The Journal of Fuzzy Mathematics
Volume 5, Number 2, June 1997
CONTENT
DETAILS
**Fuzzifying Compactifications
**
Daowen Qiu
Department of Basic Course, Guang Dong Institute of Technology,
Guang Zhou 510090, P.R. China
**Abstract:** We shall introduce the concept of compactification, and establish some of its fundamental properties as well as obtain the Alexandorff compactification theorem in the framework of fuzzifying topology.
**Keywords: **Fuzzifying topology, compactification.
**DE Morgan Algebra of Bitopology
**
Xueyou Chen
Basic Department, Shandong Institute of Technology
Zibo, Shandong 255012, P.R. China
**Abstract:** In this paper, we introduce de Morgan algebra of bitopogy, and some separation axioms, the Urgsohn¡¯s Lemma is established.
**Keywords:** De Morgan algebra of topology, de Morgan algebra of bitopogy.
**Fuzzy Inference in an Expert System of Runoff Forecasts: Fuzzy Theoretic Forecast Pattern Method**
Shouyu Chen, Huicheng Zhou and Bende Wang
Department of Civil Engineering, Dalian University of Technology
Dalin 116024, P.R. China
**Abstract: **Patterns of mid-and long-term runoff forecasts are developed according to the experts¡¯ idea of runoff inference forecasting by synthesizing the forecast factors affecting runoff. The patterns take into consideration a weighting vector for forecast factors so that they are more suitable and may provide more information for decision making. When applied to the expert system of mid-and long-term runoff forecasts, the fuzzy inference method presented here can summarize the expertise into patterns, and increase the learning ability of the expert system.
** Keywords:** Fuzzy inference, runoff forecast, expert system, forecast pattern.
**¦Ä-compactness in Fuzzy Topological Spaces
**
I.M. Hanafy
Department of mathematics, Faculty of Education
Suez Canal University, El-Arish, Egypt
**Abstract:** In this paper, we introduce and study the concept of¦Ä-compactness [6] in fuzzy topological spaces. The goodness of our definition is of interest. We give some characterizations of ¦Á¦Ä-compactness, and in a semiregular fuzzy topological spaces, the concept of¦Á¦Ä-compactness, ¦Á-compactness, ¦Á-near compactness and¦Á-almost compactness are equivalent. Also, we investigate the image and the inverse image of¦Á¦Ä-compactness under some types of continuity.
**Keywords:** Fuzzy topological spaces, fuzzy ¦Á¦Ä-compactness, fuzzy ¦Á-compactness, fuzzy ¦Ä-continuity, fuzzy super continuity, fuzzy ¦Ä-open function.
**Product Fuzzy Number Measures of Product Spaces**
Hou Renen
Department of mathematics, Shangrao Teacher¡¯s College,
Jiangxi, 334001 China
**Abstract: **This paper is the continuation of the paper [1]. In this paper, we try to introduce the concept of the product fuzzy number measures on product spaces. Now we have the result of the product fuzzy number measure theorem. And we have discussed some problems about the Fubini theorem on the product fuzzy number measure spaces.
** Keywords:** Random set, Fuzzy number measure, product fuzzy number measure, measurable space, product set-valued measure.
**Smooth Filter Structures**
A.A. Ramadan
Department of mathematics, Faculty of Science
Cairo University
Beni-Suef, Egypt
**Abstract: **We introduce the concept of smooth filter structures in the framework of smooth topology and we establish some fundamental properties of smooth filter structures.
**Keywords:** Fuzzy logic, smooth filter, smooth topology, convergence.
**Measures of Noncompactness for Fuzzy Sets
**
S.G. Gal
Department of mathematics, Universityof Oradea
Str. Armatei Romane 5, 3700 Oradea, Romania
**Abstract: **In this note we continue the study of the measures of noncompactness introduced in [5-6]. Also, by using the level sets¡¯ method, other measures of noncompactness are considered and some interesting open questions are pointed out. Finally, fuzzy measures of noncompactness for fuzzy sets are introduced.
**Keywords:** Measures of noncompactness of Kuratowski-type and of Hausdorff-type for fuzzy sets, fuzzy measures of noncompactness for fuzzy sets.
**On Smooth L-fuzzy Topological Spaces**
Halis Aygun
Department of mathematics, City University
Northhampton Square, London ECIV OHB, U.K.And
Department of mathematics, Kocaeli University
Ataturk Bulvari, Izmit, Turkey
m.w. Warner
Department of mathematics, City University
Northhampton Square, London ECIV OHB, U.K.
S.R.T. Kudri
Department of mathematics, City University
Northhampton Square, London ECIV OHB, U.K.
and
Department of mathematics, Federal University of Parana,
Curutiba, Brazil
**Abstract:** `¦Á-Scott continuous functions¡¯from an ordinary topological space to a fuzzy lattice L with its Scott topology are introduced. These functions turn out to be the natural tool to set up a goodness of extension criterion for smooth L-fuzzy topological properties. Good definitions of smooth Hausdorffness, smooth compactness and smooth local compactness in smooth L-fuzzy topological spaces are presented and some of their properties are studied.
**Keywords:** Fuzzy lattice, smooth fuzzy topology, ¦Á-Scott continuous function, good extension, smooth Hausdorffness, smooth compactness, smooth local compactness, prime level space.
**Improvement of the Fixed Point Theorem for Fuzzy Mappings in Menger PM-spaces**
Xie Jin
Department of Basic Science, Wuhan Urban Construction Institute
Wuhan 430074, P.R. China
Liu Zuo Shu
Department of mathematics and Physics, Wuhan University of Technology Wuhan 430070, P.R. China
**Abstract: **In this paper the notion family of fuzzy mappings defined on probabilistic metric spaces is introduced and its properties are investigated. A common fixed point thorem for fuzzy mappings defined on PM-spaces is proved. These mappings are assumed to satisfy some generalizations of the contraction condition.
**Keywords:** Menger PM-spaces, fuzzy mapping, fixed point.
**Neighborhoods in De Morgan Proximity Algebra
**
Xueyou Chen
Basic Department, Shandong Institute of Technology
Zibo 255012, Shandong, P.R. China
**Abstract: **In [7], De Morgan algebra of proximity was introduced, based on [1], [7], using the notion of ab, the proximity neighborhood relation is investigated, and given a straight proof of the proposition: every induced by completely regular.
**Keywords: **Proximity, proximity neighborhood relation.
**On Additivity and Pseudo-additivity of a Pseudo-additive Measure Based Integral
**
Radko Mesiar
S T U,81368 Bratislava, Slovakia and UTIA AV CR,
18200 Prague, Czech Republic
Endre Pap
Institute of Mathematics, University of Novi Sad,
21000 Novi Sad, Yugoslavia
**Abstract: **Different kinds of additivity of an integral F+ (with respect to a +-measure m) introduced by Sugeno and Murofushi are studied. As corollaries we obtain the additivity (and linearity) of the Weber integral and the pseudo-additivity (and pseudo-linearity) of the integrals of Pap and Ichihashi et al.
**Keywords:** Pseudo-addition, pseudo-multiplication, decomposable measure, integral.
**On Fuzzy Continuity in Intuitionistic Fuzzy Topological Spaces**
Hasmet Gurcay¡¯ Dogan Coker
Department of Mathematics Education, Hacettepe University
Beytepe, 06532-Ankara,Turkey
A. Haydar Es
Department of Mathematics , Hacettepe University
Beytepe, 06532-Ankara,Turkey
**Abstract:** The purpose of this paper is to introduce several types of fuzzy continuity between intuitionistic fuzzy topological spaces; namely, fuzzy semicontinuity, fuzzy almost continuity, fuzzy weak continuity, fuzzy precontinuity, fuzzy ¦Á-continuity, fuzzy ¦Â- continuity.
**Keywords:** Intuitionistic fuzzy set, intuitionistic fuzzy topological space, intuitionistic fuzzy semiopen set, intuitionistic fuzzy regular open set, intuitionistic fuzzy ¦Á-open set, intuitionistic fuzzy preopen set, intuitionistic fuzzy ¦Â-open set, fuzzy continuity, fuzzy semicontinuity, fuzzy almost continuity, fuzzy weak continuity, fuzzy precontinuity, fuzzy¦Á-continuity, fuzzy¦Â-continuity.
**Fuzzy Homological Theory in FRA -modules (I)
**
Jianli Zhao
**Abstract:** In this paper, we first introduced the concept of the kernels, cokernels in FRA -module category and some important properties are given. Then we define the concept of fuzzy exact sequences in FRA -module category and some results are studied. Finally, we introduce the concept of free FRA -module, give concrete structures and some properties of free FRA -module.
**Keywords:** FRA -module,kernel, cokernel, fuzzy exact sequence, free R-module, free FRA -module.
**Relative Membership Function and New Frame of Fuzzy Sets Theory for Pattern Recongnition
**
Shouyu Chen
Department of Civil Engineering, University of Technology
Dalian 116023, P.R. China
**Abstract:** Based on generalization of definition for classical membership function, this paper establishes a new frame of fuzzy sets theory for pattern recognition. Its theorical basis is definition of relative membership function. It includes membership functions of recongnition indexes and of ranks for samples belonging to fuzzy subset A, new indexes of recongnition for sample set, feature value vectors and so on. A real application example is given: cluster recognition for unknown chemical compound.
**Keywords: **Relative membership function, pattern recognition, fuzzy sets, rank featurevalue.
**Fuzzy Archimedean Spaces
**
Ismat Beg
Department of Mathematics, Kuwait University
P.O. Box 5969, Safat 13060, Kuwait
Misbah Ui Islam
Department of Mathematics, Indiana University
Bloomington, Indiana, U.S.A.
**Abstract: **The notions of directed fuzzy ordered linear space and fuzzy Archimedean space are defined and studied.
**Keywords:** Fuzzy ordered linear space, fuzzy Archimedean space.
**Possibilistic Linear Programming Problems with Fuzzy Constraints
**
Xiaozhong Li
Department of Computer Science, Liaocheng Teachers¡¯ College
Liaocheng, Shandong 252059, P.R. China
**Abstract: **In this paper possibilistic linear programming problems with fuzzy constraints are considered. The solving method is presented. Solutions to them are obtained.
**Keywords: **Possibilistic linear programming, fuzzy constraints, fuzzy numbers, fuzzy variables, possibility distribution.
**On the convergence of the Fuzzy Valued Functional**
Wang Gui-jun and Li Xiao-ping
Department of Mathematics ,
Tong hua Teacher¡¯s college, Tong hua,Jilin, 134002, China
**Abstract: **In this paper, we define a fuzzy valued functional on fuzzy measure spaces, discuss its important properties and give its convergence theorem.
**Keywords:** Measurable fuzzy valued functions; integrable fuzzy valued functions; fuzzy valued functional.
**Use of Projective and Scaling Algorithm to Solve Multi-Objective Fuzzy Linear Programming Problems**
M.P. Biswal
Department of Mathematics , Indian Institute of Technology
Kharagpur-721302, India
E-mail: mpb@maths.iitkgp.ernet.in
**Abstract:** In this paper projective and scaling algorithm have been used to solve multi-objective fuzzy linear programming problems. The main steps of both the algorithms to solve a linear programming problem are presented and the advantages of the algorithms are analyzed. Then the fuzzy programming algorithm to solve a multi-objective linear programming problem is presented. By considering a numerical example solution procedure is discussed. Finally, a comparison with simplex algorithm and interior point algorithm is presented.
**Keywords:** Projective algorithm, scaling algorithm, multi-objective linear programming, fuzzy programming, simplex algorithm.
**A Note on Obstinate Fuzzy Ideals in BCI-algebras**
Young Bae Jun
Department of Mathematics Education
Gyeongsang National University, Chinju 660-701, Korea
e-mail: ybjun@nongae.gsnu.ac.kr
**Abstract:** In this paper, we show that the Theorem 6 of [8] holds without the sup property. For the homomorphic image f(u) and preimage f-1(v) of obstinate fuzzy ideals u and v, respectively, we establish the chains of level obstinate ideals of f(u) and f-1(v) , respectively.
**Keywords:** Obstinate ideal, obstinate fuzzy ideal, level obstinate ideal, sup property.
**Some Weakly Forms of Fuzzy Continuous Mappingsin Fuzzy Bitopological Spaces
**
K.M. Abd El-Hakeim
Department of Mathematics Faculty of Science
Assiut University, Assiut, Egypt
**Abstract:** The aim of this paper, deals with the concepts of fuzzy semi-preopen sets and fuzzy semi-precontinuous mappings due to Park and Lee [10] have been generalized to the fuzzy bitopological setting and some of its basic properties are discussed . Characterizations of these mappings along with their relationship with certain other types of mappings are investigated.
**Keywords:** Fuzzy Pairwise weakly semicontinuous (semiopen, semiclosed) mappings, fuzzy pairwise weakly continuous(open, closed) mappings
Pseudo-metrics and ¦³-equivalences
Bernard De Baets
Department of applied Mathematics and Computer Science
University of Gent, Krijslaan 281 (S9)
B-9000 Gent, Blegium
Radko Mesiar
Department of Mathematics
Slovak Technical University, Radlinskeho 11
81368 Bratislava, Slovakia
Abstract:
In this paper, we discuss the relationship between pseudo-metrics and¦³-equivalences; the latter are a natural generalization of the classical concept of an equivalence relation. It is shown that in the construction of pseudo-metrics from¦³-equivalences triangular norms with an additive generator play a key role. Conversely, in the construction of¦³-equivalences from pseudo-metrics this role is played by triangular norms with a continuous additive generator, or equivalently, Archimedean triangular norms.
** Keywords:** Additive generator, Archimedean property, pseudo-metric, ¦³-equivalence, triangular norms.
**Decomposition Theorems and Representation Theorems of L-fuzzy Fields
**
Guangqing Wu, Ping Du
Department of Mathematics, Hebei Vocation and Technology Teachers College
Shijiazhuang 050031, Hebei, P.R. China
Fugui Shi
Department of Mathematics, Yantain Teachers College
Yantai 264025, Shandong, P.R. China
**Abstract:** In this paper, first the concept of L-fuzzy fields is introduced when L is a completely distributed lattice. Then the equivalent characterizations, decomposition thorems and representation theorems of L-fuzzy fields are given.
**Keywords**:
L-fuzzy algebra, L-fuzzy fields.
**Monotonic Intersection Decomposition of Fuzzy Sets**
Liu Huawen, Chen Guangdong
Department of Mathematics and Physics
Shandong University of Technology, Jinan 250061, P.R. China
**Abstract:** In this paper, themonotonic decomposition theorems are introduced. It shows that any fuzzy set can be described as the product or limit of some simple fuzzy sets which are countable and montonic decreasing. At the same time, the monotonic decomposition theorems of 2-fuzzy sets are given.
** Keywords:** Fuzzy set, monotonic intersection decomposition, intersection decomposition theorem. |