The Journal of Fuzzy Mathematics
Volume 14, Number 3, September 2006
CONTENT
DETAILS
On Convex Fuzzy Mapping
E.E. Ammar
Department of matchematics,Faculty of Science
Ttanta University,Egypt
Abstract: In this paper we investigated the convexity of fuzzy mappings, and gave some their properties. We used the concept of differentiability of fuzzy mappings. Definitions and properties of the convexity are introduced, also by use the concepts of differentiability of fuzzy mappings.
Properties of The Cross Product of Fuzzy Numbers
Adrian I. Ban and Barnabas Bede
Departmen of Mathematics ,University lf Orade
Str. Armatei Romane 5,410087 Oradea, Romania
E-mail:{aiban.bbede}@uoradea. Ro
Abstract: We introduce a new operation-cross product-over fuzzy numbers, the algebraic and metric properties of this binary operation are studied. Some results regarding the expected value and the behavior lf the cross product with respect to the fuzzy Henstock integral and the pointwise differentiability of fuzzy-number-valued functions are obtained. The consistency of the cross product with the classical error theory is proved.
Keywords: Fuzzy number, cross product , fuzzy Henstock integral , fuzzy differential , expected value.
A New Partition of Formula Set F(S) Based on R-operator
Cheng Han
Yancheng Teacher¡¯s College, Jiangsu 224002 P,R. China
E-mail:hanhan@163.com
Wenyan Xu and Guojun Wang
Institute of Mathematics ,Shaanxi Normal University ,Xi¡¯an 710062,P.R.China
E-mail£ºxuwenyan2003@hotmail.com (Wenyan Xu)
E-mail: gjwang@snnu.edu.cn.(Guojun Wang)
Abstract£º This paper presents an exact expression of V (A) which is an unique formula A of formula ser F(S) in revised Kleene system . It also obtains a sixteen-classification congruence partition about standard negation¦è,and discusses each one¡¯s closeness about MP and HS operations. Moreover. the case based on general strong negation is also surveyed.
Keywords: -algebra, validation set domain, partition, K ¨Cformula, nilpotent minimums, strong negation.
Properties of Fuzzy Vectors
E.Eslami and F.Khosropour
Department of Mathematics,Shahid Bahonar University of Kerman Kerman,Iran
Abstract: We define the concept of inner product and cross product of two fuzzy vectors and
Discuss the properties of them.We also define linear transformation for the fuzzy vectors based on linear transfrmations on v3. We find eigenvalues and corresponding fuzzy eigenvectors,and prove some related theorems.
Keywords: Fuzzy vector,Fuzzy dot products,Fuzzy cross product.
Characterization of The Stabiliy Set of The Second Kind for Parametric Nodifferentiable Multiobjective Convex Programming Problems with Fuzzy Parameters
Mohamed .S.A.Osman
Professor of Mathematics, Vice Dean of the Higher Technological Institute,
Tenth of Ramadan City,Egypt
Mona.M.M.M.Tarad
Lecturer of pure Mathematics,Univ.College for women,Ain ShamsUniv.Cairo,Egypt.
Asmahan.A.Khdour
Faculty of Compters and Informaion,Damascus Univ,Damascus,Syria
Abstract: This paper deals with nondifferentiable multiobjective convex nonlinear programming problems with fuzzy parameters in both of the objective functions and in the constraints. These fuzzy parameters are characterized by fuzzy numbers. The existing results concerning the qualitative analysis of some basic notions in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems without any differentiability assumptions under the concept of ¨CPareto optimality. An algorithm for the determination of the stability set of the second kind is also presented. An illustrative example is given to clarify the obtained results.
Keywords: Fuzzy numbers, nonlinear programming, Kuhn-Tucker conditions, multiobjective optimization.
Categories of Fuzzy Sets and Fuzz Groups and The Lattices Of Subobjects of These Categories
Aparna Jain
Department of Mathematics,Shivaji College,University of delhi.
Ring Road,Raja Gaeden,New dejhi,India
E-mail:jainaparna@yahoo.com
Naseem Ajmal
Department of Mathematics,Zakir Hussain college,University of Delhi,
J.L. Nehru Marg New Delhi, India.
Abstract: In this paper,we define a fuzzy subgroup of a given fuzzy group by using the cincept of a subobject in a newly constructed category of fuzzy groups. We also introduce a new categouy S,whose object class is the calss of all fuzzy sets in all sets and a morphism between two S ¨Cobjects is a family of mappings between their level subsets satisfying certain conditions. Then we define the concepts of lower well ordered and upper well ordered fuzzy subsets. The notion of fuzzy subset of fzzy set is introduced by using the concept of subobject in this category. Finally,we prove that S(¦Ì)£¬the collection of all fuzzy subsets. The notion of fuzzy set¦Ì is a complet lattice if ¦Ì satiafies the property of all fuzzy subsets of being low or upper well ordered. Finally, we prove that ? (¦Ì), the collection of all fuzzy subgroups of a fuzzy group ¦Ì, is a complete lattice¦Ì is lower or upper well order.
Keywords: Fuzzy sets,fuzzy groups,level subset,lattices,category.subobject.
Interval-valued Fuzzy Matrices
Amiya K.Shyamal and Madhumangal Pal
Department of Applied Mathematics with Oceanology and Computer
Programming Vidyasagar University,Midnapore-,INDIA.
*E-maiil:madhumangal@lycos.com
Abstract: In his paper we introduce interval-valued fuzzy matrix (IVFM) as the generalization of interval-valued fuzzy sets. Some essential unary and binary operations of IVFM and some special types of IVFMs i.e., symmetric, reflexive, transitive and idempotent, constant etc. IVFMs are defined here. The idea of trace, convergence, periodicity, determinant and adjoint of IVFM are also defined. Also, a number of properties of IVFM are presented here.
Keyword: Fuzzy set, interval-valued fuzzy set, interval-valued fuzzy matrix, interval-valued fuzzy determinant.
Fuzzy ¦Ã-irresolute Mappings on Fuzzy Topological Spaces
Young Bin Im, Eun Pyo Lee and Se Won Park
Department of Mathematics, Seonam University, Chonbuk 590-711,Korea
Abstract: In this paper, we study the characteristic properties of fuzzy ¦Ã-irresolute mappings on fuzzy topological spaces.
Keywords: Fuzzy ¦Ã-irresolute mapping,fuzzy ¦Ã-interior,fuzzy ¦Ã-closure
Genetic Based Fuzzy Approach to Multiobjective Chance Constrained Programming Problems with Continunous Random Variable Coefficients
R.k.Jana* and M.P.Biswal
Department of Mathematics Indian Institute of Technology,
Kharagpur Kharagpur-721302,India
*Email:rabin@maths.iitkgp.ernet.in
Abstract: A method for solving multiobjective chance constrained programming problems is presented in this paper. It consists of a stochastic simulation-based genetic algorithm and fuzzy programming technique. Some or all coefficents of objective functions as well as chance constraints of the problems are assu,ed to follow comtinuous probability distributions. Using the stochastic simulation-based genetic algorithm, ideal solutions are obtained corresponding to each objective function. Then fuzzy programming formulations of the problems are developed for linear and hyperbolic membership funtions. Finally, compromise solutions are obtained by using the stochastic simulation-based genetic algorithm again and obtained solutions considering different membership functions are compared. The method leads to an efficient as well as an optimal compromise solution. Numerical example are also presented to illustrate the methodology.
Keywords: Chance Constrained Programming, Fuzzy Mathematical Programming, Multiobjective Programming, Linear ad Hyperbolic Membership Function, Stochastic Simulation, Genetic Algorithm.
Applications of Metatheorem in Ideals of semigroups
Ravi Srivastva
Department of Mathematics,Swami,Shraddhanand College.
University of Delhi,Alipur,Delhi-110036,India
Anand Swaroop Prajapati
Department of mathematics,A.R.,S,D.College.
University of Delhi,Dhaula kuan,Now Delhi-110021,India
Abstract: Tom Head [2] formulated a ¡°Metatheorem¡±in 1995 to obtain fuzzy versions of classical results. Inthis paper we provide various applications of this theorem by establishing fuzz analogs of results pertaining to the notions of ideals,biideals,interior establish several characterizations of regular,intraregular and completely regular semigroups.we also provide a necessary and sufficient condition for a semigroup to be a semilattice of groups and for a semigroup to be a semilattice of semi-simple semigroups.
Keywords: Semigroup,ideals,biideals,semiprime ideals,interior ideals and quasiideals.
Generalized Fuzzy Fractional 0-1 Programming
J.K.Dash,G,Panda,S.Nande
Department of mathematics,Indian Institute of Technology,Kharagpur-721302,West Bengal,INDIA E-mail:sananda@maths.iitkgp.ernet.in,geetanjali@maths.iitkgp.ernet.in
Abstract: This paper deals with a generalized fractional programming problem in which the objective is formed in fuzzy environment and the decisions are restricted to be 0 or 1.The solution method isjustified through anumerical example.
Keywords: Generalized fractional programming, 0-1 fractional programming, fuzzy paeamter, ¦Á-cut of a fuzzy number.
Permanent of Matrices over Inclines and Its Applications
Song Chol Han
Department of Mathematics and Mechanics,Kim Il sungUniversity,Pyongyang,
D.P.RKorea.
Department of Mathematics,Beijing Normal University,berjing 100875,P.R.China
Hong Xing Li and Yun Dong Gu
Department of mathematics,Bijing Normal University,Beijing 100875,P.R.China
Abstract: Let L be an incline with 0 and 1.This paper firstly defines the permanent of a matrix over L and proves the expansion theorem for it. Secondly,it is proved that the permanents of the invertible matrices over L are equal to 1,and for the matrix equation over L where A is invertible,the expression of its solution by the permanents is obtained.Thirdly,for a matrix over an incline L without zero divisirs,two necessary and sufficient conditions for its permanent being equal to 0 are studied. Finally,two corollaries in an article of Yi and Liu are pointed out being faulty.
Keywords: Incline, permanent, invertible matrix, Laplace¡¯s expansion theorem, cramer¡¯s rule, L-fuzzy matrix.
Rank and Perimeter Preservers of Rand-1 Fuzzy Matrices
Seok-Zun song and Kyung-Tae Kang
Department Mathemaytics,Cheju National University ,Jeju690-756,Republic of Korea
E-mail:szsong@cheju.ac.kr E-mail:kangkt@cheeju .ac.kr
Abstract: For a fuzzy rank-1 matrix , we define the perimeter of as the number of nonzero entries in both a and b .we characterize the linear operators that preserve rank and perimeter of fuzzy rank-1 matrices .Conseqquently ,we obtain that a linear operator T preserves the rand and perimeter of rank-1 matrices if and only if it has the from with appropriate permutataion matrices P and Q and a positive matrix B,where denotes the Hadamard product.
Keywords: Linear operator; perimeter; (P,Q,B)-operator.
On Normed Lattice Implication Algebras
K. Y. Qin
Department of applied mathematic, Southwest Jiaotong University,Chengdu,Sichuan660031,China
E-mai address:keyunqin@263.net
Z.Pei
College of Computer and Mathematical-physical, Xiha University, Chengdu,sichuan610039,China
E-mail address:pqyz@263,net
Y. B Jun
Department of mathematic education,
Gyeongsage National University, Chinju660-701,Korea
E-mail address:ybjun@gsnu.ac.kr
Abstract: The concept of normed lattice implication algebras is introduce, and the notion of a convergent sequence and a Cauchy sequence in a normed lattice implication algebra is considered. We show that (i) every implication open/closed sphere is quasi-subalgebra and(ii)every convergent sequence in a normed lattice implication algebras is a Cauchy sequence. We prove that if a subsequence of a subsequence of a Cauchy sequence in a normed lattice implication algebra converges to a point, then the Cauchy sequence itself converges to the same point.
Keywords: Norm, normed lattice implication algebra, implication distance, \/ - distance, implication open/closed sphere,Cauchy sequence.
Fuzzy Supra Interior Operators
Y.C.Kim
Department of Mathematics,Kangnung National University,Kangnung,210-702,Korea
S.E.Abbas
Department of Mathematics,Faculty of Science,Sohag,Egypt
Abstract: We study some properties of fuzzy (supra) interior operators in the framework of Fuzzy (supra) topology and fuzzy (semi) topogenous order.We investigate relationships among fuzzy (semi-) topogenous structures,fuzzy(supra)topologies and fuzzy (supra) interior operator.
Keywords: Fuzzzy (semi-) topogenous order, Fuzzy (supra)interior operator, Fuzzy (supra-)Topology.
Fuzzy p-regular Spaces
Yong Chan Kim and Biljaana Krsteska
Department of Mathmatics,Kangnung National University,Kangung,Kangwondo210-702,Korea
Department of Mathematics and Natural Science,P.O.BOX.162Skopje,Macedonia
Abstract: We introducefuzzy (pre,almost) p-regular spaces in Sostaks fuzzy topological Spaces[11].Using the r-preclosed sets,we define r-(r-¦È-,r-p¦È) preclester points and their properties.Moreover£¬we investigate the relations among r-(r-¦È-,r-p¦È) Precluster points,fuzzy(pre,almost) p-pregular spaces and their functions.
Keywords: Fuzzy topology, r-preciosed sets, r-(r-¦È-,r-p¦È) preciuster pointsr-fuzzy (pre,Almost) p-regular spaces,(strongly,¦È-)preirreslute mappings.
Fuzzy Markov Chains
James J.Buckley
Department of Mathematics,University of Alabama at Birmingham
Birmingham,Alabama,35294,USA
E-mail:buckley@math.uab.edu
Thomas Feuring
Department of Electrical Engineering and Computer Science
University of Siegen H?lderlinstr.3,57068 Siengen,Germany
E-mail:feuring@informatik.uni-siegen.de
Yoichi hayashi
Department of Computer Science,Meiji University
Tama-ku,Kawasaki 214-8571,Japan
E-mail:hayashiv@cs.meiji.ac.jp
Abstract: We first review some of the basic results of finite Markov chains based on probability theory,then we present fuzzy finite Markov chains bases on possibility theory,and compare the results of the two theories Then we introduce finite horizon Markovian decision processes based on fuzzy Markov
chains and study an example in detail showing our solution procedure.
Keywords: Markov chains, possibility theory.
Some New Common Fixed Point Theorems in Fuzzy Metric Space
under Strict Contractive Conditions
Sushil Sharma and Deepika Bamboria
Dpartment of Maathematics,Madhav Vigyan Mahavidhyalaya Vikram University,Ujjain-456010,India
E-mail:sksharma2005@yahoo.com,deepika bamboria@rediffmail.com
Abstract: The main purpose of this paper is to give some new common fixed point theorems in fuzzy metric space under strict contractive conditions for mappings satisfying new property
Keywords: Common fixed point;Compatible maps;Weakly compatible maps,¡ |