THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 13, Number 2, June 2005

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On Fuzzy Positive Implicative Ideals of BCK-algebras

Biao-Long Meng

Department of Basic Courses, Xian University of Science and Technology, Xian 710054, P. R. China

Abstract: In the present paper we give some characterizations of fuzzy positive implication ideals in BCK-algebra x and investigate an extension property and Cartesian products of fuzzy positive implicative ideals.

Keywords: Fuzzy ideal, fuzzy positive implicative ideal, fuzzy Cartesian product

Mated Fuzzy -irresolute Functions

S.E.Abbas

Department of Mathematics, Faculty of Science, South Valley University, Sohag 82524£¬Egypt

Abstract: We introduce -fuzzy -open (closed) sets in mated fuzzy topological spaces. We investigate some properties of them. Moreover, we introduce and study fuzzy -irresolute function, fuzzy -irresolute open (close) function and fuzzy strongly semi -irresolute function in mated fuzzy topological spaces. Some of their characteristic properties are considered. Also, we investigate the relationships between these classes of functions.

Keywords: -fuzzy -open (closed) sets, fuzzy -irresolute function,, fuzzy strongly semi -irresolute function,

Domination in Fuzzy Graphs-¢ò

A. Somasundaram

Department of Mathematics, MEPCO Schlenk Engineering College, Sivakasi 626005£¬ India

Abstract: Let be a fuzzy graph on V. A subset S of V is called a dominating set of G if for every there exists a vertex in S such that . The minimum fuzzy cardinality of a dominating set in G is called the domination number of G and is denoted by or . In this paper we obtain several bounds for and discuss the effect of the removal of a vertex of G on its domination number.

Keywords: Fuzzy graph, dominating set, fuzzy cardinality, domination number

Triangular Normed Fuzzy Subalgebrasin Lattice Implication Algebras

Young Bae Jun

Department of Mathematics Education, Gyeongsang National University Chinju 660-701, Korea e-mail:ybjun@nongae.gsnu.ac.kr

Seok Zun Song

Department of Mathematics,Cheju National University ,Cheju 690-756£¬Korea e-mail:szsong@cheju.ac.kr

Yang Xu

Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, P. R. China e-mail:xuyang@home.swjtu.edu.cn

Abstract: Using a t-norm T, the direct product and T-product of T-fuzzy subalgebras in lattice implication algebras are discussed, and their properties are investigated; and the notion of T-fuzzy quasi subalgebras in lattice implication algebras is introduced, and then some of Foster¡¯s results on lattice implication homomorphic image and inverse image and inverse image sre applied to T-fuzzy topological quasi subalgebras.

Keywords: T-fuzzy (quasi) subalgebra, T-fuzzy topological quasi subalgebra

-convergences in Fuzzy Topological Spaces

M.Caldas

Department of Mathematics Aplicada, University Federal Fluminense, Rua Mario Santos Braga, 24020-140, Niteroi, RJ Brasil e-mail:gmamccs@vm.uff.br

D.N.Georgiou

Department of Mathematics, University of Patras 26500 Patras, Greece e-mail:georgiou@math.upatras.gr

S.Jafari

Department of Mathematics and Physics, Roskilde University Postbox 260,4000 Roskilde, Denmark e-mail:sjafari@ruc.dk

T.Noiri

Yatsushiro College of Technology, 2627 Hirayama shinmachi, Yatsushiro-shi, Kumamoto-ken, 866 Japan e-mail:noiri@as.yatsushiro-nct.ac.jp

Abstract: In this paper we introduce and study the notions of fuzzy ¦Á-upper limit, fuzzy¦Á-lower limit and the fuzzy¦Á-continuous converdence on the set of fuzzy¦Á-continuous functions.

Keywords: Fuzzy sets, fuzzy topology, fuzzy¦Á-upper and¦Á¡ªlower limit and fuzzy¦Á-continuous convergences

One Direction S-Rough Sets

Kaiquan Shi

School of Mathematics and Systems Science, Shandong University, Jinan, Shandong 250100£¬ P.R.China

TingCheng Chang

Department of Information Management, Ling-Tung Institute of Technology, Tai Chung 402,Taiwan, ROC

Abstract: This paper presents one direction singular rough sets, one direction singular rough sets are briefly called one direction S-rough sets, in one direction S-rough sets, has one direction dynamical characteristic. It presents a concept of an elementary transfer, in one direction S-rough sets, one direction dynamic characterisitic of is due to the family of elementary transfer F on the universe of discourse of U and the transfer movement of element by the effect of . One direction S-rough sets have the characteristic of information supply. Under some definite conditions, One direction S-rough sets may be reduced to Z-rough sets (Z.Pawlak rough sets). This paper presents general mathematical concepts of one direction S-rough sets,;basic characteristics of one direction S-rough sets; existing background of one direction S-rough sets; relationship between one direction S-rough sets and Z-rough sets.

Keywords: One direction S-rough sets, elementary transfer transfer, one direction S-seet, relationship between one direction S-rough sets and Z-rough sets

Two Direction S-rough Sets

Kaiquan Shi

School of Mathematics and Systems Science, Shandong University, Jinan, Shandong 250100£¬ P.R.China

Abstract: This paper puts forward the concept of two direction singular sets using [1], briefly called two direction S-sets. Using this concept, this paper presents two direction singular rough sets, briefly called two direction S-rough sets; it also gives the structure and characteristic of two direction S-rough sets, discusses the relationship between two direction S-rough sets and one direction S-rough sets[1], the relationship between two direction S-rough sets and Z.Pawlak rough sets[6].Using one direction S-rough sets[1], two direction S-rough sets, it discusses the heredity of knowledge and the genic variability of knowledge; heredity and variability are phenomena in biology. The discussion on the heredity of knowledge and the genic variability of knowledge is one of the important characteristics of one direction S-rough sets, two direction S-rough sets.

Keywords: Two direction S-rough sets, genetic knowledge, genic variation, principle of knowledge¡¯s heredity, theorem of knowledge¡¯s discernible characteristic.

Fuzzy k-ideals in Semirings

Young Bae Jun

Department of Mathematics Education, Gyeongsang National University Chinju 660-701, Korea e-mail:ybjun@nongae.gsnu.ac.kr

Hee Siku Kim

Department of Mathematics, Hanyang University, Seoul 133-791£¬ Korea e-mail:heekim@hanyang.ac.kr M.A.Ozturk Department of Mathematics, Faculty of Arts and Sciences, Cumhuriyet University, 58140 Sivas, Turkey e-mail:maozturk@cumhuriyet.edu.tr

Abstract: In this paper we consider an extension of a fuzzy k-ideals in a semiring, and some properties in the semiring of fuzzy numbers.

Keywords: Semiring, (fuzzy) k-ideal, fuzzy (cauchy) sequence

An Efficient Method for The Multivariate LAD Regression and Multiresponse Permutation Procedures Applied to Chemical an Overt Diabetes

Salem A.Masoud

Dept. of Math. Faculty of Science Tanta Univ., Tanta, Egypt

Abstract: The importance of multivariate least absolute deviation (MLAD) in the present paper is its logical association with Euclidean Distance based on multi-response permutation procedures (MRPP). As a further comment, multivariate residential analysis are naturally allowed for either type of comparison due to the basic nature of MRPP. The analysis of treatment effects when skewed data are involved. The method incorporates multivariate linear regression and MRPP. This method applied to nature of chemical and overt diabetes.

Keywords: Multivariate regression, nonparamtric, nonparamtric multivariate

Fuzzy Programming with Hyperbolic Membership Functions for Multiobjective Capacitated Solid Transportation Problem

A.K.Bit

Department of Mathematics, Faculty of Civil Engineering, College of Military Engineering, Pune-411031 (M.S). India

Abstract: The linear multiobjective capacitated soild (three-dimensional) transportation problem in which the supply, demand and capacity constraints are all equality type, capacity restrictions on each route by means of conveyance are specified and the objectives are non commensurable and conflicting in nature. The fuzzy programming algorithm with hyperbolic membership functions for obtaining efficient solutions as well as the best compromise solution of a multiobjective capacitated solid transportation problem has been presented in this paper. A Fortran program has been developed based on this algorithm. An example is included to illustrate the methodology. Also this this method is compared with one existing fuzzy programming algorithm with linear membership functions using same example.

Keywords: Multi criteria decision making, capacitated solid transportation problem, fuzzy programming, efficient solution, compromise solution, hyperbolic membership function.

On Existence of A Bounded Inverses for Some Differential Operators with Unbounded Coefficients

Sh.EL-Bendary, Abd EL-Nasser.Salem, E.M.EL-Abd and M.A.EL-Attar

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

Abstract: In this paper we give a new necessary and sufficient conditions in order that the linear differential operator with unbounded coefficients on the line R has a bounded inverse and Fredholm.

Keywords: Linear differential operators, inverse operators, Fedholm operators.

Some Good Typeset of Paracompactness in Sostak¡¯s Fuzzy Topology

S.E.Abbas

Department of Mathematics, Faculty of Science, Sohang 82524, Egypt

Abstract: We introduce in Sostak fuzzy topological spaceship definitions of paracompactness, almost paracompactness, and near paracompactness all of which turn to be good extensions of their classical topological counterparts. Fuzzy semi-paracompact, para S-closed and weakly paracompact spaceship are treated to a similar approach.

Keywords: Fuzzy paracompact, almost, nearly, weaklt, goodness.

Some Properties of Intuitionistic R-fuzzy Semi-open Sets

S.E.Abbas and M. Azab Abd-allah

Department of Mathematics, Faculty of Science, Sohang, Egypt

* Department of Mathematics, Faculty of Science, Assiut, Egypt

Abstract: In this paper, we introduce intuitionistic r-fuzzy semiopen (closed) sets in intuitionistic fuzzy topological space [20]. We investigate some properties of them. Moreover, we investigate the relationship between intuitionistic fuzzy irresolutity and intuitionistic fuzzy (supra) continuity.

Keywords: Intuitionistic fuzzy (supra) topological spaces, intuintionistic closure spaces, intuitionistic r-fuzzy semi-open (closed) sets, intuitionistic r-SR, spaces, intuitionistic fuzzy (supra) continuity, intuitionistic fuzzy irresolute maps.

-fuzzy Quotient Subgroups

Bingxue Yao

School of Mathemetics Science, Liaocheng University, Liaocheng, Shandong 252059£¬China

Abstract: Based on the concepts of -fuzzy subgroup [1,2,3] and -fuzzy normal subgroup [4] suggested by S.K.Bhakat, the notions of -fuzzy quotient group and -fuzzy quotient subgroup are introduced. Some properties of -fuzzy normalize and -fuzzy centralizer are discussed. At last, several isomorphism theorems of -fuzzy quotient subgroups are established.

Keywords: -fuzzy normal subgroup, -fuzzy normalize, -fuzzy centralizer, -fuzzy quotient group, -fuzzy quotient subgroup.

Induced Intuitionistic Gradation of Openness

S. E. Abbas

Department of Mathematics, Faculty of Science, Sohang, Egypt

Abstract: In this paper£¬Good definitions of intuitionistic Hausdorffiness and intuitionistic compactness in intuitionistic fuzzy topological spaces are presented and some of their interesting properties are studied.

Keywords: Intuitionistic gradation of openness, good extension, intuitionistic Hanusdorffiness, intuitionistic compactness.

Rough Boolean Algebras

B.K.Saikia

Department of Mathematics, Lakhimpur Girls¡¯College, North Lakhimpur-787031, Assam, India e-mail:bksaikia12@rediffmail.com

P.K.Das

Department of Mathematics, NERIST, Nirjuli-791109, Arunachal Pradesh, India e-mail:pkd@nerist.ernet.in

A.K.Borkakati

Department of Mathematics, Tezpur University, Tezpur-784028, Assam, India

Abstract: Htel concept of rough Boolean algebra and rough subalgebra are introduced based upon Pawlak¡¯s notion of indiscernibility relation between elements in a set. Some characterizations of rough Boolean algebras and rough subalgebras are given.

Keywords: Rough set, rough Boolean algebra, rough subalgebras

Minimal Nice-Urysohnness on Completely Distributive Lattices

Fang Jinming

Department of Mathematics, Ocean University of China, Qing Dao 266003£¬ P.R.China

Abstract: The main interest of this paper is the investigation of minimal properties about nice-Urysohnness [15] of co-topologies on lattices and the lattice is not required to have any order-reversing involution. Some of basic properties of nice-Urysohnness on lattices are discussed; for any complete and completely distributive lattices L, the existence of minimal nice-Urysohnness co-topology is obtained; characterizations of minimal nice-Urysohn co-topo;ogies on L is established in terms of -ideals.

Keywords: Topology; topological molecular lattice; nice-Urysohn; minimal nice-Urysohn; linked component; -ideal

The Series of Complex Fuzzy Valued and its Convergence

Sheng quan Ma

Department of Mathematics, Northwest Minorities University, Lanzhou 730030,Gang Su,P.R.China e-mail:mashengquan@163.com;msq@xbmu.edu.cn

Abstract: In this paper, the basic concepts of complex fuzzy number¡¯s series is given firstly, and some properties of complex fuzzy number¡¯s series is given too. Furthermore, I gave the concept of complex fuzzy-valued function¡¯s series and discussed it¡¯s convergence. In the end of this paper the discrimination principle of the convergences are given.

Keywords: Complex fuzzy number; series of complex fuzzy number; complex fuzzy-valued function; series of complex fuzzy-valued function; convergence.

A Generalization of Egoroff¡¯s Theorem on Fuzzy Measure Spaces

Jinjie Song

Department of Technology Research, Sidewave Co.,Ltd.Shimotsuruma 4374-4-410£¬ Yamato, Kanagawa, 242-0001£¬Japan

Abstract: In this paper, we introduce the concept of weak property (S) of set function and show that Egoroff¡¯s theorem in classical measure theory remains valid for the monotone set functions which are strongly order continuous and has weak property (S). Egoroff¡¯s theorem on fuzzy measure spaces is generalized and inproved.

Keywords: Non-additive measure, monotone set function, weak property (S), Egoroff¡¯s theorem

Triangular Normed Fuzzy Subalgebras in Lattice Implication Algebras

Shui-LiChen

Department of Mathematics,School of Science, Jimei University, Xiamen, Fujian 361021£¬ P.R.China

Abstract: In this paper, the concepts of an L-fuzzy order-preserving operator -space having universal signifivance and including L-fuzzy topological spaces, R-neighborhood, -closure, -interior, -closed set and -open set are first introduced. Some foundational properties are obtained. Secondly, the notion of -subspace, -base and -subbase of an L-fuzzy order-preserving operator -space are presented and discussed. Finally, the conceptions of -continuity£¬ - Openness, -closeness and -homeomorphism of L-fuzzy mapping from an L-fuzzy order-preserving operator -space into another L-fuzzy order-preserving operator -space are recommended. Theia characterizations and some interesting properties are given. Almost all the existing typeset of L-fuzzy continuous mapping and its various weaker forms between L-fuzzy topological spaces and many results concerning them are regarded as special cases of our corresponding notions and results.

Keywords: Fuzzy lattice; L-fuzzy order-preserving operator -space; L-fuzzy mapping; -closure; -base; R-neighborhood; -interior; -closed set ; -open set