THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 15, Number 4, December 2007

CONTENT

DETAILS

Cluster Sets of Functions and Multifunctions in Fuzzy Topological Spaces

A. Nouh and M. E. El-Shafei

Mathematics Department, Faculty of Science, Mansoura University, Egypt

Abstract: In this paper the concept of S-cluster fuzzy sets, of fuzzy functions and fuzzy multifunctions between fuzzy topological spaces is introduced. As an application, characterizations of fuzzy Hausdorff and -closed fuzzy topological spaces are achieved via such cluster fuzzy sets.

Keywords: Fuzzy topology, Q-neighborhood, S-cluster fuzzy set, -closedness, -closure, semi-open fuzzy sets.

Function S-rough Sets and Its Heredity Law Depending on The Extension of Attributes

.Dongya Li

Department of Mathematics, Huang huai University, Zhumadian, Henan 463000, PRC school of Mathematics and Statistics, Wuhan University, Wuhan 430072, PRC

Kaiquan Shi

school of Mathematics and Systems Science, Shandong University, Jinan, Shandong 250100, PRC

Abstract: Using function S-rough sets, this paper gives the concepts of F-generation, F-heredity, and the characteristics of F-heredity of system rough law; presents the principle of F-heredity characteristic and attributes characteristic principle of F-heredity of system rough law. F-heredity relies on the attributes complement to the attributes set . From such discussion, this paper present law mining by the method of F-heredity.

Keywords: Function S-rough sets, rough law generation, F-heredity, F-heredity principle, law, F-mining, application

The Method of Centred Systems in Fuzzy Topological Spaces

M. K. Uma, E. Roja

Department of Mathematics Sri Sarada College for Women Salem-16, Tamilnadu India

G. Balasubramanian

Department of Mathematics Periyar University Salem-11, Tamilnadu India

Abstract: In this paper we introduce maximal fuzzy centred system, the fuzzy and absolute of fuzzy space R. The purpose of this paper is to study the fundamental theorem on fuzzy irreducible and fuzzy perfect mappings.

Keywords: Maximal fuzzy centred system, the fuzzy space , absolute of fuzzy space R and the fuzzy perfect mappings.

A Generalized Fixed Point Theorem in Complete Fuzzy Metric Space

Sikha Saikia(Bordoloye)

Department of Mathematics, Gauhati University Guwahati-781014, Assam(India)

Abstract: Till now, analogue of various fixed point theorem have been established in fuzzy structure. T. Veerapandi and M. Mariappan [10] have obtained a fixed point theorem which generalizes some other fixed point theorems due to Banach[1,5], Kannan [5,7] and Ciric [2] respectively. In this paper we have established the analogue of fixed point theorem obtained by Veerapandi and Mariappan [10] in complete fuzzy metric space defined by Kaleva and Seikkala[6].

Keywords: Fuzzy Metric, Complete Fuzzy Metric Space.

Nearly Fuzzy Regular Spaces

Geetha Sivaraman

Research Scholar in Mathematics Thiagarajar College of Engineering, Madurai-625015, India

V. Lakshmana Gomathi Nayagam

Department of Mathematics, National Institute of Technology Tiruchirappalli-620015 India

Abstract: In this paper, a new notion of Nearly Fuzzy Regular Spaces is introduced and studied. Most of the theorems for regular spaces in the crisp set up have been extended to nearly fuzzy regular spaces in the fuzzy set up. Counter examples for theorems which can not be extended from the crisp set up to the fuzzy set up are studied. This new definition has been compared with the existing definitions of fuzzy regularity[3], [4], [6], [7].

Keywords: Fuzzy topology, Fuzzy Hausdorff Spaces, Fuzzy Regular Spaces, Induced topology, Induced fuzzy topology.

Intuitionistic Fuzzy Ideals

D. K. Basnet

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

Abstract: In this paper the Artinian and Noetherian rings have been characterized by Intuitionistic Fuzzy Ideals and alternative proofs of some well- known results of Artinian and Noetherian rings have been given with the help of Intuitionistic Fuzzy Ideals.

Keywords: Intuitionistic Fuzzy Set, Intuitionistic Fuzzy Subrings, Intuitionistic Fuzzy Ideals, Artinian rings, Noetherian rings.

IF Projective and Injecyive Submodule

D. K. Basnet

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

Abstract: In this paper an ideal of free intuitionistic fuzzy submodule, intuitionistic fuzzy projective and injective submodule was introduced and discussed some of their properties.

Keywords: Intuitionistic fuzzy submodule, free intuitionistic fuzzy submodule, intuitionistic fuzzy projective and injective submodule

Imprecision Sensitivity Analysis of Monochrome and Color Textural Images Using Fuzzy Higher Order Statistics

R. Sukesh Kumar

Department of Electronics and Communication Engineering, Birla Institute of Technology, Mesra, Ranchi, India.

A. K. Ray

Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology, Kharagpur, 721302, India.

S. C. Goel

Department of Electronics and Communication Engineering, Birla Institute of Technology, Mesra, Ranchi, India.

Abstract: Fuzzy statistics is capable of characterizing imprecision embedded in digital images. Second order fuzzy statistics of digital images have been proved to be very effective in extraction of features of textural images. Co-occurrence matrix is computed to find out the repetitive property of textural images in intensity of pixels, distance and direction. Then fuzzification of intensity(I), distance and using Triangular, Trapezoidal and Gaussian membership functions, yields excellent results on monochrome and color textural images, A sensitivity analysis performed on textural features computed from fuzzified co-occurrence matrices, proves the superiority of fuzzy statistics over crisp statistics, in exhibiting superlative insensitiveness to imprecision in textural images. Results obtained by image segmentation, using fuzzy co-occurrence matrix, further emphasize the superiority of fuzzy statistics over crisp statistics.

Keywords: Fuzzy Statistics, Fuzzy Co-occurrence matrix, Computation of features, Sensitivity Analysis, Image Segmentation

The Theory of Localization for Intuitionistic Fuzzy Topological Spaces

Ratna Dev Sarma

Department of Mathematics, Rajdhani College(University of Delhi) Raji Garden, Delhi-15 India

Abstract: The theory of localization is developed for intuitionisitic fuzzy topological spaces. Intuitionisitic fuzzy points(IFP) are introduced and their two types of containment into an intuitionistic fuzzy set (IFS) is discussed. The Q-nbd system is developed. Intuitionisitic fuzzy nets are introduced. Closure of an IFS is characterized by using the notion of convergence of intuitionistic fuzzy nets. Two types of fuzzy continuity at an IFP are developed. The two notions are independent of each other; however, they turn out to be equivalent when considered globally. Several characterizations of fuzzy continuity are provided, exhibiting the compatibility of the concepts of Nbd-syetem, Q-nbd system and of the convergence of intuitionistic.

Keywords: Intuitionistic fuzzy set, fuzzy topological, fuzzy continuity, intuitionistic fuzzy point, Q-nbd, fuzzy set.

On Connectedness in Intuitionistic Fuzzy Spaces

Ratna Dev Sarma

Department of Mathematics, Rajdhani College(University of Delhi) Raji Garden, Delhi-110015, India

Abstract: The notion of connectedness is further studied for intuitionistic fuzzy set. Four different types of components, namely Ci- components (i=1,2,3,4) are introduced, using four equivalence relation. Each Ci- components is a maximal Ci- connected intuitionistic fuzzy set of the space (i=1,2,3,4). The constant IFS 1 is disjoint union of its Ci- components (i=1,2,3,4).

Keywords: Ci- components (i=1,2,3,4) intuitionistic fuzzy set, intuitionistic fuzzy point, intuitionistic fuzzy spaces.

Using The Body of Evidence Approach for Optimal Drug Dosage

Andre de Korvin and Jeong-Mi Yoon

Department of Computer and Mathematical Science, University of Houston, Downtown, One Main Stree, Houston, TX 77002, USA

Abstract: In this paper we discuss a decision making model for an optimal dosage of antidepressants using the concept of the body of evidence[10,11] and type-2 fuzzy sets [3,4,8]. Throuth this example, we develop some methodologies in making optimal decisions for drug dosage under partially specified environments of each patient.

Keywords: Body of evidence, Risk Levels, Type-2 fuzzy sets, Interval Valued Sets, Similar and Dissimilar Environments, Anti-depressants.

Generalized Quantifier in The Lattice-valued First-order Logic

Zhou Ping

Dept. of Math. Sichuan Normal University, Chendu, Sichuan 610066, P.R. China

Jiang Ming

Dept. of Physics, Southwest University for Nationalities, 610041, Chendu, P.R. China

Xu Yang

Intelligent Control Development Center, Southwest Jiaotong University, 610031 Chendu, P.R. China

Abstract: In this paper, we discuss the properties of the generalized quantifier in the lattice-valued first-order logic, and get some result of fuzzy reasoning with generalized quantifier.

Keywords: Fuzzy reasoning, lattice-valued first-order logic, generalized quantifier

A Method for Solving Fuzzy General Linear Systems

S. Abbasbandy

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, 14778,

Iran

Department of Mathematics, Science and Research Branch, Imam Khomeini International University Ghazvin, 34194, Iran

T. Alliahviranloo

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, 14778, Iran

R. Ezzati

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, 14778,

Iran

Department of Mathematics, Karaj Branch, slamic Azad University, Karaj, Iran

Abstract: In this paper, the main aim is to develop a method for solving an arbitrary fuzzy linear sysem which and the right hand side is symmetric fuzzy number vector.

Keywords: Sysem of fuzzy linear equations, Fuzzy number vector.

Fuzzy Belongingness, Fuzzy Quasi-coincidence and Convergence of Generalized Fuzzy Filters

K. K. Mondal

Department of Mathematics, Kurseong College Kurseong-734203, West Bengal, INDIA.

S.K.Samanta

Department of Mathematics, Visva Bharati, Santiniketan-731235, West Bengal, INDIA.

Abstract: In this paper, concepts of ¡®fuzzy belongingness¡¯ and ¡®fuzzy quasi-coincidence¡¯ are introduced;graded q- Neighbourhood structure is developd and convergence of generalized fuzzy filters is studied in L-fuzzy topological space.

Keywords: Fuzzy belongingness, fuzzy quasi-coincidence; gradation of openness; gradation of neighbourhoodness; L-fuzzy topological space; g- filters.

On Some Generalisations of Evidence Measures

Gigi George

Department of Mathematics, Mar Thoma College for Women, Perumbavoor, Ernakulam, Kerala PIN:683542, S.India.

Sunny Kuriakose

Department of Mathematics, Union Christian College, Aluva, Ernakulam, Kerala, South India.

Abstract: In this paper we introduce two generalized evidence measures-C-valued evidence measures on Boolean algebras and on C-fuzzy sets(C-denotes a bounded chain) and study their properties. These generalizations are better suited for building evidence theoretic models in fuzzy and certain arbitrary settings.

Keywords: C-valued fuzzy measure, C-valued belief measure, C-valued plausibility measure, C-valued basic probability assignment function.

Vague Groups and Vague Fields

John N. Mordeson

Department of Mathematics, Creighton University Omaha, Nebraska 68178, USA

Kiran R.Bhutani

Department of Mathematics, The Catholic University of America Washington DC 20064, USA

Abstract: We continue with our study of vague groups. We also example the notion of a vague field. For a pair , where is a vague binary operation on X, we define in the language of fuzzy equalities, the notion of an identity and of an inverse of an element in X. We show that these definitions are equivalent to the original definitions of an identity and inverse of an element in a vague group. It has previously been shown how a vague group(vague, ring) can be constructed using a desceding chain of normal subgroups(ideals). In this paper, we show how a vague group can be constructed using an ascending chain of normal subgroups. We show that a preimage of a vague group under a homomorphism f is a ker f-vague group. Construction of a vague field using a descending chain of subfiled is presented.

Keywords: Vague group, vague fields, Galois theory

Fuzzy Pre--irresolute Functions

V. Seenivasan

Department of Mathematics, Jawahar Science College Neyveli-607803, India

G. Balasubramanian

Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chennai-600005, India

Abstract: A new class of functions called fuzzy pre--irresolute functions in fuzzy topological spaces are introduced in this paper. We also obtain some characterizations of this class and its properties and the relationship with other classes of functions between fuzzy topological spaces.

Keywords: Fuzzy pre--irresolute, Fuzzy product, Fuzzy almost irresolute, Nowhere dense fuzzy set.

Generalized Functional 0-1 Programming with Fuzzy Parameter in The Objective Function

J. K. Dash, G. Panda and S. Nanda

Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, West Bengal, INDIA

Abstract: This paper deals with a solution algorithm for a generalized fractional programming problem in which the objective is formed in fuzzy environment and the decisions are restriced to be 0 or 1. The solution method is justified through a numerical example.

Keywords: Generalized fractional programming, 0-1 fractional programming, fuzzy parameter, -cut of a fuzzy number.

On n-fold Fuzzy BBC-ideals with Operators

Jianming Zhan and Zhisong Tan

Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Provence, 445000. P. R. China

Abstract: N-fold Fuzzy BBC-ideals of BBC-algebra with operatora (i.e.M- BBC-algebra) are investigated. N-fold M-Noether M- BBC-algebra and their M-normal n-fold Fuzzy BBC-ideals are descibed. The method of extension of n-fold M-Fuzzy BBC-ideals saving the images is given.

Keywords: n-fold M-Fuzzy BBC-ideal, n-fold M-BBC-ideal, M-normalization, M- BBC-algebra

- fuzzy Subrings and - fuzzy Ideals

Bingxue Yao

Department of Mathematics, Hainan University, Haikou, Hainan 571158 P. R. China School of Mathematics Scinece Liaocheng University, Liaocheng, Shandong 252059, P. R. China

Abstract: In this paper, we intruduce the concepts of - fuzzy subrings and - fuzzy Ideals which can be regarded as a generalization of Liu¡¯s and Bhakat and Das¡¯correspondence concepys. We also introduce the concept of - fuzzy quotient ring and establish the isomorphism theorem of - fuzzy quotient ring.

Keywords: - fuzzy subring, - fuzzy Ideal, - fuzzy quotient ring, homorphism, isomorphism

Intutionistic Fuzzy g-topological Spaces

Young Bae Jun

Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea

Seok Zun Song and Kyung Tae Kang

Department of Mathematics, Cheju Natonal University, Jeju 690-756, Korea

Abstract: The notion of intutionisitic fuzzy g-topological spaces and intutionisitic fuzzy g-continuos mappings is introduced, and relations between intutionisitic fuzzy g-continuos and group homorphism are investigated.

Keywords: Intutionisitic fuzzy g-topoloy, fuzzy g-topological spaces, fuzzy g-continuos mapping.

A Remark on Balasubramaniam Fixed Point Theorem for Four Mappings in A Fuzzy Metric Space

R. P. Pant

Mathematics department, D.S.B. Campus Kumaun University Nainital, (Uttaranchal) INDIA

A. S. Ranadive

Department of Mathematics and statistics Guru Ghashidas University, Bilaspur, (Chhattisgarh) INDIA

D. Gopal

Department of Mathematics and statistics Guru Ghashidas University, Bilaspur, (Chhattisgarh) INDIA

Abstract: Most recently Balasubramaniam et.al.[1] have obtained an interesting fixed point theorem for four mapping in a fuzzy metric spaces using the notion of compatible pair of reciprocal continuous mapping which generalize a result of Pant[6] for fuzzy mapping in a fuzzy metric space. The main purpose of this note is to present an entirely different version of their main result by removing the assumption of compatibility and reciprocal continuity and relacing the completeness of the space with a set of alternating conditions.

Keywords: fuzzy metric spaces, R-weakly continuous maps, compatible maps reciprocal continuity, common fixed point.