The Journal of Fuzzy Mathematics
Volume 19, Number 4, December 2011
CONTENT
DETAILS
On Graphs and Core of Fuzzy Sets
Jiuping Xu and Zezhong Wu
Uncertainty Decision-Making Laboratory, School of Business and Administration, Sichuan University, Chengdu 610064£¬ China
Chengdu University of Information Technology, Chengdu 610225, China
Abstract:
In this paper, graph and strictly graph on fuzzy sets are introduced and discussed extensively. Then by using these concepts, different equivalent ways in which the decomposition principia and the extension principles can be expressed and investigated. Existence theorems on the core of fuzzy sets and properties of the set of core on fuzzy sets are considered under weakly conditions. And an application to fuzzy mappings is considered.
Keyword:
Graph of fuzzy sets, Strictly graph of fuzzy sets, Core of fuzzy sets, Extension principle.
Fuzzy Structures of b-open Sets
Young Bae Jun,Seong Woo Jeong,Hyeon Jeong Lee and Joon Woo Lee
Department of Mathematics Education (and RINS) Gyeongsang National University Chinju 660-701£¬ Korea
E-mail:skywine@gmail.com(Y.B.Jun),liveinworld@hanmail.net(S.M.Jeong),jfield@hanmail.net(H.J.
Lee),jwlee_ angel@hanmail.net(J.W.Lee)
Abstract:
As a new class of generalized open sets in a topological space, the notion of b-open sets is introduced and studied in [3]. In this paper the fuzzy trend of b-open sets is considered. The notions of fuzzy b-open sets and fuzzy b-interiors in a fuzzy topological space are introduced. Characterizations of a fuzzy b-open set are provided.
Keyword:
Fuzzy b-open set, Fuzzy b-interior.
On g-distance in Fuzzy Trees
K.Sameena and M.s.sunitha
Department of Mathematics, National Institute of Technology Calicut-673601 India
E-mail:sameenakalathodi@gmail.com E-mail:sunitha@nitc.ac.in
Abstract:
In this paper, we carry out a study of g-distance in a fuzzy tree G and its associated maximum spanning tree F. we show that g-eccentricity of a node v denoted by ,is the same in G and F, so that , and G and F have same set of g-eccentric nodes as well as fuzzy end nodes. Also, we show that a g-eccentric node of a fuzzy tree G is a fuzzy end node of G and a node is a g-eccentric node of a fuzzy tree iff it site a g-peripheral node of G.
Keyword:
Strong arc, g-distance, Fuzzy end node, Fuzzy tree, Maximum spanning tree.
Fuzzy Congruences on A Lattice and Homomorphism Theorems
M.J.Rani and N.R.Mangalambal
Department of Mathematics St.Joseph¡¯s College, Irinjalakuda, Kerala India-680121
E-mail:krvarghese@rediffinail.com
E-mail:thottuvai@sancharnet.in
Abstract:
In this paper the concepts of a fuzzy equivalence relation and fuzzy congruence relation on a lattice are discussed. Also the concept of similarity class for a fuzzy equivalence relation is introduced. It is seen that the set of all similarity classes for a fuzzy congruence relation is a lattice under suitably defined join and meet operations, which we call the factor lattice X/R corresponding to the fuzzy relation R on the lattice X. consequently given a lattice homomorphism where X and Y are lattices, by defining a fuzzy relation on X corresponding to a fuzzy relation R to Y, an isomorphism has been derived.
Keyword:
Fuzzy congruence, similarity class, factor lattice.
A Fuzzy Approach to Homotopy Theory
Tazid Ali
Department of Mathematics, Dibrugarh Uniersity , Dibrugarh-786004, Assam, India
E-mail:tazidali@yahoo.com
Abstract:
In this paper, first we have proved a fuzzy version of pasting lemma. Then we have introduced the concept of fuzzy homotopy and studied some properties of fuzzy homotopic mappings.
Keyword:
Fuzzy pasting lemma, Fuzzy homotopy, Fuzzy contractible space
Common Fixed Point Theorems in Intuitionisitc Fuzzy Metric Spaces under Compatible Mappings of Type()
H.M.Abu-Donia
Department of Mathematics, Faculty of Science, Zagazing University, Zagazing , Egypt
A.S.Salama
Department of Mathematics, Faculty of Science, Tanta University , Tanta, Egypt
Abstract:
The purpose of this paper is to introduce some typeset of compatibility of maps. We prove some commom fixed point theorems for mappings satisfying some conditions on intuitionistic fuzzy metric spaceship which defined by J.H.Park[25].
Keyword:
Common fixed point, metric spaces, fuzzy metric spaces, intuitionistic fuzzy metric spaces, compatible mappings of type (), compatible mappings of type ()
On Q-covering Dimension
Shakeel Ahmed
Department of Mathematics, Govt. Degree College ThannaMandi, ThannaMandi-185212£¬Jammu and Kashmir, India
E-mail : shakeelar2002@yahoo.co.in
Abstract:
There are many types of open covers in fuzzy topology (One can see pages 187-188 of liu-luo [15]). One among these open covers is called Q-open cover. In this paper, we have introduced the concept of Q-covering Dimension by using Q-open cover and studied its various properties.
Keyword:
Q-covering Dimension, Q-open cover , Good extension property , Continuity.
Retraction of Chaotic Black Hole
A.E.El-Ahmady
Mathematics Department, Faculty of Science, Taibah University, Madinah, Saudi Arabia
Mathematics Department,Faculty of Science, Tanta University, Tanta, Egypt
Abstract:
Our aim in the present article is to introduce and study a new type of metric, namely chaotic space time. The geodesics of a spherically symmetric charged black hole will be obtained from the view point of Lagrangian equations. Types of the chaotic retraction of the chaotic black hole are presented. The variations of the charges under the retraction of chaotic black hole are defined. The retractions restrictions imposed on the mass are also discussed. The relationship between the retraction of geometry and pure chaotic black hole are deduced. Some applications concerning these relationship are presented.
Keyword:
Retraction, geodesics, chaotic space time
Fuzzy Filters and Fuzzy Ideals in BE-algebras
B.L.Meng
Department of Basic Courses, Xian University of Science and Technology Xian 710054£¬ P.R.CHINA
E-mail :mengbl-100@yahoo.com.cn
Abstract:
In the present paper we introduce the notion of fuzzy filters in BE-algebras and establish some of its important proper-ties. We give some equivalent conditions of fuzzy filters, especially prove that in transitive BE-algebras, the notion of fuzzy filters is equivalent to one of fuzzy ideals.
Keyword:
BE-algebra, transitive BE-algebra, (fuzzy) ideal, (fuzzy) filter.
Partial Sequential Probability Ratio Test with Fuzzy Observations
Ruma Talukdar
Department of Statistics,Cotton College,Guwahati, Assam.India-781001
E-mail:rumatalukdar_gogo @rediffmail.com
Hemanta K. Baruah
Department of Statistics,Gauhati University. Assam.India-781014
Abstract:
Partial Sequential Probability Ratio Test (PSPRT), developed by Read (1971), for discriminating between two simple hypotheses concerning Koopman-Darmois parameters, has been fuzzified. The associated parameters and variables are considered to be triangular fuzzy numbers and the theory of fuzzification has been applied to obtain the fuzzy Average Sample Number functions and Operating Characteristics of the PSPRT. This is followed the applications of the results obtained, to some numerical example.
Keyword:
Triangular fuzzy number, fuzzy membership function, interval of confidence, fuzzy operating characteristic function, fuzzy average sample number function.
Computation of multi-objective Stochastic Transportation Problems Involving Normal Distribution with Joint Constraints
Deshabrata Roy Mahapatra,Sankar Kumar Roy
Department of Applied Mathematics with Oceanology and Computer Programming as agar University, Midnapore-721102, West Bengal, India
E-mail:sankroy-2006@gmail.com Cell No(+91)9439217733
Mahendra Prasad Biswal
Department of Mathematics,Indian Institute of Technology Kharapur-721302, West Bengal, India
E-mail:mpb@maths.iitkgp.ernet.in
Abstract:
In this paper, we consider the mathematical model of multi-objective stochastic transportation problem and constraints have joint probability distribution. We focus on the solution procedure of multi-objective stochastic transportation problem associated an inequality type of joint constraints in unbalanced transportation problem in which all parameters (supply and demand) are represented by random variables of normal distribution and objectives are in nature of conflicting and ambiguous. The initial stage of simplification with solution of this mathematical programming, the probabilistic problem is converted into an equivalent deterministic non-linear problems under chance constrained programming. Then the fuzzy programming technique with membership function has been applied to this specified problem to obtained the optimal compromise solution in which the decision maker fully satisfied with it. Lastly a numerical example has provided to illustrate the methodology.
Keyword:
Transportation Problem, Stochastic Programming, Multi-objective Decision Making, Fuzzy Programming, Chance Constrained Programming.
Cofuzzy Graphs
Muhammad Akram
Punjabi University College of Information Technology, University of the Punjab, Old Campus, Lahore-54000, Pakistan.
E-mail:makrammath@yahoo.com, m.akram@pucit.edu.pk
Abstract:
We introduce the notion of a cofuzzy graph and we study some methods of construction of new cofuzzy graphs from the old. We compute the degree of a vertex in Cartesian product, composition and union of the given cofuzzy graphs in terms of the degree of ver-tices of the graphs in some particular cases. We give automorphism of the cofuzzy graphs. We give properties of regular and totally cofuzzy graphs. We also present self complementary complete cofuzzy graphs.
Keyword:
Cofuzzy graphs, Degree of a vertex, Automorphism, N-regular cofuzzy graphs, Self complementary.
Orthogonality of A Fuzzy Set
Ranjit Kumar Misra
Department of Mathematics, Darrang College, Tezpur Tezpur-784001 Sonitpur, Assam, INDIA.
Abstract:
In this paper we have introduced orthogonality of a fuzzy subset and some basic results of the fuzzy orthogonal are also established.
Keyword:
Fuzzy orthogonal, bilinear form, semi-norm, weak topology, fuzzy linear subspace, fuzzy weakly closed set.
Economic Freedom Ranking of 171 Countries in Year 2009:A Weighted Average Approach
John N.Mordeson*,Hilary C.Wething**,Michel L.Mallenby*,Douglas W.Mallenby*** and Terry D.Clark****
*Department of Mathematics, E-mail: mordes@creighton.edu, mmall@creighton.edu
** Department of Economics, E-mail: hilarywething@creighton.edu
*** Department of Business Administration, E-mail : douglasmallenby@creighton.edu
**** Department of Political Science, E-mail: tclark@creighton.edu
Creighton University, Omaha, Nebraska, 68178
Abstract:
The Heritage Foundation has measured the economic freedom of countries for the past fifteen years. They determine the economic freedom score for a country by taking the average of scores of ten components of economic freedom. In this paper, we use a weighted average approach. We use two different mathematical techniques, the Guiasu method and the analytic hierarchy process. Our rankings of the economic freedom of the method and the analtic hierarchy process. Our rankings of the economic freedom of the countries are highly correlated to the ranking of the Heritage Foundation. We also find a new method to obtain the weights using a generalization of Dempster-Shafer theory. The weights are values of certain plausibility functions that are determined from optimization problems.
Keyword:
Economic freedom measurements; Guiasu method; analytic hierarchy process; Dempater-Shafer theory; Yen¡¯s method; correlation; population means.
Characteristics of IF functions for Optimization Problems
Lisy Cherian
Mar Thomas College for Women, Perumbavoor, Kerala, 683542 India
E-mail: lissychearian@gmail.com
Abstract:
The concept of Intuitionistic Fuzzy (IF) Set , a generalization of fuzzy set, proposed by Krassimir T. Atanassov in 1983, is well suited to dealing with vagueness and uncertainly. Most of the decision making problems pertaining to real life situations take place in certain environment. In this paper we have introduced certain preliminary concepts in IF environment and proved that optimum of the objective (s) or goal (s) of an optimization problem in the IF environment is the same as the optimum of another function if the IF function is convex and its membership and nonmembership functions are continuous.
Keyword:
Intuitionistic Fuzzy Quantity, IF convexity, IF injectivity, IF continuity, IF function, IF Maxinizing set.
Numerical Reparesentation of A max-min Transitive Fuzzy Ordering
Ismat Beg
Centre for Advanced Studies in Mathematics, Lahore University of Management Sciences, 54792-Lahore , Pakistan
E-mail: ibeg@lums.edu.pk
Samina Ashraf
Department of Mathematics, COMSATS Institute of Information Technology, Lahore ,Pakistan
Abstract:
Real-valued maps are constructed which transform the universe X to a subset of real numbers along with a max-min transitive symmetric fuzzy order L on X. it is also proved that these maps are continuous in a natural topology on X.
Keyword:
Fuzzy ordering; Debreu¡¯s gap lemma; Numerical representation.
Some Results on Fuzzy Metric Spaces
G.Rano,T.Bag and S.K.Samanta
Department of Mathematics, Visva-Bharati, INDIA
E-mai: gobardhanr@gmail.com, E-mail: tatapadavb@gmsil.com, E-mail:syamal_123@yahoo.co.in
Abstract:
Following the concept of fuzzy metric introduced by Kramosil and Michalek, a more general definition of fuzzy metric is given in this paper and a decomposition theorem of this duzzy metric into a *-quasi metrics exist. By taking ¡®min¡¯ as a particular t-norm, a decomposition theorem of a fuzzy metric into a famil of crisp metrics is deduced. Concept of a complete fuzzy metric space is introduced and Cantor¡¯s intersection theorem is proved with the help of decomposition theorem in fuzzy setting.
Keyword:
Fuzzy metric, fuzzy metric space, t-norm, *-quasi metrics.
The Notion of Fuzzy Banach Algebra
I.Sadeqi,F.Solaty Kia and A.Amiripour
Department of Mathematics, Sahand University of Technology, Tabriz-Iran
Abstract:
In this paper we frist introduce the notion of fuzzy and -fuzzy Banach algebras and then shown that if for every , is a Banach algebra then the resulting fuzzy normed linear space (X,N) is a fuzzy Banach algebra. By an example we point out that the converse dose not hold true in general, while it remains true if (X,N) is an -fuzzy Banach algebra. Therefore, the spectrum of the category of fuzzy Banach algebras is broader than the classical case and the study of fuzzy version of some results of Banach algebras is of great importance.
Key word:
Fuzzy normed linear space, Fuzzy Banach algebra , -fuzzy Banach algebra
Interval-valued Fuzzy Structures on Lie Superalgebras
Wenjuan Chen
School of Mathematical Science, University of Jinan, Jinan ,Shandong,250022£¬ P.R.China
E-mail:wjchenmath@gmail.com
Muhammad Akram
Punjab University College of Information Technology, University of the Punjab. Old Campus, Lahore-54000, Pakistan
E-mail: m.akram@pucit.edu.pk
Abstract:
In this paper we introduce the notions of interval-valued fuzzy Lie sub-superalgebras and Lie ideals of Lie superalgebras and present a number of interesting properties. We then discuss the homomorphisms between the Lie sub-surperalebras and Lie ideals of Lie superalgebras and their relationship between the domains and the co-domains of the interval-valued fuzzy Lie sub-superalgebras and Lie ideals under these homomorphisms.
Keyword:
Lie Superalgebras; Interval-valued fuzzy Lie sub-superalgebras; Interval-valued fuzzy (Lie) ideals; Homomorphisms.
The Refinement of Fuzzy Topogenous Order and It¡¯s Properties
Hong Wang
College of Science, Southwest University of Science and Technology Mianyang 621000£¬ Sichuan, P.R.China
Abstract:
In this paper, the concept of fuzzy (semi-) topogenous order, fuzzy syntopogenous structure in the framework of fuzzy topologies, fuzzy proximities and fuzzy uniformities have been introduced , the refinement of fuzzy (semi-) topogenous order have been researched. Some important properties of them have been obtained.
Keyword:
Fuzzy (semi-) topogenous order , fuzzy topologies, refinement.
Failed State Ranking of 177 Countries in Year 2009£ºA Weighted Average Approach
John N.Mordeson,Nelson C.Fong,Alex Pham
Department of Mathematics, Creighton University, Omaha, Nebraska 68178
E-mail:mordes@creighton.edu, ncfong@creighton.edu, Alex-Pham@creighton.edu
Terry D.Clark
Department of Political Science, Creihgton University, Omaha, Nebraska, 68178
E-mail: tclark@creighton.edu
Abstract:
The Fund of Peace combines social science technique with information technology to provide a conceptual framework and data gathering technique for measuring conflict risk. The fund for Peace provides a score for each country with respect to each of the 12 indicators. These 12 scores are then averaged to obtain a final score for each country. This final score gives a measure of the risk of failure for a country. In this paper, we take a weighted average approach. The weights are determined by expert opinion and mathematical techniques. The mathematical techniques are the Analytic Hierarchy Process, the Guiasu method, and a method based on Dempster-Shafer theory.
Keyword:
Failed states; Fund for Peace; analtic hierarchy process; Guiasu method; dempster-Shafer theory
Generalized Fuzzy Rough Sets Based on Complete Residuated Lattices
Hongyan Xing
Faculty of Applied Mathematics , Guangdong University of Technology Guangzhou, 510090£¬ P.R.China
E-mail :928hongy@163.com
Abstract:
In this paper, we propose a kind of generalized rough sets based on complete residuated lattices in which the binary relation R is presented as from UW to , rather than working over a fixed universal set U. the concept of -valued relations and approximation operators together with their connections between them are examined. Specifically, based on complete residuated lattice-valued logic, -valued rough sets are defined using the product operator and item residuated lattice-valued logic, -valued rough sets are defined using the product operator and its residuum provided by the residuated lattice . Depending on classes of binary fuzzy relations R from UW to , we define several classes of -valued rough sets and investigate properties of these classes.
Keyword:
Residuated lattice-valued logic, Approximation operators, -valued relations, -valued rough sets
On (L,M)-fuzzy Interior Spaces
S.E.Abbas
Department of Mathematics, Facutly of Science, Sohag university, Sohag 82524£¬ Eypt.
E-mail :sabbas73@yahoo.com
Won Keun Min
Department of Mathematics, Kangwon National University, Chuncheon, 200-701£¬ Korea.
E-mail :wkmin@kangwon.ac.kr
Abstract:
In this paper, we study some properties of (L,M)-fuzzy interior spaces. Also, we investigate the relations between (L,M)-fuzzy interior spaces and (L,M)-ifts. In particular, we prove the existence of product (L,M)-ifts¡¯s and (L,M)-fuzzy interior spaces. We investigate the relations between them.
Keyword:
(L,M)-intuitionistic fuzzy topological spaces. (L,M)-fuzzy interior spaces. Category |