THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 17, Number 3, September 2009

CONTENT

DETAILS

TL-mappyings

F. I. Sidky

Department of Mathematic, Faculty of Science, University of Zagazig, Egypt

N. A. AL-Essa

Science Department, Faculty of Education for Girls, Riyadh, Saudi Aradia

Abstract: We introduce concepts of TL-mapping, surjective TL-mapping, injective TL-mapping, TL-monomorphism, and TL-epimorphism, and we prove some of their properties.

Keywords: TL-mapping, strong TL-mapping, TL-morphism, TL-isomorphism.

Fuzzy Total Variation

Girija Kumari R.

Department of Mathematic, N. S. S. Hindu College, Changanacherry, Kerala, India

Abstract: In this paper we develop fuzzy total variation using an additive fuzzy measure. We introduce fuzzy u-null function, fuzzy u-null function, fuzzy simple function and fuzzy integral.

Keywords: Fuzzy u-null set, fuzzy u-null function, fuzzy simple function.

On Asymptotically Lacunary Statistical Equivalent Sequences of Fuzzy Numbers

Ekrem Savas

Department of Mathematic, Istanbul Ticaret University, Uskudar-Istanbul, TURKEY

E-mail: ekremsavas@yahoo.com

Abstract: This paper presents the following definition which is a natural combination of the definitions for asymptotically equivalent and lacunary statistical convergence of fuzzy numbers. The two sequences [X]=(Xk) and [Y]=(Yk) of fuzzy numbers are said to be asymptot-ically lacunary statistical equivalent of multiple L provided that for every . (denoted by) and simple asymptotically lacunary statistical equivalent if L=1. In addition, we shall also present asymptotically equivalent analogs of Kwon and Sung's theorems in [3].

Keywords: Fuzzy numbers, asymptotically equivalent, asymptotically lacunary statistical equivalent.

Linear Continuous Functionals On FN-type Spaces

Sorin G. Gal

Department of Mathematic and Computer Sciences, University of Oradea, Romania 410087 Oradea, Romania

E-mail: galso@uorade.ro

Abstract: By using the spaces of fuzzy number, in e.g. [5] have been considered several complete metric spaces (called here FN-type spaces) endowed with addition and scalar multiplication, such that the metrics have nice properties but the spaces are not linear, i.e. are not groups with respect to addition and the scalar multiplication is not, in general, distributive with respect to usual scalar adition. This paper deals with the from of liner continuous functionals defined on these spaces.

Keywords: Fuzzy numbers, fuzzy-number-valued functions, FN-type spaces, linear and continuous functions.

On Fuzzy Parametric Linear Fractional Programming Problem

E. Ammar and H. Khalifa

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

Abstract: This problem deals with the solutions of linear fractional programming problems with fuzzy parameters in both the objective function and the constrains. The concepts of fuzzy solutions of these problems are established by a parametric approach. An illustrative example is given for given for the sake of the developments.

Keywords: Linear fractional programming problem; Fuzzy number, parametric approach; Fuzzy optimal solution.

On Fuzzy Mathematical Programming Problems

E. E. Ammar

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

Abstract: Mathematical programming is one of the areas to which fuzzy set theory has been applied extensively. Primarily based on bellman and Zadeh¡¯s model of decision in fuzzy environments, models have been suggested which allow flexibility in constrains and fuzziness in the objective function in linear and nonlinear programming. This paper review major models and theories in this area.

Keywords: Fuzzy sets, mathematical programming, fuzzy linear (nonlinear) Programming, fuzzy multiobjective linear (nonlinear) Programming.

Study on The Application of The Fuzzy Fusion of The Target Track from Radar and AIS

Lin Changchuan, Sun Tengda, Hong Yuanzhu and Huang Liqing

Navigation College, Jimei University, Xiamen 361021, China

Abstract: It studies the fusion methods of the target tracks from the multiple sensors, radar and AIS, using the fuzzy correlation with multi-factor fuzzy integration decision-making and the mergence with weighed-statistics based on the theory of multi-sensor information fusion, and establishes the fuzzy sets of factor, judgment, rule, and the mathematical model. By the use of computer, the results of the simulation preliminarily verify that the methods can effectively improve the accuracy and reliability of the target tracks.

Keywords: Track; corrrelation; mergence; accuracy

Fuzzy Cosets of Prime Fuzzy Submodules

S. Bhavanari

Department of Mathematic, Acharya Nagarjuna University, Nagarjuna Nagar-522510, A. P., India.

E-mail: bhavanari2005@rediffmail.com

S. P. Kumcham

Department of Mathematic, Manipal Institute of Technology Manipal Academy of Higher Education (Deemed University), Manipal-576104, India.

E-mail: drkuncham@yahoo.com

L. R. P . Jupudi

Department of Mathematic, PG Centre, PB Sidhardha College of Arts and Science Vijayawada-520010, A. P., India.

E-mail: ran_jupudi@rediffmail.com

Abstract: Let R be a fixed (not necessarily commutative) ring with identity, and M a unitary left R-module. Some fundamental results related to the concepts "fuzzy cosets of prime fuzzy submodules" were proved. The quotient module is a prime module whenever is a prime fuzzy submodule. Conversely, if is a fuzzy submodule attaining exactly two values, and the quotient module is prime then the given fuzzy submodule is prime. Finally, it is proved that if is a fuzzy submodule of M then there exists an order preserving mapping between the sets P and Q where P is the set os all of all prime fuzzy submodules of with and ; and Q is the set of all prime fuzzy submodules of the quotient module with and .

Keywords: Prime submodule, fuzzy submodule, prime fuzzy submodule, fuzzy cosets of a fuzzy submodule.

w*Ti-Separation Axioms in Lw-Spaces

Baoguo Ma and Yanjun Wang

College of Mathematics and Computer Science, Yanan 716000, China.

E-mail: yadxmbg@163.com , Wangyanjun1977@163.com

Abstract: The main purpose of this paper is to introduce w*Ti-separation axioms (i=0,1,2) in Lw-spaces and give some of their characterizations as well as the relations of these axioms and other separation axioms. Meanwhile, a series of properties for them are investigated.

Keywords: Lw-spaces; w-remote neighborhood; w*Ti-separation axioms

Images and Preimages of L-Fuzzy Ideal Bases

A. A. Ramadan

Department of Mathematic, Faculty of Science, Beni-suef University, Egypt.

E-mail: aramadan58@yahoo.com

A.A.Abd El-Latif

Department of Mathematic, Faculty of Science, Beni-suef University, Egypt.

E-mail: ahmeda73@yahoo.com

Abstract: In this paper, we study two types of images and preimages of L-fuzzy ideal bases on a strictly two-sided commutative quantale L by using Zadeh image and preimage operators.

Keywords: L-fuzzy ideal; L-fuzzy ideal bases, L-fuzzy ideal (preserving) mappings, image and preimage of L-fuzzy ideal bases.

Folding Theory of Positive Implicative / Fuzzy Positive Implicative Filters in BL-Algebras

Celestin Lete

University of Dschang, Department of Mathematic, BP 67 Dschang, Cameroon

E-mail: lete_clele@yahoo.com

Abstract: We stuay the notion of n-folds positive implicative and fuzzy n-folds positive implicative filters in BL-algebras. Several characterizations of fuzzy n-folds positive implicative filters are given. We show that every n-fold (fuzzy n-folds) positive implicative filter is a filter (fuzzy filter), but the converse is not ture. Using a level set os a fuzzy set in a BL-algebra, we give a characterization of fuzzy n-folds positive implicative filter. Finally we establish the extension property for fuzzy n-folds positive implicative filter in BL-algebras.

Keywords: BL-algebra, filter, fuzzy filter, n-fold positive implicative filter, fuzzy n-fold positive implicative filter

On Difference Sequences of Fuzzy Numbers

Mikail Et and Yavuz Altin

Department of Mathematics, Firat unicersity,23119,Elazig-TURKEY

E-mail:mikailet@yahoo.com;yaltin23@yahoo.com

Binod Chandra Tripathy

Mathematical Sciences Division,Institute of Advanced Study in Science and Technology,Paschim BoraganmGarchuk,Guwahati-781035;INDIA.

E-mail:tripathybc@yahoo.com;tripathybc@rediffmail.com

Abstract: The idea of difference sequence spaces was first introduced by Kizamaz [7] and this Concept was generalized by Et and Colak [5].The swquence space was introduced by Sargent [14].In this paper,using the difference operator and the sequence we introduce the sequence space of sequences of fuzzy numbers.We study some of its properties like completeness, solidity, symmetricity etc. We also gice some relations related to this space.

Keywords: Fuzzy numbers, Difference sequences

On Intuitionistic Fuzzy Limit Set

Anjan Mukherjee

Department of Mathematic, Tripura University Surjyamaninagar Agartala-799130, Tripuar, INDIA.

E-mail: anjan2002_m@yahoo.co.in

Snigdhendu Bikas Chakraborty

Department of Mathematic, Tripura University Surjyamaninagar Agartala-799130, Tripuar, INDIA.

E-mail: snighendu2007@yahoo.co.in

Abstract:

In this paper we define a new concept intuitionistic fuzzy limit set and some operations on these sets and also established some results on them. Lastly we see that there are some advantages in studying intuitionistic fuzzy soft sets with the the help of intuitionistic fuzzy limit sets.

Keywords: Soft set, intuitionistic fuzzy limit set, intuitionistic fuzzy soft set.

E-mail: manikantan_slm@rediffmail.com

Fuzzy Bi-Ideals of Near-Rings

T. Manikantan

Department of Mathematic, Mahendra Engineering College Mallasamudram (west) Namakkal-637503,Tamilnadu,India

Abstract: In this paper, we introduce the notion of a fuzzy bi-ideal of a near-ring and obtain the characterization of a bi-ideal in terms of a fuzzy bi-ideal of a near-ring. We establish that every fuzzy left (resp. right) N-subgroup or fuzzy left (resp.right) ideal of a near-ring is example. Further, we discuss the properties of fuzzy bi-ideal of near-ring.

Keywords: Fuzzy subnear-ring, fuzzy two-sided N-subgroup, fuzzy ideal, fuzzy bi-ideal

On Fuzzy Syntopogenougs Structures

Hong Wang

College of Science, Southwest University of Science and Technology, Mianyang 621000, Sichuan, P. R. China

Abstract: In this paper, the concept of fuzzy (semi-) topogenous order, fuzzy syntopogenous structure in the framework og fuzzy topologies, fuzzy proximities and fuzzy uniformities have been introduced. Some important properties of them have been obtained.

Keywords: Fuzzy topologies, fuzzy proximities, fuzzy uniformities, fuzzy (semi-) topogenous order, uzzy syntopogenous structure.

Fuzziness or Probability in The Process of Learning? A General Question Illustrated by Examples from Teaching Mathematic

Michael Gr. Voskoglou

Mathematical Sciences, Higer Technological Educational Institute, School of Technological Applications, Meg.Alexandrou 1-263 34 Patras-Greece

E-mail: voskoglou@teipat.gr

Abstract: We introduce a fuzzy model to describe the process of learning a subject matter by student. Our model is presented in contrast to a probabilistic model, introduced in an earlier paper. A classroom experiment, that was performed in order to illustrate the use of the probabilistic model in practice, was repeated twice during the teaching process of the same cognitive object, with the same didactic material, the same conditions and the same method of teaching. The outputs of these two repetitions of the experiment are interpreted here in terms of the fuzzy model, so that the conclusions obtained from the application of the two models become easily comparable to each other.

Keywords: Cognitive sciences, Possibility theory, Fuzzy relations, Measures of uncertainty.

Common Fixed Point Theorems in Fuzzy Metric Spaces through Conditions of Integral Type

Shaban Sedghi

Department of Mathematic, Islamic Azad University-ghaemshr Branch Ghaemshahr, P. O. Box 163, Iran.

E-mail address: sedghi-gh@yahoo.com

Nabi Shobe

Department of Mathematic, Islamic Azad University-babol Branch, Iran.

E-mail address: nabi_shobe @yahoo.com

A. Aliouche

Department of Mathematic University of Larbi Ben Mhidi, Oum-El-Bouaghi, 04000, Algeria.

E-mail address: alioumath @yahoo.fr

Abstract: We prove common fixed point theorems for weakly compatible mappings satisfying conditions of integral type in fuzzy metric spaces using property (E. A) and common property (E. A). Our theorems extend a theorem of [1].

Keywords: Fuzzy metric spaces, weakly compatible mappings, common fixed point, property (E. A), common property (E. A).

A Common Fixed Point Theorem for Weakly Compatible Mappings and Its Application H. K. Pathak

School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur (C. G.) 492010 India

E-mail: hkpathak@sify.com

Rosana Rodriguez-Lopez1

Departmento de Analisis Matematico, Facultad de Mathematics University de Santiago de Compostela, 15782-Santiago de Compostela, Spain

E-mail: rosana.rodriguez.lopez@usc.es

Prachi Singh

Department of Mathematic, Govt. V. Y. T. PG. Autonomous College Durg (C. G.), 491001 India

E-mail:prachibksingh@gmail.com

Abstract: In this paper we establish a common fixed point theorem for a quadruple of mappings comprising two pairs of weakly compatible mapping in fuzzy metric spaces. In this paper we use thr notion of implicit relation, which is some variant of implicit relation introduced by Popa [6]. Our result extends and improves the main result of Khan, Pathak and George [4]. In the sequel, we give an application of our main result to product spaces.

Keywords: Fuzzy Metric spaces, compatible and weakly compatible mappings, implicit relations, common fixed point.

Fuzzy Endomorphism Rings of Abelian Groups

Celestin Lele

Department of Mathematic, University of Dschang, BP 67, Cameroon

E-mail address: lele_clele@yahoo.com

Abstract: The notion of fuzzy subsets of set was introduced by Zadeh in 1965 [9]. Since then, the study of fuzzy subsets and its applications to various mathematical settings has given rise to what is nowadays known as fuzzy mathematics. In the first paper on fuzzy algebra in 1971 Rosenfeld [6] only speaks, based on Zadeh's definition, of fuzzy algebraic sub-structures but not of fuzzy objects in their own right. In this note, we define a fuzzy set ( group) as a pair where X is a set (group) and is a function from X to the interval [0,1]. This enables us to introduce notion which are closer to the classical ones such as fuzzy homomorphism of fuzzy groups. We shall explore some properties of these notions and also study the fuzzy endomorphism rings of some abelian groups.

Keywords: Fuzzy set, fuzzy group, normal fuzzy subgroup, fuzzy homomorphism, matrices

Inequality with Degrees

Zhiyan Chang, Jiajun Laiand Lijun Bai

Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, Sichuan, China

E-mail: changzhiyanyantai@163.com

Yang Xu

Department of Mathematic, outhwest Jiaotong University, Chengdu 610031, Sichuan, China

E-mail: xuyang@home.swjtu.edu.cn

Abstract: In this paper and are defined, where J is a filter of lattice implication algebra L and x, y, , they are generalizations of . Incomparable elements of lattice implication algebra L are comparable in level or filter J when choose appreciate or filter J. And use it to find -resolution field.

Keywords: Lattice implication algebra, filter, inequality, degree, -resolution.

Fuzzy Programming with Nonlinear Membership Functions for Multiobjective Solid Transportation Problem with Mixed Constraints

A. K. Bit

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

E-mail: amalkbit@yahoo.com

Abstract: The linear multiobjective sold (there-dimensional) transportation problem with mixed constraints in which the supply, demand and capacity constraints are mixed type and the objectives are equally important, non commensurable and conflicting in nature. The fuzzy algorithm with nonlinear membership functions for obtaining efficient solutions as well as the best compromise solution of a multiobjective solid transportation problem with mixed constraints ahs 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 method is compared with one existing fuzzy programming algorithm with linear membership functions using same example.

Keywords: Multi criteria decision making, solid transportation problem with mixed constraints, fuzzy programming, efficient solution, compromise solution, nonlinear membership functions.

Complete Lattices in Fuzzy Real Line

Juan J. Nieto and Rosana Rodriguez-Lopez

Departmento de Analisis Matematico, Facultad de Mathematics University de Santiago de Compostela, 15782-Santiago de Compostela,Spain

E-mail: juanjose.nirto.roig@usc.es rosana.rodriguez.lopez@usc.es

Abstract: The study of structures of complete lattices in the set of fuzzy real numbers E1 is an interesting question from the point of view of the application of fixed point theorems to fuzzy functions. We give the expression for the supremum and infimum of an arbitrary subset of certain bounded sets consisting of fuzzy real numbers in relation with two different structures of partial ordering in E1.

Keywords: Fuzzy real number, Infimum, Supremum, Lattice, Complete lattice.