The Journal of Fuzzy Mathematics
volume 5,Number 3, September 1997
CONTENT
DETAILS
Is the Axiom of choice True for Fuzzy Sets?
Nistala V. E.S. Murthy
Mig-B-171
Sagar Nagar
Visakhapatnam-530043
A.p.State,India
Abstract: The definition of fuzzy sets is generalized in such a way that the product of nonempty fuzzy sets is nonempty .The definition of fuzzy map is generalized in such a way that they can be considered between fuzzy sets with truth values in a different lattices. Further, the images and inverse images of these maps are so generalized that they have several of the usual properties that
their crisp counterparts have.
Keywords: Fuzzy sets, fuzzy map, axiom of choice, category, functor, monomorphism, epimorphism, equalizer.
G-compatible Fuzzy Matrices
F.I. Sidky
Department of Mathematics, Faculty of Science
University of Zagazing, Zagazing, Egypt
Abstract: In this paper we define left (right) G-compatible and G-min compatible fuzzy matrices and prove some of their fundamental properties.
Keywords: Fuzzy matrix, left (right) G-compatible fuzzy matrix, G-min compatible fuzzy matrix.
On Fixed Fuzzy Set Theorems in Fuzzy Metric Spaces
Ranjit Biswas
Department of Mathematics, India Insititute of Technology
Kharagpur-721302, West Bengal, India
Abstract: This paper is sequel to [2]. Some fixed fuzzy set theorems are proved in fuzzy metric spaces. A generalized fixed fuzzy set theorem is proved which generalized all the fixed fuzzy set theorem proved in [1] and [2].
Keywords: Fuzzy metric,fuzzy metric space, F-convergence, F-Cauchy¡¯s sequence, F-complete fuzzy
Metric space, F-continuity, fixed fuzzy set, F-open sphere, F- closed sphere, F-neighborhood,
Fuzzy -chain, fuzzy ( , )-uniformly locally contractive mapping, fuzzy -contractive,
fuzzy local power contraction mapping.
On Stone Theorem for De Morgan Algebra
Congwen Luo
Department of Mathematics, Wuhan university
Wuhan 430072, P.R.China
Xuewen Ma
Experiment Centre, Xinyang Teachers¡¯ College
Xinyang 4644000,Henan, P. R. China
Abstract:
In this paper, we obtain the Stone theorem in De Morgan algebras, and using this theorem, we give a necessary and sufficient condition that a De Morgan algebra becomes Kleene algebra.
Keywords: De Morgan algebra, quasi-Boolean ring, Kleene algebra, reversible element, Boolean complement.
On pairwise Hausdorff Fuzzy Bitopological Spaces
Rekha Srivastava, Manjari Srivastava
Department of applied Mathematics, Insitute of Technology
Banaras Hindu University, Varanasi 221005, India
Abstract: Here we have studied eleven possible defining concepts of pairwise Hausdorffness in fuzzy bitopological spaces including four already existing in literature.
Keywords: Fuzzy bitopological spaces, fuzzy P-Hausdorffness, fuzzy P-continuity, goodness of extension.
The Properties of Congruence Ideal of Soft Algebra and
the Stucture of Quotient Soft Algebra
Wang Zhuzheng-qun
Yichang Teachers¡¯ College, China,443000
Abstract: If (b] is a congruence ideal of a soft algebra F, is the smallest congruence whose kernel is (d]. In this paper, we give a necessary and sufficient condition such that[ (b] ] is a congruence ideal of
a quotient soft algebra F/ . We give a structure of quotient soft algebra F/ and characterize absolutely indecomposable soft algebra.
Keywords: soft algebra; congruence ideal; quotient soft algebra; Boolean kernel; absolutely indecomposable soft algebra.
On Choosing Non-dominated Fuzzy Numbers
Michael Wagenknecht
Karl-Liebknecht-Str.15
01844 Neustadt, Germany
Abstract: For a giver set of fuzzy numbers we determine non-dominated ones by a two-stages procedure starting form partial ordering of intervals resettling in a global fuzzy preference relation which is tacked applying Orlovsky¡¯s approach.
Keywords: Fuzzy numbers, partial ordering, non-dominated elements
Fuzzy Homological Theory in -module (¢¢)
Zhao Jianli
Institute of Fuzzy System, Liaocheng Teachers College
Shandong 2520359, P.R.China
Abstract:
In this paper, We introduce the concept of F-tensor product of module- and -module, give concrete structure and some important properties of its.
Keywords: -module, module- , F-homomorphism, fuzzy abel group, F-tensor product
Fuzzy Analytic Hierarchy Process to Solve a Multi-objective Transportation Problem
Rakesh Veema*, M.P. Biswal and A.Biswas
Department of Mathematics
Indian Institute of Technology
Kharagpur-721320,India
Abstract: In this paper, fuzzy Analytic Hierarchy Process is applied to solve a multi-objective transportation problem, where the objective functions are not equally important as well as fuzzy.
In fuzzy Analytic Hierarchy Process, we first formulate fuzzy pairwise comparison matrice by comparing the alternatives with the alternatives with respect to the overall satisfaction of the objectives and comparing objectives with the objectives with respect to each of the alternatives.
We use triangular fuzzy numbers to to present the relative strength of the elements in the fuzzy pairwise comparison matrices. To estimate the eigenvector (corresponding to maximal eigenvalue ) of matrices, we utilize interval arithmetic, together with optimism of index .Assigning the estimated weights eigenvector, we estimate the weights of the objectives.
Assigning the estimated weights to the respective objectives, we formulate a new objective, then the problem is solved by a transportation algorithm. A numerical example is presented to illustrate the methodology.
Keywords: Multi-criteria decision making, transportation problem, fuzzy number, , interval arithmetic, fuzzy analytic hierarchy process.
Random Completely Generalized Strongly Nonlinear Quasi-complementarity Problems for Random Fuzzy Mappings
Nan-jing Huang
Department of Mathematics, Sichuan University
Chengdu, Sichuan
611064, P.R. of China
Abstract: In this paper, we introduce and study a new class of random completely generalized strongly nonlinear quasi-complementarity problems with non-compact valued random fuzzy mappings and construct a new iterative algotithm for this kind of random fuzzy quasi-complementarity problems. We also prove the existence of random solutions for this class of random fuzzy quasi-complementarity problems and the convergence of random iterative sequence generated by the algorithm.
Keywords: Complementarity problem, random fuzzy mapping, algorithm, existence, comvergence.
Fuzzy Mixed Integer Linear Programming
With Nonequivalent Objectives
R.K.Dwivedi
Department of Mathematics, Sindri College
Sindri, Dhanbad-828122,India
M.Chakraborty
Departmernt of Applied Mathematics, India School of Mimes
Dhanabad-826004,India
D.Singh
Department of Mathematics,Bithar Institute of Technology
Sindri,Dhanbad-828123, India
Abstract: This paper investigates a fuzzy linear mixed integer programming approach to avecor maximum problem with non-equivalent objectives. The overall achievement function is taken as a convex combination of the fuzzy objectives, where the coefficients of the membership functions serve the purpose of weights to reflect the relative importance of the objectives. The decision variables are restricted to take integer values while the membership functions are allowed to take fractional values too. The methodology is illustrated with sample vector maximum problems.
Keywords: Mixed integer, fuzzy objectives.
Research for a Geometric Programming Model with
T-fuzzy Variations
Cao Bing-yuan
Department of Mathematics, Changsha University of Electric Power,
Changsha,410077,China
Abstract: A geometric programming model with T-fuzzy variations is first built after the T-fuzzy variation is introduced to geometric programming in this paper. First, the model is turned into an ordinary geometric programming depending on the cone index J and a dual form with T-fuzzy variation is obtained corresponding to a prototype problem. Second, relation is developed between optimal solutions of prototype posynomial geometric programming is verified with numerical example.
Keywords: T-fuzzy variations, posynomial geometric programming, dual, cone indexn, optimal solution.
W-Ideals and W-Soft Algebras
Wang Zheng-qun
Yichang Teachers College
Hubei, China 443000
Pei Li-wen
Wuhan University
Wuhan, China 430072
Abstract: In this paper, we define a ideal and soft algebra. Our main results are as following.;
(1) Let (d], ( ] be congruence ideals of a soft algebra F and . If (d] is a ideal, then ( ] is also a ideal.
(2) We get some sufficient and necessary conditions such that soft algebra and quotient soft algebras are ideal algebras respectively.
Keywords: Soft algebra, congruence, congruence ideal, ideal, soft algebra.
Mathematical Programming Problem with Fuzzy Coefficients
-A General Analysis
Stefan Chanas
Institute of Industrial Engineering and Management,
Technical University of Wroclaw,Poland
Bronislaw Florkiewicz
Institute of Mathematics, Technical University of Wrolaw, Poland
Abstract£º In this paper the problem of mathematical programming is analyzed, in which the coefficients are intervial fuzzy numbers. The main aim of this analysis is an answer to the question: what do we have assume about the problem so that the possibility distribution of the optimal value of the objective function is of the same type as the possibility distribution generated by the fuzzy coefficients of the problem, i.e., when the optimal value of the objective function is also an interval fuzzy number.
Keywords: Mathematical programming, fuzzy number, possibility distribution.
Category of fuzzy Semi Inner Product Spaces
T.V.Ramakrishnan
School of Mathematical Sciences
Cochin University of Science and Technology
Cochin, 682022, India
Absrtact: In this paper the concept of the category of semi inner product spaces and that of fuzzy semi inner product spaces are introduced. Relation of the category of fuzzy semi inner product spaces with the categories of semi inner product spaces, fuzzy topological spaces and topological spaces are studied. We conclude with a more general approach to fuzzy semi inner product spaces by introducing the category of semi inner product in a given concrete category.
Keywords: Semi inner product space, fuzzy topological spaces, concrete category.
compatible Fuzzy Matrices
Jin Bai Kim
Department of Mathematics, West Virginia University
Morgantown, WV26506
Kya Hyuck Choi*
Wonkwang University
Iksan 570-749, Korea
Abstract: We study G-compatible fuzzy matrices, where G is a group. We also study compatible fuzzy matrices where denotes the symmetric group. We consider matrices ,where are group elements .
Keywords: G-compatible fuzzy matrices, matrices over elements.
The Expression Theorem and Extension Principle with the
Form of Intersection
Liu Huawen
Departmernt of Applied Mathematics and phsics
Shandong University of Technology
Jinan 250061, P.R. China
Abstract£º In this paper, we establish the expression the theorem and extension principles with the form of intersection which are based on the intersection decomposition of fuzzy sets. Further, we give the corresponding results of poly-ary extension and extension of fuzzy mapping.
Keywords: Intersection decomposition, expression theorem, extension principle, poly-ary extension principle, fuzzy mapping
Existence and stability of Fuzzy Differential Equations
Zouhua Ding and Abraham Kandel
Computer Science and Engineering Department
University of South Florida
Tampa, FL33620-5350,USA.
Abstract: In this paper we study (1) the existence of the solutions of fuzzy differential equations with local Lipschitz condition, (2) the stability of the solutions of fuzzy differential equations in real line and (3) the relationship between fuzzy differential equations and differential inclusions.
Keywords: Fuzzy differential equation, existence, stability, differential inclusion.
FNN Optimum Seeking Decision Making Method
Dengfeng Li
Department of Basics, Dalian Naval Academy
Dalian 116018,P.R. China
Shouyu Chen
Department of Civil Eengineering, Dalian University of Techology
Dalian116023,P.R. China
Abstract: This paper investigates multiattribute decision making problems of the decision maker preference information (i.e.,weight) which is unknown a prior. Commethod the conventional BP learning algorithm and fuzzy optimum seeking model, a fuzzy neural networks comprehence optimum seeking decision making method is established for multiattribute problems. This method can adjust the weights of objectives automatically. Therefore,the determination of weights is more objective and more exact. The method proposed in this paper is also capable of self-learning. Making comparison and analysis between the fuzzy neural networks comprehence optimum seeking model is required to solve the inverse problem of nonlinear fuzzy relation equation systems for obtaining process is difficult and is not easy to implement. Therefore, the fuzzy neural networks comprehence optimum seeking method presents a new effective way to obtain the knowledge and experience of the decision maker. Finally, the new method is applied to the evaluation and decision making of industry economics in Dalian city. The result is more satisfying. So the method proposed in this paper is effective and may be applied to other fields in future.
Keywords: Fuzzy sets, neural network, weight, membership grade, decision making, expert system.
A Necessary and Sufficient Condition of a Discrete Soft
Algebra Is a -soft Algebra
Zhueng-qun Wang
Yichang Teachers¡¯ College
Hubei 443000 P.R. China
Abstract: The main results in this paper are as follows:
1) The discrete soft algebra is -soft algebra if and only if for every join irreducible element P, if P covers ( ) where is the greatest congruence whose kernel is (0].
2) The discrete soft algebra F is a -soft algebra if and only if L(J(F)) 1 where J(F) denotes the poset of all nonzero join-irreducible elements of F. L(J(F)) denotes the length of the poset J(F).
Keywords:
Discrete soft algebra, -soft algebra, congruence, congruence ideal, join-irreducible element.
The Derived Element of Element and the Derived Operator in TML
Jian-bing Shi
Nanjing Power Institute, 78 Ban Cang Cun
Nanjing 210042,P.R.China
Abstract: In this paper,first we discuss the distributional rules of the accumulation points of elements in TML. Then we give the conclusion in a general TML similar to the C.T. Yang`s theorem concerning derived set in general topology. Finally,we introduce the concept of derived operator on molecular lattice and by which we characterize the TML.
Keywords: TML, accumulation point, derived element, derived operator.
An Existence Theorem for a Fuzzy Function Integral Equation
P.V. Subrahmanyan and S.K.Sudarsanam
Department of Mathematics, India Institute of Technology
Madras 600 036, India
Abstract: In this paper we solve the following fuzzy functional integral equation
Where h and g are given fuzzy functions and and are self-maps on [0,1]and is the unknown function to be found out. We use Krasnoselskii`s fixed point theorem to solve the above functional integral equation on a suitable subset of the space of fuzzy functions.
Keywords: Fuzzy function, fuzzy functional equation, fuzzy numbers, Zadeh`s extension principle, fuzzy solution, fixed point, embedding theorem for fuzzy sets and Krasnoselskii`s fixed point theorem.
Extending -connectedness to Fuzzy Subsets
Gunther Jager
Lessingstr. 13, D-76135 Karlsruhe, Germany
Abstract: In order to view connectedness in fuzzy topological spaces in Preuss` sense by continuous functions to certain test spaces being constant, Lowen and Srivastava introduced the concept of -connectedness. However this concept can only be applied to crisp fuzzy subsets. In this paper their definition is modified in a way that it is also applicable to non-crisp fuzzy subsets. The definition obtained moreover generalizes connectedness in the definition of Pu and Liu even for fuzzy subsets and is an absolute property.
Keywords: Fuzzy topology, connectedness, fuzzy subsets
Factorization of Fuzzy Ideals in Dedekind Domains
Kyoung Hee Lee*
Department of Liberal Arts
Korea Institute of Technology and Education
Byungcheon, Chungnam 333-860, Korea
John N. Mordeson
Department of Mathematics/Computer Science
Creighton University
Omaha, Nebraska 68178 USA
Abstract: We show that in a Dedekind domain, every fuzzy ideal can be factored uniquely as a product of fuzzy maximal ideals.
Keywords: Dedekind domain, fuzzy ideals, fuzzy maximal ideals, factorization, algebraic integer.
On Fuzzy Weak Continuity, Fuzzy Almost Continuity and Fuzzy Precontinuity
S.P. Arya
Maitreyi College, Bapudham Complex
Chanakyapuri, New Delhi-110021, India
Neeru Jain
Department of Mathematics, University of Delhi
Delhi-110007, India
Abstract: The independence of fuzzy weak continuity [2]and fuzzy precontinuity [6] has been proved by El-Monsef, Hanafy and El-Deeb [4]. The purpose of the present paper is to determine conditions under which each will imply the other and to prove the independence of fuzzy almost continuity[2] and fuzzy precontinuity. We also give an example of a fuzzy non-continuity function which is both fuzzy almost continuous and fuzzy precontinuous. Some new characterizations for fuzzy weak continuity, fuzzy precontinuity and fuzzy preopen functions [7] have been establishd. We also introduce a new weaker form of fuzzy continuity which is strictly stronger than fuzzy weak continuity but is independent from fuzzy almost continuity.
Keywords: Fuzzy weak continuity, fuzzy almost continuity, fuzzy precontinuity
Model of Fuzzy Closed-loop Control System
Ouyang Xiantai
Department of Automation Engineering
Wuhan Chemical Engineering Institute
Wuhan, Hubei 430073, P.R.China
Shi Kaiquuan
Department of Automation Engineering
Shandong University of Technology
Jinan, Shangdong 250061, P.R.China
Abstract: This paper analyzes the structure of fuzzy controller and some examples of application, based on which this paper proposes the closed-loop model of fuzzy control.
Keywords: Fuzzy control, fuzzy relation matrix, model of closed-loop. |