimization (VOP) problem. The minimum and ¦Á-level operator will be used to define the fuzzy solutions of the fuzzy problem of the fuzzy problem of the VOP problem (efficient and weak-efficient solutions) are introduced. Finally we give an ¦Á-level algorithm to solve any fuzzy optimization problem of the (linear or nonlinear) VOP problems. Illustrative example is given.
Keywords: Nonlinear VOP, Fuzzy Set Theory, Minimum Operator, ¦Á-level set.
Connectedness In FTS from Different Points of View
R.Lowen
Department Wiskunde en Informatica, Universiteit Antwerpen,Groenenborgerlaan 171,2020 Antwerpen, Belgium
Xu Luoshan
Department of Mathematics, Teachers College, Yangzhou University, Yangzhou 225002, China
Abstract: Three new kinds of connectedness closely related to level topologies in fuzzy topological spaces are introduced. They meet one¡¯s intuition well and have properties that we generally require. Relations between them, as well as with other existing connectedness concepts are extensively examined.
Keywords: Fuzzy topology, connectedness, level topology,functor.
Multicriteria Based Decision Making:A Fuzzy Approach
Ranjit Biswas
Department of Mathematics, IndianInstitute of Technology, Dharagpur-721302, West Bengal, India
Abstract: Suppose there are n almost equi-efficient decidions to a decision-marker on a certain complex situation which is not well defined or precise. The problem to the decisionmaker is to select the optimal decision and to make a panel of the alternatives, on the basis of certain number of criteria where information available to him are not all crisp but a heterogeneous mixture of numerics, linguistic hedges and fuzzy sets. In the present paper a fuzzy optimal selection procedure is suggested to this problem.
Keywords: Universal set, SFS, fum, information matrix, decision, positive (negative) criterion, neatest SFS, order (>) , nearest matrix, dominating matrix, efficiency-score.
Fuzzy Faint Continuity and Weak Forms of Fuzzy Faint Continuity I.M.Hanafy and T.M.Salman
Department of Mathematics, Faculty of Education, Suez Canal University, El-Arish, Egypt
Abstract: This paper is devoted to (i) study the concept of fuzzy faint continuity [10] by giving other characterization and some basic properties of it, (ii) introduce and study concepts of fuzzy faintly open (closed) functions, (iii)introduce four classes of functions called fuzzy faintly ¦Á-(resp.semi-,pre-,¦Â-) continuous. We obtain their characterizations, their basic properties and their relationships with other types of fuzzy functions.
Keywords: Fuzzy topology, fuzzy faintly continuous function, fuzzy ¦È-compact, fuzzy faintly open (closed) functions, fuzzy faintly¦Á-(resp.semi-,pre-,¦Â-) continuous functions.
De Morgan Closure Algebra
Xueyou Chen
Dept. of Math., Shandong Institute of Technology, Zibo Shandong 255012, P.R.China
Abstract: In this paper, the Cech-closure operator on de morgan algebra (L,Q) , and de Morgan closure algebra (L,Q,c) are firstly introduced. Secondly the compactness of (L,Q,c) is investigated. In the end, the interaction between (L,Q,¦Ä) and (L,Q,c) is investigated.
Keywords: Cech-closure operator, C-cover, de Morgan closure algebra.
L-fuzzy Almost Nice Compactness
Chen Shui-Li
Department of Mathematics, Jianghan Petroleum Institute, Jiangling Hubei 434102,P.R. China
Abstract: In this paper, the concept of almost nice compactness in an L-fuzzy topological space is introduced. The characterizations and the topological properties of the kind of fuzzy compactness are systematically studied. The mutual relationships between the almost nice compactness and the nearly nice compactness(resp. almost F-compactness, nice compactness, NS-closedness, etc.) are discussed. Some interesting results are obtained, such as the almost nice compactness is a good extension in the means of R.Lowen and hereditary for an L-fuzzy ¦È-closed set, and so on.
Keywords: L-fuzzy topological space, nice compactness, almost nice compactness, almost¦Á-RF, ¦È-cluster point.
A Fuzzy Weierstrass Approximation Theorem
Congxin Wu
Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People¡¯s Republic of China
Danhong Liu
Department of Mathematics, Tianjin University, Tianjin, 300072, People¡¯s Republic of China
Abstract: This paper shows that a fuzzy continuous function from any finite closed interval to the fuzzy number space can be approximated to any fixed degree by a generalized fuzzy polynomial. Hence,a fuzzy Weierstrass approximation theorem is obtained.
Keywords: Fuzzy number, fuzzy continuous function, generalized fuzzy polynomial
Fuzzy Semi-continuity and Fuzzy Csemi-continuity in Fuzzifying Topology
F.H.Khedr,F.M.Zeyada and O.R.Sayed
Department of Mathematics, Faculty of Sciences, Assiut University, Assiut 71516, Egypt
Abstract: The concepts of fuzzy semi-continuity and fuzzy csemi-continuity are introduced and studied essentially in order to decompose fuzzy continuity in fuzzifying topology. Furthermore, the concept of csemi-neighborhood system is presented and by making use of it a fuzzifying topology is introduced and so comparisons of motivated types of fuzzy continuity are pointed out.
Keywords: Fuzzifying topology, fuzzy continuity, semi-continuity,csemi-continuity
Fuzzy Localization of Rings
F.I.Sidky
Department of Mathematics, Faculty of Sciences, Faculty of Science, Zagazig University, Zagazig, Egypt
Abstract: We introduce the localization of commutative rings with identities with respect to certain multiplicative fuzzy sets and prove some of their properties.
Keywords: Fuzzy multiplicative sets, t-fuzzy localization of rings, fuzzy ideals
Automorphisms of Aggregation De Morgan Triplets
T.Calvo
Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra.de Valldemossa, km 7.5,E-07071 Palma de mallorca, Spain
e-mail:DMITCS0@ps.uib.es
Abstract: The aim of this work is to characterize the aggregation automorphisms of the unit interval.
Keywords: Automorphism, aggregation function, k-negation, dual aggregation function, aggregation De Morgan triplet.
Fuzzy Implicative Filters in Implicative Algebras
Young Bae Jun
Department of Mathematics Education, Gyeongsang National University Chinju 660-701, Korea
e-mail:ybjun@nongae.gsnu.ac.kr
Hee Sik Kim
Department of Mathematics Hanyang university,Seoul 133-791, Korea
e-mail:heekim@email.hanyang.ac.kr
Abstract: We consider the fuzzification of an implicative filter in an implicative algebra. We solve the problem of classifying fuzzy implicative filters by their level implicative filters, and consider characteristic fuzzy implicative filters. We also introduce the same type fuzzy implicative filters, and give its characterization.
Keywords: Implicative aalgebra, (characteristic) implicative filter, (characteristic) fuzzy implicative filter, level implicative filter, same type.
Some Properties of Convex Fuzzy Mappings
Yu-Ru Syau
Department of Industrial Engineering, Yuan-Ze University, Taoyuan, Taiwan 320,R.O.C
Abstract: In this paper, we prove that the set of fuzzy numbers equipped with a partial ordering , defined in terms of¦Á-level sets of fuzzy numbers, is a distributive lattice based on the face that sup{u,v} and inf{u,v} exist in for any pair {u,v} , and does not have a least or greatest element. We also prove that a strictly convex (resp. concave) fuzzy mapping has at most one global minimum (resp. maximum) point, and that the pointwise supremum (resp. infimum) of an arbitrary collection of convex (resp. concave) fuzzy mapping under certain conditions is convex (resp. concave).
Keywords: Fuzzy numbers, lattice, convex fuzzy mapping, generalized convexity.
On Sequences of Fuzzy Sets Yu-Ru Syau
Department of Industrial Engineering, Yuan-Ze University, Taoyuan, Taiwan 320,R.O.C
Abstract: In this paper we introduce the concept of monotonic sequences of fuzzy numbers and show that every nondecreasing sequence of fuzzy numbers which is bounded above converges levelwise to its least upper bound. We also discuss the space of convergent sequences of fuzzy sets of any Euclidean space and -spaces of sequences of fuzzy sets of
Keywords: Fuzzy numbers, sequences of fuzzy numbers, bounded and monotonic sequences of fuzzy numbers, sequences of fuzzy sets, convergent sequences of fuzzy sets.
Fuzzy Normal BCK-filters and Extensions of Fuzzy BCK-filters
Young Bae Jun
Department of Mathematics Education, Gyeongsang National University Chinju 660-701, Korea
e-mail:ybjun@nongae.gsnu.ac.kr
Jie Meng and Xiao long Xin
Department of Mathematics, Northwest University, Xian 710069, P.R.China
Abstract: In [6] and [7], Jun et al. fuzzified the concept of BCK-algebra, and investigated its properties. In this paper, we state fuzzy normal BCK-filters in BCK- algebras, and construct an extension of a fuzzy BCK-filter.
Keywords: (Fuzzy) BCK-filter, fuzzy normal BCK-filter, extension of fuzzy BCK-filter,bounded BCK-algebra, level BCK-filter.
Indistinguishability Operators and Induced Metrics by Generalized De Morgan Triplets
T.Calvo
Department of Mathematics and Computer Science, University of the Balearic Islands, Ctra. De Valldemossa, km 7.5, E-07071 Palma de Mallorca, Spain
e-mail: DMITCS0@ps.uib.es
Abstract: This work has been developed taken as starting point the following issues:
1. Basic concepts on metrics and later studies of Trillas and Alsina made in 1978 about Generalized Metric Spaces.
2. Studies on indistinguishability operators made by Trillas in 1982 and also by Valverde in 1982, Jacas between 1984 and 1986 and other authors.
In the first part of this paper we give some preliminaries and known results related with the work. After that, we will define metrics for some of the more important operators, i. e.,t-norm, t-conorm, aggregation function, etc. Also, we remind the main basic notions on indistinguishability operators. Afterwards, we make a deeper study on them and finally we give a set of results to join both concepts.
Keywords: t-norm, aggregation function, quasi-arithmetic mean, M-indistinguishability operator, -pseudometric.
Fuzzy Less Strongly Sets and Fuzzy Less Strong Semicontinuity in Fuzzy Bitopological Spaces
K.M.Abd El-Hakeim
Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt
Abstract: The concepts of -fuzzy semiopen sets due to Thakur et al. [Fuzzy Sets and Systems, 79(1996), 251-256] and -fuzzy weakly open sets due to author [J.Fuzzy Math., 5(2)(1997),455-469] are defined and studied. The present work deals with introducing of the concepts of -fuzzy less strongly semiopen and -fuzzy strongly semiopen and pairwise fuzzy less strongly semicontinuous mappings in fuzzy bitopological spaces, which is stronger than the early defined. The relation between these concepts are straightforward. Some of their basic properties cited there in.
Keywords:
On Structure of Subspaces of An Approximation Space
H.V.Kumbhojkar
Department of Mathematics, Shivaji University,Kolhapur-416004,India
Abstract: In this note we show that (strongly) connected approximation spaces, introduced by Kuroki and Mordeson, are precisely the indiscrete spaces and that this agrees with the natural topology defined on them by the upper approximation closure operator.
Keywords: Approximation space, subspace, rough set, (strongly) connected approximation space,Kuratowski closure axioms.
Integration of Generalized Fuzzy Number-valued Mappings
Byung-Soo Lee
Department of Mathematics, Kyungsung University, Pusan 608-736,Korea
Sung Jin Cho,Gue Myung Lee and Do Sang Kim
Department of Applied Mathematics, Pukyong National University, Pusan 608-737,Korea
Abstract: In this paper we introduce the notion of generalized fuzzy numbers and generalized fuzzy mappings, and obtain some results for integrals of generalized fuzzy number-valued mappings.
Keywords: Measurable set-valued mapping, generalized fuzzy number, generalized fuzzy number-valued mapping, measurable fuzzy mapping, Bochner integral, Bochner-integrable selector, measurable selector.
The Pseudo-autocontinuity of Non-additive Lattice-valued Measure on the Lattice
Guangquan Zhang and Yong-Hong Wu
School of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, Western Australia, 6845, Australia
{zhangg,yhwu}@cs.curtin.edu.au
Abstract: In this paper, the property (SPA) and the property (SPB) of non-additive lattice-valued measures are introduced. A number of theorems characterizing the pseudo-autocontinuity of non-additive lattice-valued measures are developed and the equivalent condition of pseudo-autocontinuous from above and pseudo-autocontinuous from below are given.
Keywords: Non-additive measure, fuzzy measure, lattice, pseudo- autocontinuous from above, pseudo-autocontinuity from below
De Morgan Algebra of Minimal Hausdorff Topology
Qingguo Li
Department of Applied Mathematics, Hunan University, Changsha 410082, Hunan, P.R.China
Abstract: In this paper, the concept of minimal Hausdorff is introduced and the characteristics of it and the relation between it and compactness are investigated in de Morgan algebra of topology.
Keywords: U-element, U-filter, U-net, minimal Hausdorff, compact.
On the Representation of Lattice Implication Algebras
Jun Liu and Yang Xu
Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan,
P. R. China
Abstract: Lattice implication algebra is a logical algebraic system which is constructed by combining lattice and implication algebra. In this paper, we focus on the representation of a class of lattice implication algebras, i. e. ,complete and quasi-atomic if and only if it is a direct product of finite Lukasiewicz chains.
Keywords: Many-valued logic, lattice implication algebra, implication filter, subdirect product decomposition, direct product decomposition. |