THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 16, Number 3, September 2008

CONTENT

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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.