THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 11, Number 1, March 2003

CONTENT

DETAILS

Common Coincidence Point in Fuzzy Metric Space

I.Kubiaczyk

Faculty of Mathematics and Computer Science Adam Mickiewicz University, Matejki 48/49, 60-769 Poznan, Poland E-mail: kuba@mail.amu.edu.cn

Sushil Sharma

Department of Mathematics, Madhav Science College Vikram Univrsity, Ujjain, India E-mail:sksharm2005@yahoo.com

Abstract: The purpose of this paper is to obtain some common fixedd point theorem for multivalued mappings in fuzzy metric space. Our results extended, generalize and fuzzify several fixed point theorems on metric spaces, Menger probabilistic spaces, uniform spaces and fuzzy metric spaces.

Keywords: Fuzzy metric space, sequence, common fixed point.

On Some Properties of Fuzzy T-algebras and Fuzzy F-algebras

Zheng Pei, WuMing Pan, Yang Xu and Ke Yun Qin

Dept. of Applied Math., Southwest Jiaotong University, Chengdu, Sichuan, 610031, P.R.China

Abstract: There are many paper devoted to the discussion of fuzzy universal algebras. They are constructed by the extended triangular norm and t-operator F on a fuzzy set of T-algebra and called fuzzy T-algebras and fuzzy F-algebras respectively. Then, the homomorphic image of fuzzy T-algebras and fuzzy F-algebras and some related properties are discussed. By extension principles and fundamental theorem of homomorphisms of T-algebra, the fuzzy quotient algebras was established and some of its basic properties were discussed.

Keywords: Universal algebra, fuzzy universal algebra, fuzzy homomorphism, extension principle, the extended triangular norm T , t-operator .

On Some Concepts Related to Fuzzy Sobriety

Archana Singh and Arun K.Srivastava

Department of Mathematics Banaras Hinndu University, Varanasi-221005 INFIA E-mail:aks@banaras.erent.in

Abstract: The paper introduces some concepts related to sobriety in fuzzy topology, viz, -sobriety, strong sobriety and ultrasobriety and presents a complete comparsion of these concepts.

Keywords: Sobriety, -sobriety, strong sobriety, ultrsobriety.

Mathematical Programming in The Presence of Fuzzy Quantities and Random Variables

M.K.Luhandjula

Department of Appled Mathematics National University of Rwanda P.O.Box 117, Butare, Rwanda

Abstract: This paper deals with the problem of integrating both fuzzy data (fuzzy numbers or fuzzy intervals) and random variables into a mathematical programming setting. To this end we develop first a method for incorporating fuzzy random variables into a mathematical programming framework. The method relies on the fact that -cuts of fuzzy random variables. Throughout the paper fresh light is thrown on the fact that fuzzy sets and probability theories are not antithetical and that extraordinary rewards can be gained by letting them interplay. The paper ends with concluding remarks along with perspectives for further fruitful developments in this field still at a stammering stage.

Keywords: Fuzzy, stochastic, mathematical programming.

On Fuzzy sub M-Semigroups of an M-Semigroup

AL.Narayanan and AR.Meenakshi

Department of Mathematics, Annamalai University Annamalai Nagar-Pin 608002, Tamil Nadu, India

Abstract: In this paper we shall introduce the concept of fuzzy sub M-semigroup of an M-semigroup and extend characterization theorems of an M-semigroup for a fuzzy sub-M semigroups.

Keywords: M-semigroup, idempotent, fuzzy sub M-semigroup.

Fuzzy Nets for L-Fuzzy Spaces

Ratna Dev Sarma

Department of Mathematics, Rajdhani College University of Delhi, Delhi-15

Naseem Ajmal

Department of Mathematics, Zakir Hussain College University of Delhi, Delhi-6

Charanjeet Kaur

Department of Mathematics, Jamia Millia Islamia Delhi-25

Abstract: Fuzzy nets are shown to be useful tools for studying structures in L-fuzzy spaces. A subcategory N(L) of Change-Goguen¡¯s category CG(L) is obtained by using fuzzy nets. This subcategory is found to be free from sevral shortcoming of Chang-Goguen¡¯s category. The notion of closed fuzzy graph is introduced for L-fuzzy spaces. Its study is found to be more coherent in N(L), than in CG(L).

Keywords: Fuzzy nets, L-fuzzy space, N-compactness.

Genralize Ideals

A.A.Ramadan and M.A.Abdel-Satter

Department of Mathematics, Faulty of Science, Cairo University Beni Suef, Egypt

Yong Chan Kim

Department of Mathematics, Kangnung National University Kangnung, Kangwondo 210-702, Korea

Abstract: We introduce the concept of preideals and generalized ideals. We investigate the relationship between preidealss and generanlized ideals.

Keywords: Ideal, preideal, generalized ideal.

Quasi-neighborhood Structures of Fuzzy Points

A.A.Ramadan and M.A.Abdel-Sattar

Department of Mathematics, Faculty of Science, Cairo University Ben-Suef, Egypt

Yong Chan Kim

Department of Mathematics, Kangnung National University Kangnung, Kangwondo 20-702, Korea

Abstract: In this paper, we study of theory of quasi-neighborhood systems of Pu and Liu (1980) in fuzzy topology by treating the membership relation as a fuzzy relation . We introduce the notions of fuzzy cluster, fuzzy limit points, continuous mappings and fuzzy convergence nets in fuzzy topological spaces and investigate some of their properties.

Keywords: Fuzzy topology, (quasi-)neighborhood systems, cluster points, limit points, continuous mappings.

-Almost Compactness for Crisp Subsets in A Fuzzy Topological Space

M.N.Mukherjee and Anjana Bhattacharyya

Department of Pure Mathematics, University of Calcutta 35 Ballyaunge Circular Road, Kolkata-700019, India

Abstract: In this paper, using the notion of -shading of Gantner et al. [6],the idea of -almost compactness for crisp subsets of a space X is introduced, where the underlying structure on X is a fuzzy topology. Mainly some characterizations of such subsets are incorporated here, which when interpreted for the whole space X, present formulations of an -most compact fuzzy topological space. The characterizations include those where ordinary nets and filters are employed as basic tools with the idea of their adherence defined suitably via the fuzzy topology of the space.

Keywords: -shading , -almost compact set, -regular, -adhereent point of net and filter.

A Parametic Study on Tranportation Problem under Fuzzy Environment

Omar M.Saad

Department of Mathematics, Faculty of Science, Qatar University Doha, Qatar, B.O.Box 2713

Samir A.Abass

Department of Mathematics and Theoretical Physics, Atomic Energy Authority Cairo, Egypt, B.O.Box 13759

Abstract: This paper presents a solution algorithm for solving the transportation problem having fuzzy parameters in the constraints. A parametric study is carried out for this problem. Some basic stability notions are the set of feasible parameters,the solvability set and the stability set of the first kind. Finally, an illustrativ, the solvab numerical example is given toclarify the theory and the solution algorithm.

Keywords: Fuzzy parameters, transportation problem, -level set, stability.

L-Fuzzy Topogenous Spaces and L-fuzzy Quasi-Uniform Spaces

A.A.Ramadan and M.A.Abdel-Sattar

Department of Mathematics, Faculty of Science, Cairo University Beni Suef. Egypt

M.El-Dardery

Department of Mathematics, Faculty of Science, Cairo University Faiyum, Egypt

Y.C.Kim

Department of Mathematics, Kangnung National University Kangnung, 210-702, Korea

Abstract: We introduce the concept of L-fuzzy topogenous structures in the framework of L-fuzzy topologies and L-fuzzy quasi-proximities. Some fundermental properties of them are established. We study a natural relationship between L-fuzzy topogenous structures and L-fuzzy quasi-uniformities. The family of all L-fuzzy topogenous strurctures and L-fuzzy quasi-uniformities compatible with an L-fuzzy topogenous structure on X is never empty and it contains an L-fuzzy quasi-uniformity which is the coarsest member of .

Keywords: L-fuzzy topogenous spaces, L-fuzzy quasi-uniform spaces.

Intuitionistic Fuzzy Subrings and Ideals

Baldev Banerjee Professor,

Department of Mathematics, Dibrugarh University Dibrugarh-786004, Assam, India

Dhirn Kr.Basnet

Department of Mathematics, D.H.S.K.College Dibrugarh-786001, Assam, India

Abstract: The aim of this paper is to introduce and study the concept of intuitionistic fuzzy subrings and intuitionistic fuzzy ideals of a ring. Several characterization and properties of these intuitionistic fuzzy subrings and intuitionistic fuzzy ideals and their mutual relationships are established.

Keywords: Intuitionistic fuzzy subring, intuitionistic fuzzy ideal, homomorphism.

On Adjacent Fuzzy Topologies

Sunil C.Mathew

Department of Mathematics, St. Thomas College Pala Arunapuram P.O.686574,Kottayam (Dt.), Kerala, India

T.P.Johnson

Cochin University College of Engineering Kuttanad Pulincunnu P.O.699504, Alleppey(Dt.), Kerala, India

Abstract: In this paper we study the concepts of immediate predecessor and immediate successor in the lattice of fuzzy topologies and consequently that of adjacent fuzzy topologies. We alsp investigate on situaitons providing immediate precessor and immediate successor for a given fuzzy topology and study some of its properties.

Keywords: Immediate predecessor, immediate successor, static fts, D-fts, g-closed, quasi-separated.

On Properties -Open Sets in Fuzzyifying Bitopological Space

GuangJi Zhang and MeiJuan Liu

Department of Mathematics, Dalian University Dalian 116622, P.R.China

Abstract: In this paper the concept of fuzzy -closed, -open sets have been generaliaed to fuzzifying bitpological spaces based on continuous valued logic,and some properties of -continuous functions and -compactness are studied.

Keywords: Continuous valued logic, -closure, -open sets, -continuous functions, -compactness, fuzzifying bitopological spaces.

L-Fuzzy C-Closed Mappings

A.A.Nouh Mathematics

Department, Faculty of Science Mansoura University, 35516, Egypt

Abstract: In this paper we introduce and study the concept of L-fuzzy C-closed mappings which from a generalization of L-fuzzy closed mapping and give their properties and relations with L-fuzzy continuous and L-fuzzy NC-continuous mappings. Also we introduce new classes of L-fuzzy topologize N-compact spaces [15]. At the end, we describe some new interesting characterizations of L-fuzzy C-closed mappings by having the aid of the NC-convergence theory of L-fuzzy nets and L-fuzzy ideals.

Keywords: Remoted neighborhoods , L-fuzzy C-closed set, K-space, L-fuzzy NC-continuous mappings, L-fuzzy C-closed mappings, NC-limit points, L-fuzzy nets and L-fuzzy ideals.

Generalized Closed Fuzzy Sets and Simple Extensions of A Fuzzy Topology

Sunil C.Mathew

Department of Mathematics , St. Thomas College Pala Arunapuram P.O.686574, Kottayam (Dt.), Kerala, India

T.P.Johnson

Cochin University College of Engineering Kuttanad Pulincunnu P.O.688504, Kerala, India

Abstract: In this paper we study generalized closed fuzzy sets and simple extensions of a fuzzy topology. Certain properties of g-closed fuzzy sets in relation with separation axioms have been established. Also we investigate on conditions under which certain properties.

Keywords: g-closed, simple extensions, D-fts, static fts, quasi-separated.

D-Admissible Fuzzy Subgroups

Dae Sig Kim

Department of Mathematics, Dongshin University Naju, Chonnam, 520-714, Korea

Abstract: The various fuzzy subgroups of a group which are admissible under operator domain D are studied. In particular, operator domains consisting of all inner automorphisms,all automorphsims, all endomorphisms are applied on the fuzzy subgroups of a group. As results, several theorems and examples concerning the fuzzy subgroups, fuzzy invariant subgroups are obtained.

Keywords: Fuzzy subgroups, level subset, support, operator domain, fuzzy normal subgroup, fuzzy characteristic subgroups, fuzzy fully invariant subgroup.

T-Fuzzy -Subrings of an -ring

B.Davvaz

Department of Mathematics, Yazd Unversity Yazd, Iran

Abstract: In this paper, using the concept of triangular norm, we define T-fuzzy -subring of an -ring, and we give some results in this connection.

Keywords: Hyperstructure, -ring, -subring, fundamental relation, fundamental ring, fuzzy set, t-norm.

On Fuzzy Regular Semi Open Sets and -Closed Fuzzy Topological Spaces

E.E.Kerre

Depart. Of Appl. Math. And Comp. Science Unversity of Gent, Belgium

M.A.Fath Alla

Depart. of Math., Sohg Faculty of Science Sohag-Egypt E-mail: fathallah 15@yahoo.com

Abstract: In this paper, the fuzzy regular semi open sets in a Chang fuzzy topological space, introduced in [8], are further investigated. Using -shading consisting of fuzzy regular semi open sets, a new class of fuzzy topological spaces, called -closed fuzzy topological spaces, is defined and studied.

Keywords: Fuzzy regular semi-open set, -closed fuzzy topological space.

On the Solutions of Parametric Multiobjective Nonlinear Programming Problems Using Fuzzy Mathematics

Dr. Elsaid Ebrahim Ammar

Dert. of Mathematics, Facltiy of Science Tanta Unversity, Egypt

Abstract: In this paper, a formulation of multiobjective nonlinear programming problem with general paremeters in the both of the objective and constrains functions in fuzzy mathematics is presented as a fuzzy nonlinear programming problems. A special and general fuzzy problem will be consideres. We use the fuzzy concepts to deduce the solutions and the efficient and weak sfficient solutions of the ordinary problems are also introduced. Moreover, a parametric analysis of the two fuzzy problems is defined. An illustrative example is given.

Keywords: Vector optimization, parametric programming, (weak) efficient solution, fuzzy sets theory, fuzzy solutions.