The Journal of Fuzzy Mathematics
Volume 16, Number 3, September 2008
CONTENT
DETAILS
Tietze Theorem and Urysohn¡¯s Lemma for Fuzzy G??-normal Sp
aes
E. Roja, M. K. Uma
Department of Mathematics, Sir Sarada College for Women,Salen-636016 Taminadu
G. Balasubramanian
Ramanujan Institute for Advanced Study in Mathematics
University of Madras Chennai-600005 Tamilnadu
Abstract: In this paper, the concept of fuzzy G??-normal spaces is introduced. Urysohn¡¯s Lemma for fuzzy G??-normal spaces and Tietze extension theorem for fuzzy G??-normal spaces are established
Keywords:
The ¦Ò-interior, the ¦Ò-closure, fuzzy G??-normal spaces, generalized fuzzy F¦Ò set and lower/upper fuzzy semi G??-continuous.
Vague Normal Subgroups
Sevda sezer
Department of Mathematics, Faculty of Science and Arts
Akdeniz University, 07058-Antalya/Turkey
E-mail: sevdasezer@akdeniz.deu.tr
Abstract: Although the general theory of vague algebraic notion has been established by Demirci, the concept of vague normal subgroup has not yet been examined. So, the concept of vague normal subgroup is introduced, and some basic properties of this concept are obtained in this work.
Keywords: Fuzzy equality, strong fuzzy function, vague group, generalized vague subgroup, vague normal subgroup.
On Fuzzy C-compact Spaces
G. Palani Chetty
Department of Mathematics I. R. T. Polytechnic College
Krihnagiri-635 108, Tamilnadu, INDIA
G. Balasubramanian
The Ramanujan Institute of Advanced Studies in Mathematics
University of Madras Chepauk, Chennai-600 005, INDIA
Abstract: In this paper the concept of fuzzy C-compactness is introduced in ordinary fuzzy topological spaces as well as in fuzzy bitopological spaces. In both cases interesting properties and characterizations of these spaces are discussed.
Keywords: Fuzzy C-compact, Fuzzy H-closed, Pairwise fuzzy C-compact, Pseudo fuzzy C-compact, Semi fuzzy C-compact, Adjoint fuzzy topology, Pairwise fuzzy C-compact?, Fuzzy filter base, Ultra filter base.
Analysis of Fuzzy Markov Model Using Fuzzy Relation Equations
R. Sujatha and B. Praba
Department of Mathematics, SSN College of Engineering Kalavakkam 603110
E-mail: brprasuja@yahoo.co.in
Abstract:
Fuzzy Markvo Model is widely applied to model many practical situations and performing steady state analysis is essential to study the long realization of the model. In this paper we propose a method to view any fuzzy Markov model using fuzzy relations and we have analyzed the steady state behavior using fuzzy relation equations.
Keywords: Fuzzy Markvo model, fuzzy relations, fuzzy relation equations, steady state analysis
Urysohn Lemma and Tiezte Extension Theorem for Fuzzy Pre-normal Spaces
E. Roja and M. K. Uma
Department of Mathematics, Sri Sarada College for Women, Salem-636016 Taminadu, India
G. Balasubramanian
Ramanujan Institute of Advanced Study in Mathematics,
University of Madras, Chennai-600005 Taminadu, India
Abstract: In this paper fuzzy pre-normal spaces is introduced and discussed on some interesting properties and characterization of fuzzy pre-normal spaces are done. The purpose of this paper is also to discuss Tietze theorem and Urysohn¡¯s Lemma for fuzzy pre-normal spaces.
Keywords: Fuzzy pre-normal spaces, Fuzzy lower (resp. upper) semi pre-continuous.
Generalized Closed Sets in Intuitionistic Fuzzy Topology
S. S. Thakur
Department of Applied Mathematics Government Engineering
College
Jabalpur (M.P.) 482011, India
E-mail: samajh_singh@rediffmail.com
Rekha Chaturvedi
Department of Mathematics Mata Mahila Mahavidyalaya
Jabalpur (M.P.) 482001, India
Abstract: The aim of this paper is to extend the concept of generalized closed sets in intuitionistic fuzzy topological spaces. Furthermore the concept of intuitionistic fuzzy GO-connectedness and intuitionistic fuzzy GO-compactness have been introduced and studied.
Keywords: Intuitionistic fuzzy topology, Intuitionistic fuzzy points, Intuitionistic fuzzy g-closed sets and Intuitionistic fuzzy g-open sets, Intuitionistic fuzzy GO-connectedness and Intuitionistic fuzzy GO-compactness.
Selection of The Optimal Traffic Counting Locations and Estimation of OD Trip Matrix from Fuzzy Traffic Counts
C. M. Sushama
Lecturer, Department of Mathematics, National Institute of Technology,
Calicut, 673601. KERALA India
E-mail: sushama@nitc.ac.in
Revati Rajagopalan
Professor,
Department of Mathematics, National Institute of Technology,
Calicut, 673601.KERALA India
E-mail: revati@nitc.ac.in
Abstract: The estimates of OD matrix are an essential source of traffic demand information and transportation planning process, and for the management and control of transportation system. Generally the quality of an estimated OD matrix depends much on the selection of links as well as the reliability of the input data. The purpose of this study is to formulate a model that selects the optimal links, that is, to choose minimum number of most essential links for a reliable OD matrix estimate, and to suggest efficient solution algorithm for the estimation. As a first step of the procedure the optimal number of links and their locations are identified. Considering the practical difficulty of obtaining precise values for the traffic counts at the aforementioned locations, in the next step, fuzzy values are suggested with appropriate membership functions. Using Wardrop¡¯s principle a cost minimization problem satisfying the link traffic counts is formulated. Solution procedure presents a fuzzy set solution for the above model. Computational results on a sample network are also included.
Keywords: OD matrix, traffic counting locations, fuzzy link counts.
Intuitionistic Fuzzy Almost Compactness in Intuitionistic Fuzzy Topological Spaces
M.N.Mukherjee
Department of Pure Mathematics University of Calcutta
35 Ballygunge Circular Road, Calcutta 700019
Sumita Das
Sammilani Mahavidyalaya E. M. Bypass Calcutta 700075
Abstract: In this paper we have introduced and discussed intuitionistic fuzzy almost compactness for intuitionistic fuzzy topological spaces. Moreover we have characterized this idea via intuitionistic fuzzy nets, filterbases, ¦È-closure operator and interiorly finite intersection property.
Keywords: Intuitionistic fuzzy almost compact, intuitionistic fuzzy nets, intuitionistic fuzzy filterbases, intuitionistic fuzzy ¦È-closure.
Some Fixed Point Theorems in Fuzzy Metric Space
R. P. Pant
Department of Mathematics Kumaon University,
D. S. B. Campus Nainital-263002, INDIA.
Vyomesh Pant
A-24, J. K. Puram. Choti Mukhani, Haldwani
Naintial-263139, Uttarakhand, INDIA
E-mail: vyomeshpant@yahoo.co.in
Abstract:
The present paper in aimed an obtaining some fixed point theorems in a fuzzy metric space by using the (¦Å, ¦Ä) contractive condition. For this purpose we first formulate and then employ an (¦Å, ¦Ä) contractive condition. Our results give proper generalizations of recent due to Chugh and Kumar [5] and Vasuki [18], fuzzify several well known fixed point theorems, and initiate the application of (¦Å, ¦Ä) technique for investigating fixed points of mappings in fuzzy metric spaces.
Keywords: Fuzzy metric space, Compatible maps, Common fixed point, R-weak commuting maps, (¦Å, ¦Ä) contractive condition.
Absorbing Maps and Fixed points
A. S. Ranadive, U. Mishra and D. Gopal
Dept. of pure and applied mathematics G. G. University, Bilaspur, C. G. India
E-mail: mishra.vrmila@gmail.com
asranadiveoy@yahoo.co.in
gopal.dhanjay@rediff.com
Abstract: The aim of this present paper is to obtain a common fixed point theorem in a fuzzy metric space by employing a new notion of absorbing maps. We illustrate that the class of absorbing maps is neither a subclass of compatible maps nor a subclass of non-compatible maps and that absorbing maps need not commute at their coincidence point. We also prove that point wise absorbing map is necessary condition for the existence of common fixed point for contractive type mapping pairs in fuzzy metric spaces. Our results generalize the recent result of B. Singh and Chauhan [10].
Keywords: Fuzzy metric space, compatible map, non-compatible map, continuous t-morn, reciprocal continuity, absorbing map.
Polarity of A Fuzzy Set
N. R. Das
Department of Mathematics Gauhati University Guwahati-781014 Asom, India
R. K. Misra
Department of Mathematics Darrang College Tezpur-784001 Asom, India
Abstract: In this paper we have introduced polarity of a fuzzy subset and some basic results of the fuzzy polar are also established.
Keywords:
Fuzzy polar, bilinear form, fuzzy balanced set, balanced hull, fuzzy convex, semi norm, weak topology, fuzzy weakly closed, fuzzy absorbing set, fuzzy weakly bounded set.
Solution of Non Linear Programming Problems Using Fuzzy Data
Aparna Dutta
Institute of advanced Study in Science and Technology, Guwahati-781035, Assam, India
E-mail: aparand_iasst@yahoo.co.in
Hemanta K. Baruah
Department of Statistics, Gauhati University, Guwahati-781014, Assam, India
E-mail:hemanta_bh@yahoo.com
Abstract: In this article we have attempted to fuzzify a Non Linear Programming Problem and then we have fuzzified Kuhn Tucker¡¯s necessary and sufficient condition for solving the fuzzified problem under fuzzy non-linear constraints.
Keywords:
Fuzzy non-linear programming problem, fuzzy non-linear constraints, Kuhn Tucker¡¯s condition,
triangular fuzzy numbers.
On Somewhat Fuzzy ??-continuous Functions
G. Thangaraj
Department of Mathematics, Jawahar Science College, Neyveli-607803, Tamilnadu, India.
G. Balasubramanian
Ramanujan Institute for Advanced Study in Mathematics, University of Madras,
Chepauk Chennai-600005, Tamilnadu, India.
Abstract: In this paper the concept of somewhat fuzzy ¦Á-continuous functions, somewhat fuzzy ¦Á-open functions, fuzzy almost ¦Á- continuous functions, weakly somewhat fuzzy ¦Á-open functions are introduced and studied. Besides giving characterizations of these functions, several interesting properties of these functions are also given. More examples are given to illustrate the concepts introduced in this paper.
Keywords: Somewhat fuzzy ¦Á-continuous, somewhat fuzzy ¦Á-open, fuzzy ¦Á-dense set, fuzzy almost ¦Á-continuous, weakly somewhat fuzzy ¦Á-open, fuzzy ¦Á-resolvable, fuzzy ¦Á-irresolvable.
Characterizations of Fuzzy Idempotent Matrices
Kyung-Tae Kang, Seok-Zun Song and Young-Oh Yang
Department of Mathematics, Cheju National University
Jeju 690-756, Republic of Korea
Abstract: An n¡Án matrix A is called idempotent if A2= A. We show that a fuzzy matrix A= [ai j] is idempotent if and only if all ai,j-patterns of A are idempotent matrices over the Boolean algebra ??={0,1}.In particular, we obtain that a fuzzy (0,1)-matrix is idempotent if and only if it can be expressed as a sum of linear parts and rectangle parts of certain specific structure.
Keywords: Idempotent, frame, rectangle part, line part, ¦Á-pattern.
Fuzzy Nabla Products in Connection with Fuzzy box Products
D. Susha
Department of Mathematics, Catholicate College, Pathanamthitta Kerala, India
E-mail: sushasivam@yahoo.com
Abstract: In this paper we introduce the notion of fuzzy nabla product and study the relation connecting fuzzy box products introduced earlier by the author and fuzzy nabla products.
Keywords:
Fuzzy box product, fuzzy uniformity, fuzzy entourage, fuzzy nabla product.
Fuzzy Discrete Distribution: The Binomial Case
Pranita Goswami
Department of Statistics, Pragiyotish College, Guwahati, Assam, India.
Hemanta K. Baruah
Department of Statistics, Gauhati University, Guwahati, Assam-781014, India.
Abstract: Addition of two fuzzy Bernoulli distribution and the sum of subsequent fuzzy binomial distributions have been discussed in this paper. Extensions of these ideas would be of use to study fuzzy randomness and the concept of measure.
Keywords: Fuzzy randomness, fuzzy probability distribution, interval of confidence, fuzzy random variable.
On Soft Relation and Fuzzy Soft Relation
T. Som
Department of Mathematics Assam University, Silshar-788011, INDIA
E-mail: som_tanmoy@yahoo.co.in
Abstract: In this physical world, we come across many complex problems pertaining to the areas of Engineering, Medical Science, Environmental Science, Economics, Social Science etc, which involve data that are not always crisp and precise. These problems have various types of uncertainties, some of which can be dealt with using the existing theories, viz., theory of probability, theory of fuzzy sets, theory of rough sets, theory of vague sets, or the theory of approximate reasoning etc. However, all these techniques lack in parameterization of the tools, due to which these could not be applied successfully in talking such problems. Taking into account of this fact, Molodtsov (1999) introduced the application in many directions, some of which are shown by him in his pioneer work and later by Maji et. Al. (2001, 2003). With the motivation of this new concept, in this paper we define soft relation and fuzzy soft relation, which are certain extension of crisp and fuzzy relations respectively. Further we apply these concepts in solving decision-making problems.
Products of T-equalities
Yong Chan Kim
Department of Mathematics, Kangnung National Univesity, Gangnueng,Korea
Keumseong Bahn
Department of Mathematics, Catholic University, Bucheon, Korea
Abstract: We investigate the properties of A-operators (resp. A-generators, A-transforms) and P-operators (resp. P-generators, P-transforms).Furthermore, we construct products of T-equalities induced by A-operators and P-operators.
Keywords: A-operators (A-generators, A-transforms), P-operators (P-generators, P-transforms), metrics, T-transform, products of T-equalities.
On Fuzzy ??-resolvable and Fuzzy ??-irresolvable Spaces
G. Thangaraj
Department of Mathematics, Jawahar Science College,
Neyveli-607803, Tamilnadu, India.
G. Balasubramanian
Ramanujan Institute for Advancedd Study in Mathematics, University of Madras,
Chepauk Chennai-600005, Tamilnadu, India.
Abstract: In this paper the concept of fuzzy ¦Á-resolvable, fuzzy ¦Á-irresolvable, fuzzy strongly ¦Á-irresolvable spaces are introduced. We study several interesting properties of the fuzzy strongly ¦Á-irresolvable spaces. Also we have given characterizations of the fuzzy ¦Á-irresolvable spaces by means of somewhat fuzzy ¦Á-continuous functions, somewhat fuzzy ¦Á-open functions.
Keywords:
Fuzzy ¦Á-resolvable, fuzzy ¦Á-irresolvable, fuzzy strongly ¦Á-irresolvable, somewhat fuzzy ¦Á-continuous function and somewhat fuzzy ¦Á-open function.
The Fuzzy ARIMA (1, 1) Process
Pranita Goswami
Department of Statistics, Pragjyotish College, Guwahati, Assam, India
Hemanta K. Baruah
Department of Statistics, Gauhati University, Guwahati, Assam-781014, India
Abstract:
In Fuzzy ARIMA (1, 1) process the choice of distance plays a very important role which is obtained in this paper through interval approach. Through this choice of distance we obtained near exactness.
Keywords: Fuzzy variables, constant distribution, interval approach, fuzzy function.
Fuzzy Filter Bases on BL-algebras
Yong Chan Kim and Jung Mi Ko
Department of Mathematics, Kangnung National University,
Gangneung, Gangwondo 210-702, Korea
Abstract: We introduce the notions of fuzzy filter bases on BL-algebras. We introduce the images and preimages of fuzzy filter bases induced by functions. We investigate the properties of them.
Keywords: BL-algebras, BL-homomorphisms, fuzzy filter, fuzzy filter base, fuzzy filter (preserving) maps, the images (the preimage) of fuzzy filter bases. |