The Journal of Fuzzy Mathematics
Volume 3, Number 4, December 1995
CONTENT
DETAILS
Smoothed max-min Methods for Identifying Fuzzy Systems
A. Blanco, M. Delgado and I. Requena
Departamento de Ciencias de la Computaci?n e Inteligencia Aritificial de la Universidad de Granada
Facultada de Ciencias 18071 Granada Espana
Abstract:
In this article we analyze in depth the identification of fuzzy relational equations by means of max-min fuzzy neural networks, using the smoothed derivative method developed by the authors in previous papers.
Keywords: Fuzzy relational equations, neural networks, smoothed derivative.
A Remark on a Decision Procedure for Aggregated Parametric-transitive Fuzzy Relations
Michael Wagenknecht
Technical University of Berlin, Institut f¨¹r Proze¦Â-und Anlagentechnik
Projekt SVT Rudower Chaussee 5 (Geb 10.5), 12484 Berlin, Germany
Abstract: A ranking procedure for alternatives using single stochastic transitive fuzzy relation is extended to collective choice problems with parametric-transitive relations. It turns out that in a group of experts their ¡°degree of concordance¡± must be high enough to get an aggregated preference relation permitting a rank-ordering of the alternatives. Quantitative connections between the aggregation (mean) operator, the kind of parametric-transitivity and the quality of the experts¡¯ decision are derived.
Keywords: parametric-transitive fuzzy relations, aggregation of preferences, ranking procedure.
Strong Connectedness in L-fuzzy Topological Spaces
Bai Shi-Zhong
Department of Mathematics, Xiangtan University, Xiangtan Hunan 411105, Chian
Abstract: In this paper, the concept of strong connectedness in L-fuzzy topological space is introduced and studied. It possesses the following properties: (1) The sets between strongly connected set and its strong semiclosure are strongly connected. (2) The images of S-irresolute order-homomorphisms of strongly connected sets are strongly connected. (3) For strong connectedness the K. Fan¡¯s Theorem holds.
Keywords: L-fuzzy topological spaces; strongly semiclosed sets; strong semi-closureS; Q-remote-neighborhoods; strongly connected sets.
Possibility Measure Extension on Arbitrary Set ClassL
Zhipeng Zhang
P. O. Box 78, Bengdu 223013, Anhui, P. R. China
Abstract: In this paper, we give a concept of the free element on arbitrary set class and U-closure in L. Given an arbitrary value on , we can uniquely extend it to a possibility measure on L, and also extend it to possibility measure on complete filed generated by L
. Keywords: Possibility measure, extension, free element.
Separation of Fuzzy Points in Fuzzy Topological Spaces
M. A. Amer
Department of Mathematics and Physical Science, Faculty of Engineering, El-Mansoura University, El-Mansoura, Egypt
Abstract: In this paper we use the concept of a fuzzy point introduced by Wong in [11] to study fuzzy and topological spaces. Also we give a survey in some existing definitions of fuzzy spaces. Comparison between those definitions is presented. New proofs are established to show that the property of -ness is both productive and hereditary. Classification of fuzzy points into major and minor fuzzy points is introduced and carefully examined in fuzzy spaces. A fundamental property of an ordinary topological space is shown to be not extendible to the fuzzy case. On the other hand, a new definition of fuzzy spaces is given. With this definition, the property of fuzzy -ness is still shown to be productive and hereditary, and moreover, it extends its topological counterpart. Finally, it is shown that a fuzzy topological space is (in Srivastava¡¯s sense [8]) iff it both and (in our sense).
Keywords:
Fuzzy topology, fuzzy sets.
Mixed Fuzzy Topological Spaces
N. R. Das and P. C. Baishya
Department of Mathematics, Gauhati University Guwahati-781014, ASSAM, India
Abstract: A fuzzy topology called mixed fuzzy topology is constructed in this paper from two fuzzy topologies on same ground set X. Structural properties of such mixed fuzzy topology are studied and illustrated with examples.
Keywords: Fuzzy topological space, mixed topology;
BCI Quotient Algebras on Fuzzy Ideals of BCI Algebras
Qin Keyun
Department of Mathematics, Henan Normal University, Henan, China
Xu Yang
Department of Applied Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, China
Abstract: In this paper, we discuss the properties of BCI quotient algebras which is defined by fuzzy ideals.
Keywords: BCI algebra, ideal, fuzzy ideal, BCI quotient algebra.
Distance Functions for Fuzzy Sets
Wang Geping
Department of Mathematics, Xuzhou Teachers¡¯ College, Jiangsu 221009, China
Abstract: The main purpose of this paper is to introduce a distance function D which assigns each pair of nonempty fuzzy sets to a real number. Such a function is called a setwise fuzzy p.q.metric. The restriction d of D, which assigns each pair of molecules (a special kind of fuzzy points) to a real number, is called a moleculewise fuzzy p.q.metric. The relationships among Erceg¡¯s, setwise and moleculewise fuzzy p.q.metrics are investigatedin detail. Some applications of them are obtained.
Keywords:
Fuzzy p.q.metric; setwise fuzzy p.q.metric; moleculewise fuzzy p.q.metric; fuzzy topology.
Some Results on Separation Axioms and Compactness on Fuzzy Topological Spaces
A. M. Zahran
Mathematics Department. Fac. of Science, Al-Azhar University, Assiut, 71511, Egypt
A. A. Ramadan
Math. Dept. Fac. of Science, Cairo University, Bane Swef, Egypt
Abstract: The concept of -open fuzzy sets is introduced in [2,7] and the concepts of -closed sets and -continuous functions are introduced in [15,18]. In this paper we define several notions of fuzzy separation axioms by using the concept of quasi coincident and we introduce the relationship between the ordinary topological space and the fuzzy topological space which defined in [12]. Also, we introduce the relationship between the fuzzy topological spaces and , where the collection of all -open fuzzy sets in . Finally we define -almost continuous and - -continuous functions and by using these concepts and the concepts of -continuity and -closed sets we improve some results on fuzzy compactness.
Keywords:
Fuzzy topology, -continuity, quasi coincident, fuzzy separation axioms, fuzzy -compactness, fuzzy -Lindel?f, fuzzy -countable compactness.
Differential Inclusions with Set-valued Perturbations
Liu Zuoshu
Department of Mathematics and Physics Wuhan University of Technology Wuhan 430070, China
Chen Hongjin
Electrical and Computer Engineering Department
University of Manitoba, Winnipeg, Canada. R3T 2N2
Abstract£º On the basis of the study of theory of population control, we consider set-valued perturbations in the abstract differential equation in the mathematical model of population control systems. In this case, differential inclusions are introduced, we will give the existence theorem of the solutions with two different types of set-valued perturbations. We all also give a stability result.
Keywords: Differential inclusions, upper (lower) semicontinuous, K-M continuous, set-valued perturbation.
Fuzzy Normed Algebra and the Related Fuzzy Semi Inner Product Space
T. V. Ramakrishnan
School of Mathematical Sciences
Cochin University of Science and Technology
Cochin-682022, India
Abstract: Using the set of non negative fuzzy real numbers , we construct the fuzzy normed algebra . On a module , we introduce the idea of fuzzy semi inner product, which generates a fuzzy norm.
Keywords: Fuzzy real numbers, the fuzzy normed algebra ; fuzzy semi inner product space.
Fuzzy Subgroups of Fuzzy Groups and Fuzzy Ideals of Fuzzy Rings
Luis Mart¨ªnez
Department of Mathematics, University of the Basque Country, Spain
E-mail: mtpmafel@lg.edu.es
Abstract:
The notion of fuzzy subring and fuzzy ideal are related in this paper and a new approach to the definition of the fuzzy subgroup of a fuzzy group is introduced. The concept of homomorphism between fuzzy rings (resp. fuzzy groups) is given. A definition of quotient of a fuzzy ring over a fuzzy ideal ( resp. quotient of a fuzzy group over a fuzzy subgroup) is given that generalizes the known one. The fundamental operations between fuzzy ideals (resp. fuzzy subgroups) are studied and, finally, the two fundamental isomorphism theorems are established for fuzzy rings (resp. fuzzy groups).
Keywords: fuzzy group (resp. ring), fuzzy subgroup (resp. subring), fuzzy ideal, homomorphism between fuzzy groups (resp. rings), fuzzy quotient group (resp. ring), fuzzy kernel.
On Completely Induced Fuzzy Topological Space
Fang Jinming
Department of Applied Mathematics, Qing Dao Ocean University, Qing Dao, 266003 China
Abstract: In this paper, we discuss the properties of so called completely include mapping C and the question when an fts can completely be induced from an ordinary topological space. These results deepen the conclusions about this problem which showed by R. N. Bhaumik and A. Mukherjee.
Keywords: The mapping C; the initial and the final topology; the semi-regularization; the completely induced topology.
Oscillation and Nonoscillation Theorems of the First and Second Order Fuzzy Differential Equations
P. C. Nayak
Department of Mathematics, F. M. College, Balasore, Orissa, India
S. Nanda
Department of Mathmatics, I. I. T. Kharagpur, W. B., India
Abstract: The purpose of this paper is to introduce and discuss the concept of Fuzzy second order differentical equation and the existence problem associated with its solution. We have actually extended the existence and the uniqueness problem for the solution of first order fuzzy differential equation into second order fuzzy differential equation which has been studied by Osmokaleva [7]. We then study the oscillatory and nonoscillatory behavior of the solutions of the second order fuzzy differential equation using the concept of fuzzy function and its corresponding imbedded integral equation as already established by Osmokaleva in his recent paper.
Keywords: Fuzzy differential equations, existence, uniqueness, oscillation and nonoscillation.
Stability of General Fuzzy Parametric Multiobjective Nonlinear Programming Problems Without Differentiability
Mohamed Abd EI-Hady Kassem
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
Abstract: This paper deals with multiobjective nonlinear programming problems without differentiability, involving general fuzzy parameters in the objective functions. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the stability notions of parametric multiobjective programming problems without differentiability are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of -pareto optimality without differentiability.
Keywords: Multiobjective nonlinear programming problems, Stability, Fuzzy parameters, Fuzzy numbers, -pareto optimality.
Obstinate Fuzzy Ideals in BCI-algebras
H. M. Khaild and B. Ahamad
Centre for Advanced Studies in Pure and Applied Mathematics,
Bahauddin Zakariya University, Multan 60800, Pakistan.
Abstract: In this paper, we define and study obstinate fuzzy ideals in BCI-algebras.
Keywords£º Level ideals, closed ideals, obstinate ideals, fuzzy ideals, closed fuzzy ideals, obstinate fuzzy ideals.
Fuzzy Group Subalgebras ¢ò
John N. Mordeson
Department of Mathematics/Computer Science Creighton University, Omaha, Nebraska 68178 USA
Abstract:
In this paper, we continue the examination of how the concept of a fuzzy group subalgebra of a group algebra can be used to make a connection between fuzzy field extensions and fuzzy subgroups. We describe pure inseparable fuzzy field extensions whose supports are tensor products of simple purely inseparable field extensions. We give a structure result for a fuzzy field extension which is constructed from a fuzzy subgroup. We show for any fuzzy field extension which is constructed from a fuzzy subgroup of a commutative group G that the lattice of neutral closures of all the fuzzy intermediate field extensions which are constructed from fuzzy subgroups in is lattice isomorphic to the lattice of all fuzzy subgroups which are in .
Keywords: group algebra, fuzzy group subalgebra, fuzzy field extension, modular, linear disjoint, tensor product, pure inseparable, lattice of fuzzy subgroup.
On Fuzzy Compactness in Intuitionistic Fuzzy Topological Spaces
Dogan Coker and A. Haydar Es
Department of Mathematics Education-Department of Mathematics
Hacettepe University, Beytepe, 06532-Ankara, Turkey
Abstract: Compact fuzzy topological spaces were first introduced by Chang [5]. The concept of the intuitionistic fuzzy compactness was later given by Coker [6]. In this paper, we discuss fuzzy almost compactness, near compactness, countable compactness and light compactness of intuitionistic fuzzy topological spaces. Also we investigate the behavior of fuzzy compactness under several types of fuzzy continuous functions.
Keywords: Intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, fuzzy almost compactness, fuzzy near compactness, fuzzy countable compactness, fuzzy light compactness(TOPO).
Fuzzy Cyclic Subgroups and Fuzzy Cyclic p-subgroups
Y.Alkhamees
Department of Mathematics, King Saud University
P. O. Box 2455, Riyadh 11451, Saudi-Arabia
Abstract: In this paper we introduce the notion of a fuzzy cyclic subgroup of a group as well as of fuzzy cyclic p-subgroup of a group and use them to obtain characterizations for finite cyclic grup and finite cyclic p-groups.
Keywords£º
Cyclic group£¬cyclic p-group£¬fuzzy cyclic subgroup£¬fuzzy cyclic p-subgroup£¬fuzzy direct product.
Some Properties of Fuzzy Vector Spaces
Lu Tu
Department of Mathematics, Chang Chun Teachers College,
Chang Chun, Ji Lin, 130032, China
Gu Wen-Xiang
Department of Computer Science, Northeast Normal University,
Chang Chun,Ji Lin, 130024, China
Abstract:
In this paper, we study some properties of fuzzy vector space in [2], and we give some relations among fuzzy linearly independent vectors and structures of fuzzy vectors spaces. We also study how to fix the basis and dimension (this is the unsolvable problem in [2]).
Keywords: Fuzzy vector space, fuzzy linearly independence, invariant linearly independence, maximal invariant linear independence, fuzzy basis, dimension of fuzzy vector space.
Some Theorems in Fuzzy Metric Spaces
A George and P. Veeramani
Department of Mathematics Indian Institute of Technology, Madras, India 600036
Abstract: In this paper we prove Ascoli-Arzela theorem for fuzzy metric spaces. We also prove that every fuzzy metric space has a basis that is countably locally finite. We use this result to conclude that every fuzzy metric space is metrizable.
Keywords: Fuzzy metric space, equicontinuous, compact, complete.
Approximate Selections for Fuzzy-set-valued Mappings and Applications
S. G. Gal
Department of Mathematics, University of Oradea
Str, Armatei Romane 5, 3700 Oradea, Romania
Abstract: In this paper we obtain some fuzzy variants of known results in -approximate selections theory. As applications, the Weierstrass-type approximation theorem for real fuzzy mapping in [7] is extended to the more general case of approximation of fuzzy-set-valued mapping.
Keywords: Fuzzy-set-valued mapping, Hausdorff distance between fuzzy-set-valued mapping, -approximate selection for fuzzy-set-valued mappings. |