THE JOURNAL OF FUZZY MATHEMATICS
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The Journal of Fuzzy Mathematics

Volume 15, number 3, September 2007

CONTENT

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On Some Generalizations of Fuzzy Lindelof Spaces

G. Thangaraj

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

G. Balasubramanian

Department of Mathematics, Periyar University Salem-636011, Tamilnadu, India.

Abstract: In this paper, the concepts of Fuzzy nearly Lindelof spaces, Fuzzy almost Lindelof spaces, Fuzzy weakly Lindelof spaces, Fuzzy almost regular Lindelof spaces are introduced. Few interesting properties of these spaces are given. We also study the interrelations among the various fuzzy Lindelof spaces introduced.

Keywords: Fuzzy nearly Lindelof spaces, Fuzzy almost Lindelof spaces, Fuzzy weakly Lindelof spaces, Fuzzy almost regular Lindelof spaces, fuzzy semi regular space.

Fuzzy Time Series Analysis

Pranita Goswami

Department of Statistics, Pragjyostish College, Guwahati-781009, assam, India

Hemanta K. Baruah

Department of Statistics, Guwahati University, Guwahati-781014, India

Abstract: Time series analysis with fuzzy parameters has been studied in this article from the standpoint of fuzzy regression analysis with a non fuzzy regression analysis with a non fuzzy regressor variable. The calculations have been illustrated with the help of a numberical example.

Keywords: Time series, fuzzy regression analysis.

Intuitionistics Fuzzy Subframes

Rajesh. K. Thumbakara

Department of Mathematics, Mar Athanasius College Kothamangalam-686666, Kerala, INDIA. E-mail: rthumbakara@ahoo.com

Abstract: Frame theory is the study of topology based on its open set lattice and it was studied extensively by various authors. In this paper we have introduced the concept of frames in the intuitionistic fuzzy context and some related results are obtained.

Keywords: Intuitionistic fuzzy frames, Level subframe, Frame homomorphism.

Fuzzy Programming Algorithm with Linear and Non-linear Membership Functions for A Stochastic Formulation of the Multiple-objective Transportation Problem

U. K. Bhattacharya

India Institute of Management Indore M. P, 453331 India E-mail: utpalb@iimider.ac.in

Abstract: This paper presents the stochastic formulations of multi-objective transportation problems. Here the multi-objective transportation problems have been modeled with different cost and volume parameters are as random variables. It has been assumed that a random variables are independent and normally. distributed with known mean and standard deviations. A fuzzy programming technique has been developed for solving the transformed multi-objective stochastic transportation problem. The same problem has been studied with both hyperbolic as well s exponential membership functions. Numerical examples have been presented in each case to illustrate the solution algorithm.

Keywords: Transportation Problems£¬Stochastic Programming, Multi-Objective Decision Making Problems, Fuzzy Subsets.

On -generalized Closed Fuzzy Sets

M. E. El-Shafei

Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt.

Zakari

Girls College of Education in Gazan, Kingdom of SaudiArabia

Abstract: In this paper the concepts of -closed fuzzy set, -generalized close fuzzy set and fuzzy -generalized continuous mapping have been introduced. It is seen that every -closed fuzzy set is -generalized closed fuzzy set but the converse is not true. The notion of -space has been introduced and studied.

Keywords: -closed fuzzy set, -generalized close fuzzy set£¬ -space£¬ fuzzy -generalized continuity.

Related Fixed Point Theorems for Two Pairs of Mappings on Two Fuzzy Matric Spaces

Funda G¨¹ndogdu

Department of Primary Education, Faculty of Education, Trakya University, 22030 Aysekadin-Edirne, Turkey E-mail: fundagundogdu@hotmail.com

Mustafa Telci

Department of Mathematics, Faculty of Science and Arts, Trakya University, 22030, Edirne, Turkey E-mail: mtelci@trakya.edu.tr

Abstract: Two related fixed point theorems for two pairs of mappings on two fuzzy metric spaces are proved. These results extends the result of Fisher and Murthy [6] to G-complete fuzzy metric spaces.

Keywords: Fixed point, Fuzzy metric spaces.

On Tensor Product of Fuzzy Submodules

Surajit Borkotokey and Baldev Banerjee

Department of Mathematics Dibrugarh University Dibrugarh, Assam, India-786004 E-mail: surajitbor@yahoo.com

Abstract: In this paper the ideal of tensor product of fuzzy submodules over a commutative ring with unity is introduced and some interesting properties are discussed. The tensor product discussed here is more general in nature than the tensor product of ordinary R-modules.

Keywords: Tensor product, Fuzzy submodules, Fuzzy homomorphisms.

Two Direction S-rough Communication and Its Heredity-variation Characteristics

Shoufeng Yin, Haiqing Hu and Kaiquan Shi

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

Abstract: On the basis of S-rough sets theory in [1], this paper extends rough communication model in [10], gives two direction S-rough communication model; by using of two direction S-rough communication model, this paper presents concepts of two direction S-rough communication F-heredity, two direction S-rough communication F-variation, and gives discussion on their characteristics. It also gives dynamic rough communication characteristic theorem on positive region of two direction S-rough sets, dynamic rough communication characteristic theorem on negative region of two direction S-rough set. Two direction S-rough communication model is extension of rough communication model and one direction S-extension communication model, it has important theoretical and application value on two direction S-rough communication heredity-variation characteristics.

Keywords: S-rough sets, two direction S-rough sets, rough communication, two direction S-rough communication.

Some Topological Properties of Information Systems

M. E. Abd El Monsef, B. M. Taher and A. S. Salama

Mathematics Department, Faculty of Science, Tanta University, Egypt

Abstract: In this paper, we classify information systems with respect to the values sets of the attributes of these systems into complete information systems. The fundamentals of some types of information systems are studied. We demonstrated that a topological extension of rough sets can be used for generating rules from incomplete information systems. We studied some new topological methods for reduction of attributes and the induction of core.

Keywords: Incomplete information system, topological spaces, rough sets, data reduction, induction rules.

Sequential Probability Ratio Test with Fuzzy Observations

Ruma Talukdar

Department of Statistics, Cotton College, Guwahati Assam. India-781001

Hemanta K. Baruah

Department of Statistics, Gauhati Unversity, Assam. India-781014

Abstract: In this article we consider fuzzification of Wald¡¯s sequential probability ratio test, which is constructed as a sequential test of one simple hypothesis against another. We consider here, a special case of the problems, when the distribution is normal with known variance and the parameter of interest is the mean. The corresponding fuzzy operating characteristic function and fuzzy average sample number function have been found. This is followed the applications of the result obtained, to a numerical example.

Keywords: Fuzzy triangular number, fuzzy operating characteristic function, fuzzy average sample number function.

A New Measure on Intuitionistic Fuzzy Set Using Hausdorff Metric and Its Application to Edge Detection

Tamalika Chaira, Swades De and Ovidio Salvetti

C. N. R, Area della ricerca di Pisa, via G. Moruzzi 1, 56124 Pisa, Italy E-mail: imtamalika@yahoo.com, swades.de@isti.cnr.it, voidio.salvetti@isti,cnr.it

Abstract: Intuitionistic fuzzy set (IFS) proposed by Attanassov has gained much importance to the researchers for its application in various fields i.e. pattern recognition. It takes into account the membership, non-membership function also another term hesitation degree. Hesitation degree is the lack of knowledge in assigning the membership function in particular, the similarity measure between IFSs has increased its interest and several algorithms have been developed. In this paper a new method for measuring the distance between two intuitionistic fuzzy sets based on Hausdorff metric is proposed. The distance measure is the intuitionistic fuzzy divergence using Hausdorff metric. Our proposed method has been applied in image processing in detecting the edges of different kinds of practical images, demonstrating to be a tool for processing monochrome images.

Keywords: Intuitionistic fuzzy set, divergence, Hausdorff metric, edge detection.

Common Fixed Points Theorems in ?-fuzzy Ordered Sets

Abdelkader Stouti

Unit¨¦ de Recherche: Math¨¦matiques et Applictions Uniersity Cadi Ayyad, Faculty of Sciences and Techniques P. O. Box 523. Beni-Mellal 23000, Morocco E-mail: stouti@math.net

Abstract: In this paper, we prove the existence of: maximal, minimal, the least and the greatest common fixed points of a commutative family of -fuzzy monotone maps defined on a nonempty -fuzzy ordered set.

Keywords: Fuzzy set, -fuzzy order relation, -fuzzy monotone map, common fixed point.

Fuzzy Topological Generated by Fuzzy Bilinear Form

N. R. Das

Department of Mathematics Gauhati University Guwahati-781014 Assam, India

R. K. Misra

Department of Mathematics Darrang College Tezpur-784001 Assam, India Intuitionistic Fuzzy Relations over Intuitionistic Fuzzy Sets

Motilal Panigrahi and Sudarsan Nanda

Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, West Bengal, INDIA E-mail: motilal.panigrahi@gmail.com snanda@math.iitkgp.ernet.in

Abstract: In this paper we have defined intuitionistic fuzy relation from an intuitionistic fuzzy set to another intuitionistic fuzzy set. Defined some operations on these intuitionistic fuzzy relations and studied some properties.

Keywords: Fuzzy sets, intuitionistic fuzzy sets.

On Fuzzy Ordered Groupoids-semigroups

Niovi Kehayopulu and Michael Tsingelis

University of Athens Nikomidias 18, 16122 KESARIANI, Greece E-mail: nkehayop@cc,uoa.gr

Abstract: We have seen in [1] that if S is an ordered groupoid (resp. ordered semigroup),then the set F of all fuzzy subsets of S is a poe-groupoid (resp. poe-semigroup) having a zero element and S is embedded in F. A poe-groupoid is an ordered groupoid S having a greatest element usually denoted by ¡°e¡± (i.e. for all ). In the present paper we go a step further and we prove that for an ordered groupoid S the set F of all fuzzy subsets of S is a complete, distributive lattice ordered groupoid (i.e. le-groupoid) which is m-complete (that is, complete with respect to the multiplication). Combining this result with the result given in [1], each ordered groupoid (resp. ordered semigroup), os embedded in the complete, distributive, m-complete le-groupoid F of all fuzzy subsets of S, the least element of F being the zero of F. Each ordered groupoid (resp. ordered semigroup) is embedded into a poe-groupoid (resp. poe-semigroup) by means of pseudoideals [2]. Each ordered groupoid (resp. ordered semigroup) is embedded into a poe-groupoid (resp. poe-semigroup) in terms of fuzzy sets [1]. Each ordered semigroup S is embedded into an le-semigroup by means of the set of allsubsets of S [3]. Each ordered groupoid (resp. ordered semigroup) is embedded in a complete, distributive le-groupoid (resp. le-semigroupoid) arising from S by the adjunction of a zero element [4]. According to this paper, each ordered groupoid S is embedded in an le-groupoid (i.e. lattice ordered groupoid) in terms of fuzzy sets.

Keywords: Ordered groupoid (po- groupoid); poe-groupoid; poe-semigroupoid; le-groupoid; m-complete le-groupoid; Embedding; Fuzzy sets.

Fuzzy Reliability Analysis of The Desirable Movement of An Electric Robot Using (The Weakest t-norm) on Vague Set Arithmetic Operations

Amit Kumar and Shiv Prasad Yadva

Department of Mathematics, I. I. T Roorkee, Roorkee, India.

Surendra Kumar

Department of Electrical Engineering, I. I. T Roorkee, Roorkee, India.

Abstract: In general fuzzy sets are used to analyze the fuzzy system reliability. Chen [9] used vague set theorem for fuzzy system reliability. For analyzing the fuzzy system reliability ¡®Chen¡¯ represented the reliability of each component of the system as a triangle vague set defined in the universe of discourse [0,1] and also assumed that the product of two or more triangle vague sets is again a triangle vague sets. The above assumption, that the product of two or more triangle vague sets will be again a triangle vague sets, is not necessarily always true. In this paper, we have used -based arithmetic operations over L-R type triangle vague sets to preserve the shape of triangle vague sets. Also expressions for computing the fuzzy reliability of a series system, a parallel system and an algorithm (with the help of a fuzzy success tree) for computing the fuzzy reliability (the fuzzy probability of occurrence) of the desirable movement of an electric robot is presented. To compute the fuzzy reliability of the above systems the reliability of each component of the systems is presented by a L-R type triangle vague sets defined in the universe of discource [0,1].

Keywords: Fuzzy success tree; Fuzzy probability; Fuzzy system reliability; Robotics.

The Theory of Localiztion for Intuitionistic Fuzzy Topological Spaces

Ratna Dev Sarma

Department of Mathematics, Rajdhani College University of Delhi, Raja Garden, Delhi-15, India E-mail: ratna_sarma@yahoo.com

Abstract: The theory of localization is developed for intuitionistic fuzzy topological spaces. Intuitionistic 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. Intuitionistic 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 IPF 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-system, Q-nbd system and of the convergence of intuitionistic fuzzy net.

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

On Connectedness in Intuitionistic Fuzzy Spaces

Ratna Dev Sarma

Department of Mathematics, Rajdhani College University of Delhi Delhi-110015, India E-mail: ratna_sarma@yahoo.com

Abstract: The notion of connectedness is further studied for intuitionistic fuzzy space. Four different types of components, namely -compononents are introduced, using four equivalence relations. Each -compononents is an maximal -connected intuitionistic fuzzy set of the space . The constant IFS 1 is disjoint union of its -compononents .

Keywords: -compononents ; intuitionistic fuzzy set; intuitionistic fuzzy point; intuitionistic fuzzy topology.

Function S-rough Sets and System State Recognition

Yuqiang Shi

Department of Compute Science and Technology, Qiong zhou University Wuzhishan, Hainan 572200, P. R. China

Kaiquan Shi

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

Hongyu Wang

Department of Mathematics and Compute, Sanming College Sanming, Fujian 365004, P. R. China

Abstract: [1,2] puts forward a kind of new rough sets: function S-rough sets (function singular rough sets), which has two forms: function one direction S-rough sets, function two direction S-rough sets. Function S-rough sets is defined by R-function equivalence class (rough sets [13] and S-rough sets [3-12] are both defined by R-element equivalence class ), function S-rough sets is the new form of S-rough sets [3-12] (the function form), which can be used to recognize the system state and the recognition method will be introduced. This paper firstly introduces the form and structure of function S-rough sets, then gives its application in state recognition in the communication system. Function S-rough sets is a new theorem and method in the state recognition of system.

Keywords: Function S-rough sets, the state recognition of system, recognition criteria, application.

Intuitionistic Fuzzy Ideals and Intuitionistic Fuzzy Complete Inner-Unitary Subsemigroups in Semigroups

AL. Narayanan and T. Manikantan

Department of Mathematics, Annamalai Unversity Annamalai Nagar-608002, Tamilnadu, India E-mail: manikantan_slm@rediffmail.com

Abstract: In this paper, we characterize the intuitionistic fuzzy interior ideal and we introduce the notions of intuitionistic fuzzy semiprime ideal and intuitionistic fuzzy complete inner-unitary subsemigroup. We also discuss some of their properties.

Keywords: Intuitionistic fuzzy interior ideal; Intuitionistic fuzzy semiprime ideal; Intuitionistic fuzzy complete inner-unitary subsemigroup.