THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 16, Number 1, March 2008

CONTENT

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Method of Solution to A Finite Lattice Implication Algebraic Equation

Pan Xiao-dong and Xu Yang

Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, People¡¯s Republic of China E-mail: xdpanl@163.com

Abstract: A finite lattice implication algebraic equation in lattice implication algebras is investigated. Firstly, the notion of LRPC lattice is introduced. Based on it, secondly, when is a meet irreducible or has an irredundant finite meet-decomposition, the problem of solvability of the equation is considered, respectively; and the method to solve in a complete lattice implication algebra is also given, respectively. Finally, the results are applied to a numerical example.

Keywords: Lattice implication algebra; Lattice implication algebraic equation; LRPC lattice; Maximal solution; Solution set.

On Smooth Fuzzy Bitopological Spaces

S. A. El-Sheikh

Sultanate of Oman-College of Education P. O. Box 1376, Postal code 611, Nizwa

Abstract: We characterize the notions of r-fuzzy semi-open (semi-closed) sets [12], in smooth fuzzy bitopological spaces in view of the definition of A. P. Sostake [15].We obtained generalization of the notions, fuzzy pairwise continuous (open, closed) mappings (FP. Continuous, FP. open and FP. closed, for short),FP. Semi-continuous (semi-open, semi-closed) mappings, FP. irresolute (irresolute open, irresolute closed) mappings and FP .almost open mappings, introduced in [11,13,14],to smooth fuzzy bitopological spaces. We investigate some properties of these mappings. Finally, we have given some counter examples to show that these types of mappings are not equivalent.

Keywords: Fuzzy bitopological spaces, fuzzy semi-open, fuzzy semi-closed, fuzzy pairwise continuous (open, closed) mappings, fuzzy pairwise irresolute, smooth fuzzy topology.

Indexing of Fuzzy Groups Algorithm and Classification

Venkat Murali

Department of Mathematics, Rhodes University, South Africa E-mail: v.murali@ru.ac.za

Laxmi P Gewali

Department of Computer Science, University of Nevada, Las Vegas E-mail: laxmi@cs.unlv.edu

Abstract: A notion of indexing fuzzy groups is introduced for a classification of fuzzy subgroups of finite Abelian groups. Techniques for enumerating indices are presented .Finally, we discuss extensions of this problem, and the development of an algorithm for generating such indices.

Keywords: Equivalence, fuzzy subgroups, chain, keychain, index, string.

Discontinuity and Fixed Point in Fuzzy Metric Space

Vyomesh Pant

Department of Mathematics, Kumaon UniversityD. S. B. Campus Nainital-263002 INDIA. E-mail: vyomeshpant@yahoo.co.in

Abstract: In the follows pages we find an affirmative answer to the problem of Rhoades (see page 245 in [15]) in fuzzy metric space. For this purpose, in Theorem 1 infra, we prove a fixed point theorem in fuzzy metric space using the (¦Å, ¦Ä) contractive condition, however, without using the continuity of the mapping. In Theorem 2 we show that a Matkowski type ? ¨Ccontractive condition [8] also need not force the map to be continuous at the fixed point. The following results can be seen as fuzzy analogue of the results of Pant, R. P. [9(Theorem 1)] and Pant, Vyomesh [14].

Keywords: Fuzzy metric space, discontinuity, fixed point.

Economic Production Lot-size Model with Deteriorated and Imperfect Products in Fuzzy Sense

G. C. Mahata, A. Goswamiand D. K. Gupta

Department of Mathematics Indian of Technology Kharagpur-721302, India E-mail address: goswami@maths.iitkgp.ernet.in

Abstract: This paper investigates the Economic Production Quantity (EPQ) inventory model with finite production rate, fuzzy demand rate and fuzzy deterioration rate. The effect of loss of production quantity due to old/faulty machines, manufacturing defect etc. have also been taken into consideration. Three fuzzy models have been proposed. To derive the estimate of the fuzzy total cost, we have used the concept of signed distance method. Numerical examples are provided to illustrate the computational procedure. The effect of changes in different parameters on the decision variables has been discussed.

Keywords: Signed distance; Fuzzy inventory model; Fuzzy total cost; Fuzzy demand rate; Fuzzy deterioration rate.

On Intuitionistic Fuzzy Hyperideals of Hypernear-rings

Jianming Zhan

Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province, 445000, P. R. China E-mail: zhangjianming@hotmail.com

Abstract: In this paper, we consider the intuitionistic fuzzication of the hyperideals of hypernear-rings and investigate some properties of such hyperideals. In particular, we investigate some natural equivalence relations on the set of all intuitionistic fuzzy hyperideals of hypernear-rings and discuss the characterization of the fundamental relation on a hypernear-ring.

Keywords: Hyperoperation; (Intuitionistic) fuzzy hyperideal; Hypernear-ring; Fundamental relation; Fundamental ring.

On Fuzzy Real Valued I-convergent Sequences

Binod Chandra Tripathy

Mathematical Sciences Division Institute of Advanced Study in Science and Technology PASCHIM BORAGAON; GARCHUK; GUWAHATI-781035; INDIA. E-mail: tripathybc@yahoo.com; tripathybc@rediffmail.com;

Mausumi Sen

Mathematical Sciences Division Institute of Advanced Study in Science and Technology PASCHIM BORAGAON; GARCHUK; GUWAHATI-781035; INDIA. E-mail: mausumi_sen12@sify.com

Abstract: In this article we introduce the concept of fuzzy real valued I-convergent sequences and study different properties of fuzzy real valued I-convergent and I-bounded sequences spaces. We give the Cauchy criteria for I-convergence for sequences of fuzzy numbers.

Keywords: Fuzzy real numbers, I-convergence, solid space, symmetric space, monotone, complete.

On Fuzzy Real-valued Difference Double Sequence Spaces

Binod Chandra Tripathy

Mathematical Sciences Division Institute of Advanced Study in Science and Technology Paschim Boragoan; Garchuk; GUWAHATI-781035; ASSAM: INDIA E-mail: tripathybc@yahoo.com; tripathybc@rediffmail.com

Amar Jyoti Dutta

Mathematical Sciences Division Institute of Advanced Study in Science and Technology Paschim Boragoan; Garchuk; GUWAHATI-781035; ASSAM: INDIA E-mail: amar_iasst@yahoo.co.in

Abstract: In this paper we introduce fuzzy difference double sequence space. We study their different properties like solidness, symmetricity, convergence free, sequence algebra etc. We prove some inclusion results.

Keywords: Fuzzy real-valued sequences, solid space, symmetric space, convergence free, sequence algebra and difference sequence space.

R-neighborhood Structure in I-fuzzy Topological Spaces

Rui Ying Wang, Siqin Mengke and Zhi Fang Ji

College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, P. R. China E-mail: wangruiying709@sohu.com

Shang Zhi Wang

Department of Mathematics, Captical Normal University, Beijing 100037, P. R. China

Abstract: In this paper, the concepts of I-fuzzy R-neighborhood structure of a fuzzy point, I-fuzzy closure, I-fuzzy interior and I-fuzzy continuity are introduced and their fundamental properties are obtained, and furthermore, net convergence is discussed in the framework of I-fuzzy topology (fuzzy topology in Sostak¡¯s sence).

Keywords: Fuzzy logic; I-fuzzy topology; net convergence.

On -fuzzy Closed Sets

H. M. Abu Donia and Rodyna A. Hosny

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

Abstract: In this paper, we first introduce the concept of a new type of fuzzy sets, named -fuzzy closed sets Which is a special case of fuzzy generalized closed sets. Using this new notion, we define and study various types of continuous functions. In addition, we also introduce and study fuzzy -connectedness, fuzzy -extremely disconnectedness and fuzzy -compactness. We study some fundamental properties of these concepts.

Keywords: -fuzzy closed sets, -fuzzy continuous function, fuzzy -connectedness, -fuzzy extremely disconnectedness and fuzzy -compactness.

Extensions of Strongly -topological Spaces of Fuzzy Sets

K. C. Chattapodhyay

Department of Mathematics, The University of Burdwan, Burdwan-713104, India

H. Hazra

Bolpur College, Bolpur, Birbhum

S.K.Samanta

Department of Mathematics, Visva Bharati, Santiniketan-731235, W. Bengal, India E-mail: syamal_123@yahoo.co.in

Abstract: The main aim of this paper is to study extensions of strongly T0 -topological spaces of fuzzy sets. We also construct strongly T0 principal extension of topological spaces of fuzzy set.

Keywords: Fuzzy topological, principal extension, strongly T0 space.

On The Lattice of Stratified L-topologies

V. K. Jose

Department of Mathematics, St. Thomas College, Pala Arunapuram P. O. 686 574, Kottayam (Dt), Kerala, India

T. P. Johnson

School of Engineering, Cochin University of Science and Technology, Kochi-682 022, Kerala, India

Abstract: We investigate the lattice structure of the stratified L-topologies on a given set X. It is proved that the lattice of stratified L-topologies is semi-complemented. Some other properties of this lattice is also discussed.

Keywords: Stratified L-topology, complete lattice, atoms, dual atoms, join complements, meet complements, semi complements, complements.

(L, ?)-fuzzy Quasi-uniform Spaces

Yong Chan Kim and Jung Mi Ko

Department of Mathematics, Kangnung National University, Gangneung, Gangwondo 210-702, Korea

Abstract: In categories related to complete quasi-monoidal lattices, we introduce the notion of (L, ?) - (respectively, (L, ?)-, (L, ¡÷)-) fuzzy quasi-uniform spaces and investigate the properties of them. In particular,-fuzzy quasi-uniform spaces induce (L, ?, ¡Ä)-fuzzy topological spaces and (L, ?, ¡Ä)-fuzzy interior spaces. Moreover, we study the relations among them.

Keywords: (L, ?) -fuzzy quasi-uniform spaces, LF- quasi-uniformly continuous maps, (L, ?, ¡Ä)-fuzzy topological spaces, LF- continuous maps, (L, ?, ¡Ä)-fuzzy interior spaces.

Fuzzy Lattices and Fuzzy Boolean Algebra

B. K. Tripathy

School of Computing Science, V. I. T. University, Vellore-632 014 TN., INDIA

P. K. Choudhury

Department of Mathematics Tara Tarini College Purusottampur, Orissa INDIA

Abstract: In this article, the notion of a fuzzy lattice is introduced as a set with a fuzzy partially ordered relation defined over it and its properties are studied. Also, the concept of a fuzzy Boolean algebra is introduced and studied.

Keywords: Dominating class, Dominated class, Fuzzy lattice, Fuzzy Boolean algebra.

Solution of Horizontal Linear Complementarity Problems Using Multi-objective Programming Approach and Fuzzy Approach

B.Chakraborty, M. P. Biswal and S. Nanda

Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India

Abstract: In this paper, solution of Horizontal Linear Complementarity Problem (HLCP) are studied using multi-objective programming approach and fuzzy approach. Multi-objective programming based approach either solves the HLCP or under certain condition shows that the HLCP is unsolvable. The approximate solution of the infeasible HLCP can then be obtained to some degree of satisfaction when a minimum relaxation is allowed in the inequality and equality relations of the given problem. Also some examples are provided and discussed.

Keywords: Horizontal Linear Complementarity Problem, Multi-objective Programming Problem, Efficient Solution, Minimax Optimization Problem, Weighted Problem, Fuzzy Approach.

Gradation of Compactness in L-topological Spaces

Sadik Bayhan

Hacettepe University, Faculty of Science Department of Mathematics 06800-Beytepe-Ankara/TURKEY E-mail: bayhan@hacettepe.edu.ir

Abstract: The present paper studies the degrizations of several compactness notions based on the quadruble , where,and respectively denote a complete lattice and binary operations on ,was introduced by U. Hhole and A. P. Sostak [10,13].

Keywords: Fuzzy topology, Fuzzy compactness, Fuzzy continuity Fuzzy inclusion.

The Problem to Define Normally Distributed Random Fuzzy Sets

Volker Kratschmer and Joachim Oberlinger

Statistics and Econometrics, Faculty of Law Economics, University of Saaraland, D-66041 Saarbrucken, Germany

Abstract: A new concept to define normally distributed random fuzzy sets is introduced. Further investigations yield that up to a fuzzy constant normally distributed random fuzzy sets degenerate to normally distributed random vectors, thus generalizing notions already known in literature. Furthermore it turns out that in the view if the central limit theorem for random fuzzy sets the normal distributions fail to play the same important role as the normal distributions for random vectors.

Keywords: Random fuzzy sets, normally distributed random fuzzy sets, central limit theorem for random fuzzy sets.

Fuzzy Ordered Fuzzy Algebraic Structures

A. K. Ray

Department of Mathematics, Dibrugarh University Dibrugarh-786004, INDIA

Abstract: In the present work we have introduced the concepts of fuzzy partially ordered and fuzzy totally ordered fuzzy subgroups of a group, and fuzzy partially ordered and fuzzy totally ordered fuzzy subrings of ring. Attempts have also been made to characterize these concepts.

Keywords: Fuzzy order relation; Fuzzy partially ordered fuzzy subgroup; Fuzzy totally ordered fuzzy subgroup; Fuzzy partially ordered fuzzy subring; Fuzzy totally ordered fuzzy subring.

Fixed Point Theorems in Felbin¡¯s Type Fuzzy Normed Linear Spaces

T. Bag and S. K. Samanta

Department of Mathematics Visva-Bharati Santiniketan-731235West Bengal, INDIA E-mail: syamal_123@yahoo.co.in

Abstract: In this paper, some modifications are made in the definition of fuzzy norm on a linear space as given by C. Felbin. The concepts of ¡®fuzzy normal structure¡¯ and ¡®uniform convexity¡¯ have been introduced in such a fuzzy normed linear space. Kirk-Browder type fixed point theorems have been extended in this setting.

Keywords: Fuzzy normal structure, fuzzy nonexpansive mapping, uniformly convex fuzzy normed linear space, fixed point.