The Journal of Fuzzy Mathematics
Volume 11, Number 2, June 2003
CONTENT
DETAILS
Multiple Correlation of Fuzzy Sets
Nishikanta Jana and Madhumangal Pal*
Department of Applied Mathematics with Oceanology and Computer Programming
Vidyasagar University,Midnapore,721102,India
Abstract: In this paper, we propose a method of multiple correlation analysis on fuzzy sets to investigate the multiple relationship between fuzzy attributes when the values of one attributes are associated with or influenced by other attributes ..The linear relationship between many variables and the value of one fuzzy attributes may be influenced by many other .We are interested in studying the joint effect of a group fuzzy attributes upon a single attributes. Our study is on of multiple correlation.
Keywords: Fuzzy set,correlation coefficient,fuzzy multiple correlation.
On -closed Sets, -continuity and -almost Compactness
for Crisp Subsets in A Fuzzy Topological Space
M.N.Mukherjee and Anjana Bhattacharyya
Department of Pure Mathematics,University of Calcutta 35,
Ballygunge Circular Rood,Kolkata-70019,India
Abstract: This paper is a continuation of the study of -almost Compactness for crisp subsets in a fuzzy topological space,initiated in [5] in terms of the notion of -shading of Gantner et al.[4]. A class of ordinary subsets,called -closed Sets,which inherit -almost Compactness of a space X (endowed with a fuzzy topology) is introduced and studied.Incidentally,we require to independent functions between two fuzzy topological spaces are also defined and it is shown that -almost Compactness of crisp subsets remains invariant under each of these maps.
Keywords: -shading, -almost Compactness set, -closed Sets, -continuity.
Some Fixed Point Theorems in Complete Fuzzy Metric Space Representing It as A Uniform Space
Sikha Saikia (Bordoloye)
Department of Mathematics,Gauhati University
Guwahati-781014,Assam,India
Abstract: In this paper,we have proved fuzzy analogue of two fixed point theorems for ( ,k) uniformly locally contractive mapping and a self mapping in complete fuzzy metric space.
Keywords: Fuzzy metric space,uniform space, fuzzy ( ,k) uniformly locally contractive mapping,fuzzy -chainable metric space.
On Fuzzy Uniform Space
A.A.Ramadan
Department of Mathematics,Facully of science
Beni-Suef,Egypt
Y.C.Kim
Department of Mathematics,Kangnung National University
Kangnung,Kangwondo 210-702,Korea
M.K.El-Gayyar
Department of Mathematics,Faculty of Engineering,Suez-Canal University
Port Said,Egypt
Abstract: In this paper, we introduce the notions of fuzzy uniform spaces and investigate some properties of them. We defind the subspaces of fuzzy uniform space. We study the fuzzy topologies induced by a fuzzy uniform space.
Keywords: Fuzzy topological space, fuzzy continuous functions, fuzzy uniform spaces, fuzzy uniform continuous functions.
S-quasi L-proximity Space
F.M.Zeyada and K.M.Abd El ¨CHakiem
Department of Mathematics,Facully of science, Assiut University
Assiut 71516, Egypt
Abstract: The concept of -quasi proximity was introduced (E.Hayashi,1983[4]) and it was extended to fuzzy setting in 2000,by the concept of classal -fuzzy quasi-proximity (M.H.Ghanim et al.,2000[2]). The category of - topological space was defined in 1999 (U,Hohle and A.Sostak [5], S.E.Rodabaugh,1999[8]), using notation of T.Kubiak [6] and S.E.Rodabaugh [7] ,and studied extensively in [5]. In the present paper the category of -quasi - proximity space and the category of principal - proximity space are introduced and two functors from to and are given and some properties of them are studied.
Keywords: - topological space, -continuity, classal -fuzzy quasi-proximity, topological categories.
Intuitionistic Fuzzy -compactness
I.M.Hanafy
Department of Mathematics,Faculty of Engineering,Suez-Canal University
El-Arish,Egypt
Abstract: A new class of compactness,in intuitionistic fuzzy topological space,called intuitionistic fuzzy
-compact, is introduced and studied. This class is contained in the class¡¯s of intuitionistic fuzzy semi-compactness and intuitionistic fuzzy pre-compactness,and contains the class of intuitionistic fuzzy -compactness.A characterizations of intuitionistic fuzzy -compactness is given, and
also we investigate the image and the preimage of it under some types of functions.
Keywords: Iintuitionistic fuzzy sets, intuitionistic fuzzy topological space, intuitionistic fuzzy -compactness intuitionistic fuzzy -continuity.
The Neural Network with Fuzzy Inference Function
Shou Wei Li and KaiQuan Shi
School of Mathematics and System Science Shandong University
Jinan,Shandong 250100,
Abstract: Based on structure and algorithm of neural network and the characteristic of fuzzy inference system, the paper presents one new model of neural network which is merged with the function of fuzzy reasoning. In the model, the power of fuzzy reasoning is merged into the neuron of hidden layer so that the fuzzy neural network cound excite fuzzy reasoning automatically according to the system input,At the same time, it cound finish the nonlinear mapping using the algorithm. In the paper,we give some detailed algorithms of fuzzy rules extraction and fuzzy neural network.
Keywords: Fuzzy inference, network, rule extraction, learning algorithm
Fuzzy Satisfactional Method by Fuzzy Multi-objective Linear Problem Inrtoducing Two Fuzzy Goals from Possibility Production Function into DEA
Yashili Uemura
Faculty of Education, Mic University
Tsu,Mic,514 Japan
Abstract: Evaluation of efficiency for every DMU (Decision Making Unit) in a company is a very important issue. Thus, the studies of evaluation of efficiency are being actively carried out ,on the basic of the production function. Unit now,loglinear production function (Cobb-Douglas model) has been used for the evaluation method. This loglinear model evaluates DUMs by measuring the average. Recently, DEA (Date Envelopment Analysis) has been focused as the available method,invading for example CCR(Charnes-Cooper-Rhodes) and BBC (Banker-Charnes-Cooper) model. However, the DEA model do not have the lower limit of the production set but the upper limit of one. Furthermore, as we consider that the real problem have the production set from lower limit to upper limit,we propose the possibility production function by introducing the fuzziness into the loglinear production function. As we try to evaluate the efficiency by this possibility production function, this method can obtain two efficiency ratings: for the upper and lower limits. Though DEA and fuzzy loglinear model belong to the evaluating method in the sense of including all DMUs¡¯Date. DEA approach is that we obtain lower limit inputs by the present output, and fuzzy loglinear approach is that we obtain the possibility output by the present inputs. Making full use of difference of two approach, we try to fuse DEA and fuzzy loglinear model in the evaluation of efficiency for DMUs by introducing two fuzzy goals, where we formulate fuzzy multi-objective problem.We propose to construct two fuzzy goals by two evaluating rating for individual outputs by fuzzy loglinear analysis,and introduce this fuzzy goals into DEA. At all, by this fusion we can cover the important weak point in DEA which often evaluates one output and ignores the other outputs,and we can obtain the satisfactional evaluating ratings which considers possibility outputs from the present inputs.
Keywords: DEA, Cobb-Douglas model, fuzzy multi-objective problem.
Some Properties of Smooth Filters
A.A.Ramadan
Department of Mathematics,College of Science,King Saud University
Kingdom of Saudi Arabia
M.A.Abdel-Sattar
Department of Mathematics,Faculty of science,Cairo University
Beni-Suef,Egypt
Y.C.Kim
Department of Mathematics,Kangnung National University
Kangung,210-702,korea
Abstract: In this paper, we introduce the notion of smooth filter convergence in fuzzy topological space, Also, we study some of their properties and give examples of those.Wedefine the product of proper smooth filters. Inparticular, we investigate relations between fuzzy continuous maps and smooth filter convergence maps.
Keywords: Fuzzy topologies, smooth filters, smooth filter convergence.
On Fuzzy Preproximity Space
A.A.Ramadan
B.
Department of Mathematics,College of Science,King Saud University
Kingdom of Saudi Arabia
Y.C.Kim
D
epartment of Mathematics,Kangnung National University
Kangung,210-702,korea
M.K.El-Gayyar
Department of Mathematics,Faculty of Engineering,Suez-Canal University
Port Said,Egypt
Abstract: In this paper, we introduce the notions of fuzzy preproximity spaces and investigate some properties of them. We defind the subspaces of fuzzy preproximity space. We study the fuzzy topologies induced by a fuzzy preproximity space. Moreover, we investigate the relationships among fuzzy preproximities, fuzzy topologies and fuzzy preuniformities.
Keywords:
Fuzzy topological space, fuzzy continuous functions, fuzzy preuniform spaces, preuniformly continuous , . fuzzy preproximity space, preproximally continuous .
-convex and -quasiconvex Fuzzy Processes
Jye Chen and Ching-Jung Ting
Depaetment of Industrial Engineering and management,Yuan Ze University
Taoyuan,Taiwan 320,R.O.C
Yu-Ru Syau*
Department of Industrial Engineering, Da Yeh University
Chang-Hwa, Taiwan 515,R.O.C
Abstract: In this paper we introduce the concept of -convexity and -quasiconvexity for fuzzy sets.Based on these notions, fuzzy processes such as -convex fuzzy processes and -quasiconvex fuzzy processes are proposed and their basic properties are studied. We also investigate the relationship between these fuzzy processes and their graphs. Furthermore, we establish characterization theorems for -convex and -quasiconvex fuzzy sets.
Keywords:
-convex fuzzy sets, -convex fuzzy processes, convexity, generalized convexity.
Rough Sets on A Fuzzy Approximation Space
Supriya Kumar
De*
XLRI,Jamshedpur,C.H.Area(E)
Jamshedpur-831001,India
E-mail:skde@xlri.ac.in
Ranjit Biswas
Department of Computer Science, Hamdard University
Hamdard Nagar, New Delhi-62,India
Akhil Ranjan Boy
Department of Mathematics,Institute of Technology
Kharagpur-721302,West Bengal, India
Abstract: We define a fuzzy approximation space and study some existing as well as new results on rough sets over a fuzzy approximation space. A case-study is presented as an application of a fuzzy approximation space in knowledge engineering.
Keywords: Fuzzy set, roung set, indiscernible relation -similar, -identical,fuzzy approximation space, -dependency, degree of -dependency.
Stability of Multiple Knapsack Problem under Fuzzy
Environment
Samir Abdou Abass
Department of Mathematics and Theoretical Physics, Nuclear Research Center Atomic Energy Authority, B.O.Box,13759,Egypt
Abstract: This paper deals with multiple knapsack with fuzzy parameters in the constraints( FMKP).This problem is to assign a subset of n items to m knapsacks with maximize the total profit of the selected items. The existing results concerning the qualitative and quantitative analysis of basis notions in parametric fuzzy multiple knapsack problems. These notions are the set of feasible parameters, the solvability set and the stability set of the first kind.
Keywords:
Knapsack problem, fuzzy parameters, stability, integer programming.
Fuzzifying Topologies and Fuzzifying Proximities
A.K.Katsaras and C.G.Petalas
Department of Mathematics,University of Ioannina,
Greece
Abstract: Some of the properties of the fuzzifying topological spaces are investigated and several of the theorems on classical topologies follow from the results obtained in the paper. Also the fuzzifying proximities are introduced.
Keywords:
Fuzzifying topology, neighborhood,fuzzifying proximity, proximal convergence.
Fuzzy Topology Induced by L-fuzzy Filters
ZhenYi Liu and Ke Yun Qin
Department of Applied Mathematics.Southwest,Southwest Jiaotong University
Chengdu 610031,Sichuan
Abstract: This note is devoted to the discussion of fuzzy topology which is induced by fuzzy filters.
Keywords: Lattice implication algebra, fuzzy topology, fuzzy filter.
Categories Isomorphic to LFNS
JinXuan Fang and Huan Huang
Department of Mathematics,Najing Normal University
Nanjing Jiangsu,210097,China
Abstract: This main purpose of this paper is to prove that the categories of linear fuzzy neighborhood spaces, linear fuzzifying topological spaces and co-tower topological vector spaces are isomorphic to each other.
Keywords: Fuzzy topology, linear fuzzy neighborhood space, linear fuzziyfing topological spaces, co-tower of vector topologies.
Fixed Point Theory for Fuzzy Monotone Multifunctions
Abdelkader Stouti
Department of Mathematics,Faculty of Sciences and Techniques University Cadi Ayyad
P.O.Box 523,Beni-Mellal 23000,Morocoo
E-mail:stouti@yahoo.com
Abstract: By using two different definitions of fuzzy order, we prove the existence of maximal, minimal, least and greatest fixed points of fuzzy monotone multifunction.
Keywords: Fuzzy set, fuzzy order relation, monotone multifunction, fixed point.
The Construction of Fuzzy Sexs from A Family of Closed Intervals and Its Application in Fuzzy-valued Integrals
Hsien-Chung Wu
Department of Information Management, National Chi Nan U niversity
Puli, Nantou 545, Taiwan
Abstract: The procedures for constructing the fuzzy number and fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known ¡°Resolution Identity¡± (decomposition theorem). Under this setting, we discuss the fuzzy-valued integrals.
Keywords: Fuzzy numbers, fuzzy-valued function, fuzzy-valued integral, resolution identity, dominated convergence theorem.
Fuzzy Incidence Functions
Boniface I.Eke
Department of Mathematics,Morgan State University
Baltimore, Maryland 21251
Abstract: This paper creates a fuzzy analogue of the concept of an incidence algebra often encountered in the study of combinatorics. Starting from a crisp incidence algebra (K,P) of a locally finite partially ordered set P over a field K of characteristic 0 we create a structure (A,K,P) whose elements are a class of fuzzy subsets of called fuzzy incidence functions of P. The paper examines the properties of the fuzzy structure (A,K,P) against those of (K,P). We then proceed to use the fuzzy techniques developed here to show that, for concrete combinatorial applications, the crisp incidence algebra (K,P) can be replaced with a smaller substructure of (K,P) where is properly embeddable (as a subring) in what is usually called a reduced algebra of (K,P).
Coarsening of Fuzzy States in A Finite Continuous-time Markov Chain
D.Jayaraman
Department of Mathematics,CMB College
Coimbatore,India
K.Kadambavanam
Department of Mathematics, CMB College
Coimbatore,India
E-mail: Krajstat@etn.net
Abstract: A continuous-time Markov Chain has a wide filed of applications in Queueing theory, Inventory management, Branching process etc., In decision-making problem, a complete study of the underlying system is repuired. In this study the state space of a continous-time Markov Chain in fuzzified. For the finite continuous-time Markov Chain with fuzzy states and with coarsening of a fuzzy states, transition probabilities are defined. Chapman-Kolmogrov¡¯ s equations are verified. Numerical example is given.
Keywords: Markov Chain-transition probability-lattice of fuzzy set.
Fuzzy Penalty Cenetic Algorithm for Optimization of Network System Reliability*
Guo Long Chen and Guo Qiang Cai
Department of Computer Science and Technology, Fnzhou University
Fnzhou 35002, P.R.China
Abstract: In this paper we concentrated on the generalized problem of network system reliability optimization, namely optimizing the system reliability by keeping the balance between component reliability and redundancy number. It is a nonlinear mixed-integer programming problem (MINLP) and NP-HARD problem. Traditional approximate algorithms and heuristic algorithma both can not solve it. This paper presents fuzzy penalty genetic algorithms for this kind of network system reliability optimization problem. Fuzzy penalty fitness function will secure more rational and objective evaluation to chromosome, and guide the search properly. For simulating the feature of the evaluation factors changing constantly in nature evolution, two kinds of fuzzy fitness function are used in our algorithms. Compared with other genetic algorithms, the experimental result indicates that our genetic algorithms are efficiency and effective, and it can be applied to the above problem.
Keywords: Reliablity optimization, genetic algorithms (Gas), fuzzy fitness function, nonlinear mixed integer programming. |