The Journal of Fuzzy Mathematics
Volume 10, Number 1, March 2002
CONTENT
DETAILS
On the Solution of Bicriterion Integer Nonlinear Fractional Programs with Fuzzy Parameters in the Objective Functions
Omar M. Saad
Department of Mathematics, Faculty of Science
Helwan University, Egypt
Mohamed-El-Fadel A. Abdelkader
Scientific Computer, Helwan University, Egypt
Abstract:
In this paper we consider integer nonlinear fractional programs having fuzzy parameters in the object -ive functions. For such programs, a solution algorithm is described to solve the formulated model. The results obtained in this paper are implemented by an illustrative numerical example.
Keywords: Bicriterion, integer nonlinear fractional programming, fuzzy parameters, fuzzy numbers, -optima ¨Clity.
On Fuzzy -open Sets and Fuzzy -continuity in Intuitionistic Fuzzy Topological Spaces
M. Hanafy
Department of Mathematics, Faculty of Educations
Suez Canal University, El-Arish, Egypt
Abstract:
The purpose of thispaper is introduce and study the concepts of fuzzy -open sets and fuzzy -co -ntinuity in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionist -ic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy -open sets and intuitionistic fuzzy -continuity and other results related topological concepts.
Keywords:
intuitionistic fuzzy set, intuitionistic fuzzy point, intuitionistic fuzzy topological space, intuitionistic fuzzy-open set, intuitionistic fuzzy -continuity, intuitionistic fuzzy -closure(-interior).
A Note on Fuzzy Ordered Filters of Implicative Semigroups
Young Bae Jun
Department of Mathematics Education
Gyeongsang National University, Jinju 660-701, Korea
E-mail:ybjun@nongae.gsnu.ac.kr
Kyung Ho kim
Department of Mathematics
Chungju National University,Chungju 380-720, Korea
E-mail:ghkim@gukwon. Chungju.ac.kr
Abstract:
We verify that the family of fuzzy ordered filters is a completely distributive lattice. Using a collecti -on of orderd filters having additional conditions, we state a fuzzy ordered filter. In a commutative implicative semigroup,we make a new fuzzy ordered filter by using a fuzzy set.
Keywords: (commutative) implicative semigroup, (fuzzy)ordered filter.
Fuzzy Congruences on Completely 0-simpel Semigroups
Chuanzhi Zhang
Department of Mathematics. Shangdong University
Jinan, Shangdong 2501000,P. R. China
Abstract: In this paper we introduce the concepts of 0-fuzzy congruence and the t-fuzzy congruence on 0-simp
-le semigroup, and disuss the correspondence between them. Then the 0-fuzzy congruences on complet ¨Cely 0-simple semigroup in investigated, we show that there is an order-preserving bijction from the set of 0-fuzzy congruences onto the set of fuzzy admissible triples. Finally, the proper fuzzy congruences on completely 0-simple semigroups are described.
Keywords: Algebra; Completely 0-simple semigroups; Fuzzy congruences; Normal fuzzy subgroups; fuzzy admissible triples.
Characterization of Fuzzy Properties in I-topological Spaces
Gunther Jager
Deutsches Zentrum fur Luft-und Raumfahrt DLR;Institute fur Hoochfreqenztechnik und Radarsysteme;
Postfach 11 16;D-82230 WeBing,Germany
Abstract: In former papers,based on the concept of limit of profitters and residual implication, the notions of closedness, continuity and compactness were fuzzified in the sense that for each notion the grade to
Which it is fulfilled is measured. Here we characterize them in the special case of stratified I-topological spaces.
Keywords:
Fuzzy topological spaces, fuzzyconvergence, compactness, closedness, continuity.
Smooth Fuzzy Topology on Fuzzy Sets
A.A. Ramadan*,M. A. Fath Alla** and S. E. Abbas**
*Department of Mathematics, Faculty of Science,Beni-Suef, Egypt
**Department of Mathematics, Faculty of Science,Sohag, Egypt
Abstract:
The concept of a smooth fuzzy topology on a fuzzy sets has been introduced. Also, smooth fuzzy subspace, smooth fuzzy contiuity and smooth fuzzy compactness are studied.
Keywords: Smooth fuzzy topology, proper function ,smooth fuzzy subspace, smooth fuzzy contiuity,
smooth fuzzy compactness.
Fuzzy -continuity in Sostak,s Fuzzy Topology
A. A. Ramadan*, S. E. Abbas** and D. Coker***
*Department of Mathematics, Faculty of Science,Beni-Suef, Egypt
**Department of Mathematics, Faculty of Science,Sohag, Egypt
***Department of Mathematics,Akdeniz University,07058-Antalya,Turker
Abstract:
We introduce -fuzzy -open and -closed sets in fuzzy topological spaces in the sense of Sostak[14]. We investigate some of their properties. Moreover, we investigate the relationships between fuzzy continuity, fuzzy semicontinuity, fuzzy -continuity.
Keywords:
-fuzzy -open, fuzzy semicontinuity, fuzzy -continuity, fuzzy -open mapping.
Functors of thr Category of Lattice Implication Algebras*
Wang Wei
Department of basic,PLA Foreign Languange Institute,P.R.China
Xu Yang and Song Zhen Ming
Department of applied Mathematic,Southwest Jiaotong University, P.R.China
Abstract:
This paper presents the basic concept of functor on category of lattice implication algebras,and discu
-ssed its properties and the products of objiect in category of lattice implication algebras.
Keywords: Category, lattice implication algebra, functor.
On The Theory of Fuzzy Bags and Fuzzy Lists
S. P. Jena,S. K. Ghosh
Department of Mathematics,Khallikote Autonomous College
Berhampur-760 001,Orissa,India
B. K. Tipathy
Department of computer Science,Berhampur University,
Berhampur-760 007,Orissa,India
E-mail:bktripathy@yahoo.com
Abstract: The concept of bags with fuzzy elements introduced by Yager [4],was futher studied by Chakrobarty,
Biswas and Nanda [2]. In this article we have introduced new operations like symmetric difference and
Cardinality of fuzzy bags and established results involving these and existing operations.
The notion of list [1] is redefined by us recently [3].As an extension to this and fuzzy bags,lists with fuzzy elements have been introduced and results involving list operations are established.
Keywords: Fuzzy bag, Fuzzy list, concatenation of fuzzy lists, revers of fuzzy lists, Cardinality of fuzzy lists.
Fuzzifying Proximity and Strong Fuzzifying Uniformity
F. H. Kheder,K. M. Abd El-Hakiem,F. M. Zeyada and O. R. Sayed
Department of Mathematics, Faculty of Sciences
Assiut University, Assiut,71516,Egypt.
Abstract:
We introduce and establish some fundamental properties of a notion of fuzzifying proximity and a type of fuzzifying uniformity stronger than fuzzifying proximity due to M.S.Ying [4].It is a classical uniformity but in the sense of M.S.Ying may not be. The connections between fuzzifying proximity and our fuzzifying uniformity are investigated.
Keywords:
Fuzzifying topology; fuzzifying uniformity; proximity; uniformity.
A Fixed Point Therorem for Fuzzy Mappings in Quasi-pseudo-metric Spaces
Mustafa Telci and Ilker Sahin
Department of Mathematics, Faculty of Science and Arts,Trakya U niversity,
2030 Edirne,Turkey
E-mail:mtelci@trakya.edu.tr or isahim@trakya.edu.tr
Abstract: In this paper,we establish a fixed point theorem for generalized fuzzy contraction mapping in left K-sequentially complete quasi-pseudeo-metric spaces.
Keywords:
Fuzzy mapping, fixed point, quasi-pseudeo-metric, left K-sequentially complete.
The Relation Between Bag Function and Functions in Euliean Space
Jian Hou
Department of Basic Courses,Shan Xi Finance and Economical University,
Tai Yuan,030006.P.P.China
Abstract: In this paper, we discuss the relations between bag function and a family of functions. A family of n- ary functions can be determined by a bag mapping. Contrarily, we can structure a bag mapping by a family of n-ary functions.
Keywords: Bag mapping,value functional,fixed-identity
Some Operations on Lattice Implication Algebras(¢ò)
Eun Hwan Roh
Department of Mathematics Education,Chiju National University of Education,
Chiju 660-756,Korea
E-mail:ehroh@cue.ac.kr
Yang Xu
Department of applied Mathematic,Southwest Jiaotong University,
Chengdu,Sichuan 610031,China
Young Bae Jun
Department of Mathematics Education,Gyeongsang National University,
Chiju 660-701,Korea
E-mail:ybjun@nongae.gsnu.ac.kr
Abstract:
We introduce the concept of a -closed set and -homomorphism in lattice implication algebras, and we discuss their some properties.Next,we discuss the relation between and ,fuzzy fliters and fuzzy implicative fliters.
Keywords:
Lattice implication algebra, -closed , -homomorphism, fuzzy implicative fliters.
Outer Measures and Inner Measures on Fuzzy Measure Spaces*
Minghu Ha and Ruisheng Wang
Department of Mathematics, Hebei University,Baoding,071002
Congxin Wu
Department of Mathematics,Harbin Institute of Technology,Harbin,150001
Abstract: A pair of new measures,outer measure and inner measuer,are introduced on fuzzy measure spaces. They are generalizations of outer measure and inner measure on classical measure space respectively. Some primary properties of the outer measure and the inner measure induced by a fuzzy measure are discussed.
Keywords:
Fuzzy measure; outer measure ; inner measure.
Fuzzy Filters of BCK-algebras
Young Bae Jun
Department of Mathematics Education,Gyeongsang National University,
Chiju 660-701,Korea
E-mail:ybjun@nongae.gsnu.ac.kr
Tel.+82-55-751-5674;Fax. +82-55-751-6117
Seok Zun Song
Department of Mathematics,Cheju National University,
Chiju 690-756, Korea
E-mail:szsong@cheju.cheju..ac.kr
Abstract: We introduce the concept of a fuzzy -closed (resp. -closed) system and a fuzzy D-filter in a BCK-algebra, and investigate some related properties. We give characterizations of D-filter. We establish a relation between fuzzy prime idals and fuzzy -closed systems. We show that, in a bounded implicative BCK-algebra , The concept of fuzzy D-filter and BCK-filters coincide.
Keywords: Fuzzy BCK-filter, fuzzy D-filter, fuzzy prime ideal, fuzzy -closed (resp. fuzzy-closed) system.
Some Properties of Generalized Fuzzy Method-of-Cases
Quan Xi Qiao and Chao Ping Chen
Jiaozuo Institute of Technology,
Jiaozuo,Henan 454000, P.R.China
Ke Yun Qin
Southwest Jiaotong University,
Chengdu,Sichuan 610031,P.R.China
Abstract: Fuzzy method-of-cases is a fuzzy reasoning model first introduced and studied by R.Da and E. E. Kerre. B.Yuan and Y.Pan investigated a generalized version of fuzzy method-of-cases (GFMC for short
).In this paper,with respect to implication operators induced by some T-Norms,we will dicuss GFMC reasoning model with the inputs being , and ,respectively.
Keywords: Fuzzy method-of-cases, generalized fuzzy method-of-cases, fuzzy reasoning, fuzzy implication operators.
On the Algebraic Properties of Some Fuzzy Numbers
Luigi Di Lascio* and Alessandro Gisolfi
Dipartiment di Matematica ed Informatica Universita di Salerno
84081 Baronissi,Italy
E-mail:dilascio@unisa.it
Abstract: In this paper, beginning from a suitable analysis of the information contained in a triangular fuzzy number (T3FN, for short) and in trapezoidal fuzzy number (T4FN, for short), a MV-algebra is defined on the set of T3FNs and T4FNs on [0,1]. It is worth noting that the new operations allow composing T3FNs and T4FNs and that the negation of a T3FN is a T4FN, and viceversa. The MV-algebras so obtained is a MV-chain and an Hajek,s liner BL-algera so obtained is a sub-algera of Lukasiewicz structure. Then the linguistic varable Truth is implemented and a procedure is introduced that alloes, on one hand, associating a T3FN or a T4FN with an arbitrary linguistic term and, on the other hand, associ
-ating a linguistic term with a rational number on [0,1].In such way computing on a set of truth-values for a linguistic fuzzy logic becomes very simple.
Keywords: MV-algebra, fuzzy logic, linguistic fuzzy logic, fuzzy number, multi-valued logic,trinagular fuzzy numbers , trapezoida fuzzy numbers.
Cauchy-Nets in Fuzzy Uniform Spaces
T.M.G.Ahsanullah*
Department of Mathematics, University of Dhaka
Dhaka-1000,Bangladesh
Abstract: The motive behind this artice is to introduce the notion of Caucy-nets in Lowen fuzzy uniform spaces and to study its impact on some of the fuzzy uniformizable spaces. In an attempt to do so,we introduce the notion in question in arbitrary fuzzy uiniform spaces and study some of its elegant features.As an application, we look into the behavior of Caucy-nets on Burton¡¯s fuzzy uiniformization of function spaces and then finally study some results on fuzzy neighborhood groups,liner spaces,rings and modules with the observation that in all of thes spaces Caucy-nets behave well.
Keywords: Fuzzy topology, fuzzy uiniform space,fuzzy neighborhood space, Caucy-net£¬group£¬liner space,ring,
Module.
Fuzzy Cycles and Fuzzy Trees
John N. Mordeson
Department of Mathematics and Computer Science Creighton University,
Omaha,Nebraska 68178 U.S.A
E-mail:mordes@creighton.edu
Y. Y. Yao
Department of Computer Science University of Regina,
Saskatchewan,Canada S4S 0A2
E-mail:yyao@cs.uregina.ca
Abstract:
In the design of a network, it is important to analyze connectedness by levels. The structural properti
-es of fuzzy finite graphs provides a tool that allows for the solution of Operatuons Research problems. In this paper,examine the properties of various types of fuzzy cycles,fuzzy trees,fuzzy bridges,and fuzzy cutvertices in fuzzy graphs.Most of these various types are defined in terms of levels.Our purpose is to compare these various types given here and compare them with othe types given elsewhere.
Keywords: Fuzzy cycle, fuzzy tree,fuzzy bridge, fuzzy cutvertex
Further Study on Right Regular Maps of Lattice Implication Algebras
Xue Fang Wang, Ke Yun Qin and Yang Xu
Department of applied Mathematic, Southwest Jiaotong University,
Chengdu 610031, Sichuan,P. R. China
Abstract: Lattice implication algebra is an algebraic structure that is established by combining lattice and impl
-icative algebra. In this paper,we further investigated on right regulat maps of lattice implication algebr
-as based on references [2,3]. We gave several equivalent conditions about right regular maps and right regular endomorphisms and proved that all right regular endomorphisms of lattice implication algebra are idempotent. A condition for judging whether a lattice implication algebra is a lattice H implication algebra was obtained. Furthermore,we discussed the relations between filters and lattice dual ideals and gave the conditions for the epuivalence of them.Finally,we investigated some properties of the operatio
-n ¡°¡± which will help to further study lattice-valued logic system with truth-values in a lattice implica
-tion algebra.
Keywords: Lattice implication algebra, right regular map, filter,direct sum.
Lattice-valued Zp-pan-integrals I:For Lattice-valued Simple Functions on Lattice
Guang Quan Zhang1,Yong Hong Wu2 and Jie Lu1
1Facutly of Information Technology,University of Technology,Sydney
P.O.Box 123,Broadway,Nsw 2007,Australia
E-mail:jielu@it.ust.edu.au
2School of Mathematics and Statistics, Curtin University of Technology
GPO Box U1987,Oerth,Wester Australia,6845, Australia
E-mail:zhangg@it.uts.edu.au
Abstract: In this paper,we introduce and study a new type of integral,namely the lattice-valued Zp-pan-integral
,for lattice-valued simple functions on lattice.A number of theorems characterzing the properties of the integral are developed and presented in the paper.
Keywords: Non-additive measure,fuzzy integra, lattice-valued simple functions, pan-integral.
Lowen Fuzzy Convergence Spaces Viewed as [0,1]-Fuzzy Convergence Spaces
Gunther Jager
Department of Mathematics, RchodesUniversity,
6140 Grahamstown,South Africa
Abstract: The category of stratified L-fuzzy convergence spaces recently introduced by the author, is a cartes-
ian closed topological category which contains the category of stratified L-topological spaces as a refle
-ct,ive subcategory . In this paper we address the question of relationship this category of fuzzy converg -ence spaces due to Lowen and Lowen.We will find that the category of fuzzy neighborhood converg -ence spaces is isomorphic to a subcategory of stratified [0,1]-fuzzy convergence spaces.
Keywords:
L-fuzzy convergence, L-topology, fuzzy convergence, fuzzy convergence neighborhood spaces.
On the Fuzzy LI-Ideals and Fuzzy Filters of Lattice Implication Algebras*
Guang Feng Zhao
Dept. of Appl. Mathematics, Southwest Jiaotong University,
Chengdu 610031, P. R. China
Dept. of Mathematics, Tangshan Teachers¡¯College,
Tangshan 063000, P. R. China
Yang Xu and Ke Yun Qin
Dept. of Mathematics, Southwest Jiaotong University,
Chengdu 610031, P. R. China
Abstract: In this paper,we pointed out a family of congruence relations induced by a fuzzy filter of a lattice im
-plication algebra and dicussed the properties of these relations and the homomorphisms between the
Quotient lattice implication algebras induced by this family of congruence relations. And at the end of this paper,we proved that there exists a one to one correspondence between the family of fuzzy LI-ideal
-s and that of fuzzy filters.
Keywords: Lattice implication algebra, fuzzy LI-ideal, fuzzy filter, congruence relation.
Some Cardinal Functions on Induced L-fuzzy Topological Spaces*
Bin Zhao
Department of Mathematics, Shanxit Normal University
Xi¡¯an 710062, P. P. China
Abstract: In this paper, we discuss the relations between net weight,Lindelof degree and celluarity of induced
L-fuzzy topological spaces and that of their generated spaces ,and prove that the net weight of equeals the product of net weight of and L,that the Lindelof degree of is bigger than the product of Lindelof degree of and L,smaller than the product of Lindelof degree of and cardinality of L,and the celluarity of equals the celluarity of
for a regual fuzzy lattice L.
Keywords: Induced L-fuzzy topological spaces; cardinal function; net weight; Lindelof degree ;celluarity. |