THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 19, Number 2, June 2011

CONTENT

DETAILS

Some Fixed Point Theorems in-metricSpaces

Shaban Sedghi

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

Nabi Shobe

Department of Mathematics, Islamic Azad University-Babol Branch, Iran

Abstract: In this paper, we present some new definitions of T-metric spaces and prove some fixed point theorem for self-map in complete T-metric spaces. Also we improved some fixed point theorem in compleye D- metric spaces.

Keywords: Weakly compatible mappings, D- metric spaces, implicit relation, common fixed point theorem.

Coincidence and Fixed Points for Mappings Satisfying Tangential Condition

H.K.Pathak

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

Prachi Singh

Department of Mathematics, Govt.V. Y. T. PG. Autonomous College, Durg(C.G..)492010, India

Abstract: In this paper, we intruduce the concept of weak tangent point and pair-wise tangential property for mapping in fuzzy metric spaces and prove some coincidence and fixed piont theorems by using a new implicit relation which involves a functional inequality relation between arguments.

Keywords: Fuzzy metric space, weak tangent point, pair-wise tangential mapping and weekly compatible mapping, implicit relations, common fixed piont.

On Fuzzy--irresolute and Fuzzy--homeomor-phisms in Fuzzy Topological Spaces

Sadanand N.Patil H.O.D.,

Department of Mathematics, KLS¡¯s V.D.R. Institute of Technology (V.D.R.I.T.) HALIYAL-29 (UK). KARNATAKA-STATE, INDIA

Abstract: The aim of this paper is to introduce a new class of fuzzy set, namely --closed fuzzy sets for fuzzy topological spaces. This class is obtained by generalizing g-open fuzzy set via fuzzy -closure. This new class is properly placed between the class of -closed fuzzy sets and the class of -closed fuzzy sets. Applying --closed fuzzy sets, we introduce and study some new spaces fuzzy spaces and fuzzy spaces. Further, the concept of fuzzy --continuous, fuzzy --irresolute mappings, fuzzy --closed maps, fuzzy --open maps and fuzzy --homeomorphism in fuzzy topological spaces are also introduced, studied and some of these properties are obtained.

Keywords: --closed fuzzy maps, --continuous, -- irresolute, -- open, -- closed mappings and -- homeomorphism.

On-open Fuzzy Sets and Fuzzy-irresolute Mappings in Fuzzy Topological Spaces

Sadanand N.Patil, S. B. Madagi and S. R. Sadugol H.O.D.,

Department of Mathematics, KLS¡¯s V.D.R. Institute of Technology (V.D.R.I.T.) HALIYAL-29 (UK). KARNATAKA-STATE, INDIA

Chairman,

Dept. of Bio Informatics, KSWU, Bijapur, Karnataka State, India.

A.S.Patil

College of Commerce, BCA Dept., Bijapur Department of E&E B. L. D. Engineering college, Bijapur-586103

Abstract: The aim of this paper is to introduce a new class of fuzzy set, namely -closed fuzzy sets for fuzzy topological spaces. This class is obtained by generalizing g-open fuzzy sets via- g-open fuzzy set. This new class is properly placed between the class of -closed fuzzy sets and the class of g -closed fuzzy set. we also introduce and study fuzzy spaces. Further, the concept of fuzzy -continuous, fuzzy -irresolute mappings, fuzzy -closed maps, fuzzy -open maps and fuzzy -homeomorphism in fuzzy topological spaces are also introduced, studied and some of these properties are obtained.

Keywords and phrases: -closed fuzzy maps, -continuous, - irresolute, - open, - closed mappings and - homeomorphism.

On-closed Fuzzy Sets and Fuzzy-irresolute Mappings in Fuzzy Topological Spaces

Sadanand N.Patil H.O.D.,

Department of Mathematics, KLS¡¯s V.D.R. Institute of Technology (V.D.R.I.T.) HALIYAL-29 (UK). KARNATAKA-STATE, INDIA

Abstract: The aim of this paper is to introduce a new class of fuzzy set, namely -closed fuzzy sets for fuzzy topological spaces. This new class is properly lies between the class of closed fuzzy sets and the class of g -closed fuzzy set. we also introduce and study some new spaces, namely fuzzy cT-spaces, fuzzy cT-spaces, as applications of -closed fuzzy set, the concept of continuous, fuzzy -irresolute mappings, fuzzy -closed maps, fuzzy -open maps and fuzzy -homeomorphism in fuzzy topological spaces are also introduced, studied and some of these properties are obtained.

Keywords: -closed fuzzy maps, -continuous, - irresolute, - open, - closed mappings and - homeomorphism.

-equalizer and-regular Monomorphism in The bi-induced Mapping Type

Zhang Hong, Tang Jian Gang and Li Guo Hua

Mathematics college, Sichuan University, Sichuan 610064, China

Department of Mathematics,Yili normal University, Xinjiang 835000, China

Abstract: This paper firstly gives the definition of the bi-induced mapping type of category of L set whose true value set is a complete Heyting algebra a Locale and the definitions of - monomorphism and -epimorphism in this category. In particular, the paper gives the definition, determinant theorem and properties of -equalizer in this category, meantime the paper defins -regular monomorphism and proves its determinant theorem, finally it concludes an important result: the bi-induced mapping type of category of L sets are finitely complete.

Keywords: Bi-induced mapping; - monomorphism, -epimorphism, -equalizer, -regular monomorphism.

Injective-modules

Nazek. A. Al-Essa

Math Department, Faculty of Science, Princess Noura University,Riyadh, Saudi Arabia

Abstract: In this paper we intruduce the concept of injective L-modules by using L-mappings and LR- homeomorphism and categories of L-modules, and we prove some of their properties. Also, we introduce the relations between injective L-modules and injective R-modules.

Keywords: L-modules, injective L-module, categories of L-modules, direct product of L-modules, direct sum of L-modules.

On Somewhat Fuzzy-continuous Functions

G. Thangaraj and V. Seenivasan

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

Abstract: In this paper the concept of somewhat fuzzy -continuous functions, somewhat fuzzy -open functions are introduced and studied. Besides giving characterzations of these functions, several interesting properties of these function are also given. More examples are given to illustrate the concepts introduced in this paper.

Keywords: Somewhat fuzzy -continuous, somewhat fuzzy -open, fuzzy -dense set, weakly somewhat fuzzy -open, fuzzy -resolvable, fuzzy -irresolvable.

Fixed Point Theorem in Fuzzy Metric Space Using Implicit Relation via Absorbing Maps

Abhay. S. Ranadive

Dept. of Pure and Applied Mathematics, Guru Ghasidas University, Bilaspur(C.G.). India.

Anuja. P. Chouhan

Dept. of Mathematics, Dr. W.W.Patankar PG Girls College Durg

Abstract: In this paper, we prove a common fixed point in fuzzy metric spaces using absorbing maps for three self maps satisfying an implicit relation. We proposed to reanalysis the theorem of Singh et al[7], and many other similar results too.

Keywords: Fuzzy metric spaces, absorbing mapping, Semi-compatible mapping, reciprocal continuity.

Extension of Certain Intuitionistic Fuzzy Ideals of Semirings on Strong Lattices

T. K. Dutta and A. Ghosh

Department of Pure Mathematics,University of Calcutta 35, Ballygunge Circular Road, Kolkata-700019, India.

Abstract: In this paper we extend an intuitionistic fuzzy set from the minimum component of a strong lattice of semirings to the whole semiring. With this approuch, we are able to construct intuitionistic fuzzy ideals of semirings from small ones to large one and a number of relatd results on intuitionistic fuzzy ideals in the literature are hence extended in this way.

Keywords: Intuitionistic fuzzy ideals, Intuitionistic fuzzy quasi ideals, Intuitionistic fuzzy pseudo-symmetric ideals, Intuitionistic fuzzy h-ideals, strong lattice of semirings, Intuitionistic fuzzy 3-weakly completely prime ideals, Extension of intuitionistic fuzzy ideals, etc.

Gradation of Continuity in-fuzzy Topological Spaces

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, gradation of continuity, gradation of mapping-openness, gradation of mapping-closedness and gradation of homeomorphism of an L-fuzzy mapping are defined and some of their properties are studied in an L-fuzzy topological spaces. Graded compactness and graded Hausdorffness are also defined and their topological properties are studied.

Keywords: Gradation of openness, gradation of closedness, gradation of continuity, gradation of compactness, gradation of Hausdorffness.

Subparacompactness in-topological Space

T. Baiju Department of Mathematics Naional Institute of Technology Calicut, Calicut-673601, KERALA.India

Sunil Jacob John

Department of Mathematics, Naional Institute of Technology Calicut, Calicut-673601, KERALA.India

Abstract: In this paper the concept of Subparacompactness in-topological space is introduced by means of -discrete families of L-fuzzy sets. This fuzzy Subparacompactness is a natural generalization of lowen fuzzy compactness. Further some characterizations of fuzzy subparacompactness and flintily subparacompactness in the weakly induced -topological space are also obtained.

Keywords: -topology, Fuzzy subparacompactness, Flintily subparacompactness, -discrete family.

A Fuzzy Dynamic Model of Population Growth

Kangkana Sarmah Baruah and Hemanta K. Baruah

Department of Statistics Gauhati University, Guwahati-781014 Assam, India.

Abstract: In this paper we have studied what will be the fuzzified form of future population of West Bengal for the year 2011 and 2021 on the basis of the population of previous three years, applying fuzzy arithmetic on dynamic model of population projection. This article is an effort to demonstrate the use of fuzzy arithmetic in.

Keywords: Fuzzy population projection, fuzzy numbers.

A Core Solution to An Extended Fuzzy Game Using LPP on Symmetric Trapezoidal Fuzzy Numebers

Surajit Borkotoey and Rupok Neog

Department of Mathematics, Dibrugarh University, Dibrugarh, Assam-786004, India

Abstract: Cooperative games, subject to fuzzy coalitions and vague expectations together, are recently studied in the literature. In this paper, the notion of a core solution to such games is proposed. We have show that this core solution is consistent and can be identified with a solution to the minimization problem pertaining to a fuzzy linear programming problem.

Keywords: Economics, Core, Fuzzy LPP, fuzzy Coalitions, Vague Expectation.

A-Summability and Fuzzy Korovkin-type Approximation

George A. Anastassiou

Department of Mathematics sciences, The University of Memphis, TN38152, USA

Kamil Demirci

Sinop University, Faculty of sciences and Arts, Department of Mathematics, 57000 Sinop, Turkey

Sevda Karakus

Sinop University, Faculty of sciences and Arts, Department of Mathematics, 57000 Sinop, Turkey

Abstract: The aim of this paper is to present a fuzzy Korovkin-type approx-imatiion theorem by using a matrix summability method. We also study the rates of convergence of fuzzy using a matrix summability method. We also study the rates of convergence of fuzzy positive linear operators.

Keywords: Matrix summability, fuzzy positive linear operators, fuzzy Korovkin type approximation theorem, fuzzy modulus of continuity, rates of convergence.

A-Summability and Fuzzy Trigonometric Korovkin-type Approximation

George A. Anastassiou

Department of Mathematics sciences, The University of Memphis, TN38152, USA

Kamil Demirci and Sevda Karakus

Department of Mathematics, Faculty of sciences and Arts, Sinop University,57000 Sinop, Turkey

Abstract: The aim of this paper is to present a fuzzy trigonometric Korovkintype approximatiion theorem by using a matrix summability method. We also study the rates of convergence of fuzzy positive linear operators in trigonometric environment.

Keywords: Matrix summability, fuzzy positive linear operators, trigonometric fuzzy Korovkin theoy, fuzzy modulus of continuity, rates of convergence.

Stratified-grill Structure

Wei Yao, S. E. Abbas and A.A.Abd-Allar

Dep.Of Math. Beijing Institute of Techonlogy, 100081 Beijing. PR China

Department of Mathematics, Faculty of science. Sohag 82524, Egypt.

Abstract: In this paper, we introduce the notion of stratified L -grill and L-grillbass on a strictly two-side, commutative quantative quantale lattice L. We define two types of the images and preimages of L-grillbass using Zaden image and preimage operators. We study the images and preimages of L-grillbass induced by functions. Also, we investigate the relationships between L ¨Cgrill structure and the stratification of it.

Keywords: L ¨Cgrill, L-grillbass, L ¨Cgrill(preserving) maps, the image (preimage) of L-grillbass, stratification

Strictly Convex Fuzzy Normed Linear Spaces

S. Mukherjee and T. Bag

Department of Mathematics, Visva Bharati Santiniketan-731235, W,Bengal, India

Abstract: Ideals of strictly convex and strong strictly convex fuzzy normal linear spaces are introduced and study some properties of such spaces. Taylor-Foguel theorem is established in fuzzy setting.

Keywords: Strictly convex, strong strictly convex, fuzzy normal linear spaces.

Prediction of Software Reliability Using Fuzzy ARIMA Model

S. Chatterjee

Department of Applied Mathematics, ISM, Dhanbad, Indai-826004

L. N. Upadhyaya, J. B. Singh and S. Nigam

Research Scholar, Department of Applied Mathematics, ISM, Dhanbad, Indai-826004

Abstract: In this paper a Fuzzy ARIMA(FARIMA) time series model has been proposed to analyze the reliability of software. The concpet of interval model and parameter has been used in the proposed model which is useful for predicying the time between failures(TBFs) of software. This concept makes it possible for decision makers to predict the best and worst possible situations based on fewer observations than the ARIMA model in which at least 50 and preferably 100 observations or more are used. Usefulness of the proposed model has been demonstrated using real software failure data.

Keywords: Software reliability, time between failures(TBFs), time series, ARIMA model, fuzzy ARIMA model

Normal Fuzzy Subgroups and Characteristic Fuzzy Subgroups of A Fuzzy Group and Their Lattices

Iffat Jahan

Department of Mathematics, Ramjas College, University of Delhi, Delhi-110007, India

Abstract: In this paper, we investigate the properties of the notion of normal fuzzy subgroup of a fuzzy group which was introduced by Wu[17]. We provide their characterizations in terms of level subsets and strong level subsets. Further, we introduce the notion of characteristic fuzzy subgroup of a fuzzy group and provide its characterization. We establish the compatibility of these notions like its counterparts in classical group theory. Moreover, we investigate the lattice structure of the set of normal fuzzy subgroupsof a fuzzy group and characteristic fuzzy subgroupof a fuzzy groupand establish that constitute a complete sublattice of the lattice. In addition, we prove that is a modular lattice.

Keywords: Normal fuzzy subgroup of a fuzzy subgroup; characteristic fuzzy subgroup of a fuzzy subgroup; lattice; modularity.