THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 9, Number 2, June 2001

CONTENT

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Discrete Warehouse Location in Imprecise Environment

B.Mohanty

Department of Business Administration, Utkal University, Bhubaneswar, India.

J.K.Dev

Indian Administrative Service, Bhubaneswar, India.

U.K.Bhattacharya

Xavier Institute of Management, Bhubaneswar, India.

Abstract: This paper presents a fuzzy goal programming model to determine which warehouse sites should be used among the potential warehouse locations and the Assignment of customers to warehouses in order to minimize the total Cost per period. This model has been developed to tackle the warehouse location problem where certain parameters aspiration level for the goals and basing these on a comparison of (flat) fuzzy numbers, the original fuzzy problem is transferred into a crisp satisfactory model. To determine a suitable solution we have maximized the minimum of the surpluses over the aspiration been given to illustrate the solution prodedure.

Keywords: Discrete warehouse location, fuzzy sets.

Fuzzy Quasi-Ideals in Semigroups

J.Ahsan and R,M,Latif

Department of Mathematical Sciences King Fahd University of Petroleum And Minerals, Dhahran 31261, Saudi Arabia

M. Shabir

Department of Mathematics, Quaid-l-Azam University Islamabad, Pakistan

Abstract: In this paper we define fuzzy quasi-ideals in semigroups and use their properties to characterize regular and intra-regular semigroups.

Keywords: Regular and intra-regular semigroups, fuzzy ideal, fuzzy bi-ideals, fuzzy quasi-ideals in semigroups

On -groups and fuzzy homomorphisms

B.Davvaz

Department of Mathematics, Yazd University, Yazd, Iran Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran

Abstract: In this paper, we introduce the concepts of strong fuzzy homomorphism, inclusion fuzzy homomorphism and fuzzy - homomorphism between two fuzzy -groups by a natural way, and we prove some results in this connection.

Keywords: -group, fuzzy set, fuzzy-subgroup, fuzzy homomorphism, fuzzy point, fundamental relation, fundamental group.

A Study on the Solutions of Multiobjective Fraction Programming Problems Using Fuzzy Mathematics

Elsaid Ebrahim Ammar

Department of Mathematics, Faculty Of Science, Tanta University, Egypt

Abstract: In this paper, a formulation of multiobjective nonlinear fractional programming problems with general parameters in the both ratio of the objectives and the constrains functions in fizzy mathematics as a fuzzy nonlinear programming problems will be considered. We use the fuzzy concepts to deduce the solution sets of the above two fuzzy problem. Also, the relations between problems are also introduced. Moreover, a parametric analysis of the two fuzzy problems are defined. An illustrative example is given.

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

On L-smooth Paracompactness

A.A.Ramadan

Department of Mathematics, Faculty Of Science, Beni-Suef, Egypt

S.E.Abbas

Department of Mathematics, Faculty of Science, Sohag, Egypt

Abstract: In this paper, we introduce a good definition of smooth paracompactness and smooth local paracompactness in smooth L-fuzzy topological spaces, where L is s fuzzy lattice. We define smooth paracompactness on general L-fuzzy subsets and study its properties.

Keywords: Fuzzy lattice, smooth fuzzy topology, -scott continuous function, smooth paracompactness, smooth local paracompactness, good extension.

Fuzzy Cosets and Fuzzy Subpolygroup

Naseem Ajmal

Department of Mathematics, Zakhir Husain College University of Delhi, J.L.N.Marg, New Delhi-110002, India

Anand Swaroop Prajapati

Department of Mathematics, Atma Ram Sanatan Dharma College Dhaula Kuan, New Delhi-110054, India

Abstract: In this paper, we continue to investigate the structure and properties of fuzzy subpolygroup of polygroup which was introduced by Zahedi et. al. We introduce the notion of fuzzy cosets of a fuzzy subpolygroup using this we redefine the concepts of fuzzy -cosets by following approach of Wangming Wu and which is a natural generalization of a fuzzy cosets of a fuzzy group.

Keywords: Polygroup, fuzzy subpolygroup, fuzzy cosets, fuzzy normal subpolygroup, strong isomorphism, quotient polygroup, fuzzy algebra.

Deformation Of Some Fuzzy Manifolds And Its Folding

M.EI-Ghoul

Mathematics Department, Faculty of Science Tanta Univerdity, Tanta, Egypt.

H.EI-Zohny and S.Radwan

Mathematics Department, Faculty of Science Al-Azhar-University for Girls, Cairo, Egypt.

Abstract: In this article we introduce the difference between the geometric retraction of fuzzy manifold and the fuzzy retraction of the physical character. The deformation of some types of fuzzy manifolds are discussed. Theorems governing the relation between the retraction and the folding are deduced.

Keywords: Fuzzy manifolds, retraction, deformation.

Application of Sequential and Net Convergence in Various Fuzzy Neighborhood Structure

T.M.G.Ahsanullsh

Department of Mathematics, University of Dhaka Dhaka-1000, BANGLADESH

Abstract: In this article we establish some fundamental results in the lowen fuzzy neighborhood spaces and fuzzy probabilistic metric neighborhood groups. In so doing, we use the concepts of sequence and net convergence introduced earlier in fuzzy neighborhood spaces.

Keywords: Fuzzy topology, fuzzy neighborhood system, fuzzy probabilistic metric, sequence, net, groups.

On Fuzzy 2-Normed Linear Spaces

A.R.Meenakshi And R.Cokilavany

Department of Mathematics, Annamalai University Annamalainagar-608002, India

Abstract: In this paper, the notion of Fuzzy 2-normed linear spaces is introduced. Standard results in 2-normed linear spaces are extended to Fuzzy 2-normed linear spaces. The famous Hahn-Banach theorem is proved in the realm of fuzzy 2-normed linear spaces.

Keywords: Fuzzy normed linear, fuzzy pseudo-norm, fuzzy linear functional, fuzzy metric space.

Some Minimization Theorems For Fixed Point Theorems In Fuzzy Metric Spaces With Applications

H.K.Pathsk

Department of Mathematics, Kalian Mahavidyalaya Bhilainagar 490006(m.p.), India. e-mail: gkg@bom6.vsnl.net.in

S.N.Mishra

Department of Mathematics, University of Transkei, Untata 5100, South Africa e-mail: mishra@getafix.utr.ac.za

Abstract: Some minimization theorem in fuzzy metric spaces with application to Menger spaces are proved.

Keywords: Fixed point theorm, minimization theorem, fuzzy metric space, Menger space.

A Kind of Simplified Formal Deductive System for the System

Wu Hongbo

Department of Mathematics, Sichuan university, Chengdu Sichuan, 610064, China

Department of Mathematics, Tang Shan Normal College, Tangshan Hebei, 063000, China.

Abstract: The formal deductive system for fuzzy propositional calculus and the revised Kleene logic systems , that are relevant to the former in semantics, have been studied, both of them are first proposed by professor Guo-jun Wang. The main results of this paper are:(1)A kind of simplified formal deductive system for the system has been established; (2)The equivalence between the system and has been proved. This work offers a useful tool for further studying and developing the system

Keywords: Fuzzy propositional calculus, formal deductive system , simplified formal deductive system .

On Lattice-Valued Functions : Borel Functions on Lattice

Guangquan Zhang and Yong-Hong Wu

School of Mathematics And Statistics, Curtin University of Technology GPO Box U1987, Perth, Western Australia, 6845, Australia {zhang, yhwu}@cs.curtin.edu.au

Abstract: In this paper, Borel functions and lattice-measurable functions on lattice are introduced. A number of theorems characterizing their properties are developed and the relationships between Borel functions and lattice-measurable functions are given.

Keywords: Non-additive measure, fuzzy measure, Borel function, lattice-measurable function

Stratifications of Smooth Fuzzy Topological Spaces

Yong Chan Kim

Department of Mathematics, Kangnung National University Kangnung, Kangqondo 210-702, Korea e-mail address: yck@knusun.kangnung.ac.kr

Abstract: We introduce the stratification of a smooth fuzzy topology. We investigate the relationship between smooth fuzzy topological spaces and stratifications of them.

Keywords: Smooth fuzzy topological spaces, stratified smooth fuzzy topological spaces, stratifications.

An Application of Raw Sets to Scoring Function on -Dimensional Space

Yuxi Chen

Department of Computer Science, Binghamton University, New York, USA

Abstract: The alignment of -dimensional space is addressed based on raw sets theory[1]. A new scoring function is Rsum() deduced. It convinces us that Rsum() is the only in similar applications.

Keywords: Scoring function, raw set, -dimensional space, primary edge, primary path, distance.

On Several Types of Continuity in Fuzzy Bitopological Spaces

A.A.Ramadan

Department of Mathematics, Faculty of Science, Ben-Suef, Egypt S.E.Abbas

Department of Mathematics, Faculty of Science, Aohag, Egypt

Abstract: We introduce r-fuzzy strong semi-open, r-fuzzy preopen and r-fuzzy semi- preopen sets in a fuzzy bitologoical spaces in view of the Sostak[10]. We investigate some properties of them. Moreover, we investigate the relationship between fuzzy pairwise continuity, fuzzy pairwise semi-continuity, fuzzy pairwise semi-continuity, fuzzy pairwise strong semi-continuity, fuzzy pairwise precontinuity and fuzzy pairwise semi- precontinuity

Keywords: r-fuzzy strong semi-open, r-fuzzy emi- preopen, fuzzy pairwise semi-continuity, fuzzy pairwise semi- precontinuity.

A Note on Fuzzy Volterra-Hammerstein Integral Equations

H.K.Pathak

Department of Mathematics, Kalian Mahavidyalaya Bhilai Nagar 490006, M.P., India e-mail:gkg@bom6.vsnl.net.in

S.N.Mishra

Department of Mathematics, University of Transkei Umtata 5100, South Africa e-mail: mishra@getafix.utr.ac.za

Abstract: In this note we prove existence theorems for certain Volterra-hammerstein integral equations involving fuzzy set-valued mappings whose values are normal, convex, upper semicontinuous and compactly supported fuzzy sets in .

Keywords: Fuzzy function, fuzzy integral equations, nonlinear Volterra-hammerstein integral equation, fuzzy solution.

Stratiform L-Fuzzy Topologies and L-Fuzzy Bitopological Spaces

Zhang Xingfang,Meng Guangwu, Guan Enrui

Department of Mathematics and Systems Science, Liaocheng Teachers University, Shandong 252059,PR,China

Chen Shuli

Department of Mathematics, Jimei University, Xiamen, Fujian 361021,PR. China

Abstract: In L-fuzzy topological spaces, stratiform L-fuzzy topologies are presented. Two concepts are put forward that -closure-preserving family and -cushion. Based on this, some characterizations of type strong paracompactness are given for -regular L-fuzzy topological spaces.

Keywords: Fuzzy topology, fuzzy paracompactness, stratiform L-fuzzy topology, -closure-preserving family, -cushion, -regular set, fuzzy lattice.

Fuzzy Topological Product Group Zou Kaiqi

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

Abstract: The fuzzy topological group was introduced by D.H. Foster[1] in 1979. In this paper we continue to study some of its properties. The author uses the concept of product of two fuzzy subsets to discuss the following problem: the relations between fuzzy open sets and fuzzy closed sets of a fuzzy topological space which is induced from a fuzzy topological group, the characters of fuzzy coset spaces, and generalization of two isomorphism theorems about topological groups. So that the study of fuzzy topological groups extends further.

Keywords: fuzzy topological group, relative closed set, fuzzy coset space.

On Solving Stochastic Fuzzy Goal Programming Programming Problem Using A Suggested Interactive Approach

Maged George Iskander

Economics Department, The American University In Cairo, Egypt

Abstract: This paper presents a suggested approach to solve a stochastic fuzzy goal programming problem. All goal constraints are stochastic and fuzzy simultaneously. The coefficients in the left hand side and the tolerance measures are considered fuzzy numbers with trape-funcrions, for the two fuzzy numbers, is assumed, in which one has a trspezoidal-shaped other hand, the aspiration levels are assumed to be independent random variables with known probability distribution functions. The concept of -optimality and the chance-constrained approach are utilized to transform the stochastic fuzzy goal programming problem to its equivalent deterministic-crisp. Solving such deterministic-crisp model is performed through an interactive approach and is illustrated by a numerical example.

Keywords: Stochastic fuzzy goal programming, chance-constrained approach, -optimality, interactive approach

Asymptotic Structural Characteristics of Signed Fuzzy Number-Valued Measure and Convergence in Monotone Measure

Li Jun

Department of Applied Mathematics, Southeast University, Nanjing, 210096, China

Zhang Qiang

School of Management And Economices Beijing Institute Of Technology, Beijing, 100081, China

Abstract: In this paper, we generalize the concept of pseudometric generating property of set function in three kinds of way and investigate the connections among some asymptotic structural characteristics of monotone measure, the convergence in measure and the convergence pseudo-in measure of sequence of measurable function on monotone measure space.

Keywords: monotone measure, fuzzy measure, pseudometric generating property, convergence in measure

Hahn and Jordan Decompositions of Signed Fuzzy Number-Valued Measure on the Fuzzy Set

Zhao Fen-Xia and Zhang Guang-Quan

Department of basic science, Tianjin university of commerce, Tianjin, 300400, R R. china

Abstract: In this paper, a necessary and sufficient condition concerning the existence of Hahn decompositions with respect to signed fuzzy number-valued measure is given. Based on this, Jordan decomposition id later discussed.

Keywords: Fuzzy set, fuzzy number, signed fuzzy number-valued measure, Hahn decomposition, Jordan decomposition

On Intuitionistic Fuzzy -Subgroups Of -Groups

Kyung Ho Kim And Jong Geol Lee

Department of Mathematics, Chungju National University, Chungju 380-702, Korea

Abstract: The intuitionistic fuzzification of a subgroup in a -group is considered, and related results are investigated. The notion of equivalence relations on the family of all intuitionistic fuzzy subgroup of a -group is introduced, and then some properties are discussed.

Keywords: -group, fuzzy -group, intuitionistic fuzzy -group, (resp.) level -cut, homomorphism.

Some Weakly Forms Of Fuzzy Continuous Mapping In L-Fuzzy Bitopogical Spaces

Y.C.Kim,

Department of Mathematics, Kangnung National University, Kangwondo, Korea

A.A.Ramadan

Department of Mathematics, Faculty Of Science, Beni-Suef, Egypt S.E.Abbas

Department of Mathematics, Faculty of Science, Sohag, Egypt

Abstract: We introduce r-fuzzy weakly semi-open, andfuzzy -open sets in an L-fuzzy bitopological spaces in view of the definition of Sostak. We investigate some properties of them. Moreover, we investigate the relationship between FP continuity, FP semi-continuity, FP weakly semi- continuity, FP -continuity and some of their properties are studied.

Keywords: -fuzzy weakly semi-open, -fuzzy -open, FP weakly semi- continuity, FP - continuity.

Pre-Semiclosed Sets And PS-Convergence In L-Fuzzy Topological Spaces

Bai Shi-Zhong

Department of Mathematics, wuyi university jiangmen, 529020, Guangdong, p.r. china

Abstract: We introduce and study the concepts of pre-semiopen set, pre-semiclosed set, pre-semiinterior, pre-semicloseure and PSC-remote-neighborhood in L-fuzzy topological space, and establish the Moore-Smith PS-convergence theory of nets and ideals.

Keywords: L-fuzzy topology, pre-semiclosed set, remote-neighborhood, ideal, molecular net, convergence