**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2346

# Search results for: Fuzzy Metric Space

##### 2346 Analysis on Fractals in Intuitionistic Fuzzy Metric Spaces

**Authors:**
R. Uthayakumar,
D. Easwaramoorthy

**Abstract:**

**Keywords:**
Fractal Analysis,
Fixed Point,
Contraction,
Iterated Function System,
Intuitionistic Fuzzy Metric Space.

##### 2345 Hutchinson-Barnsley Operator in Fuzzy Metric Spaces

**Authors:**
R. Uthayakumar,
D. Easwaramoorthy

**Abstract:**

**Keywords:**
Fractals,
Iterated Function System,
Hutchinson- Barnsley Operator,
Fuzzy Metric Space,
Hausdorff Fuzzy Metric.

##### 2344 Hutchinson-Barnsley Operator in Intuitionistic Fuzzy Metric Spaces

**Authors:**
R. Uthayakumar,
D. Easwaramoorthy

**Abstract:**

The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.

**Keywords:**
Contraction,
Iterated Function System,
Hutchinson- Barnsley Operator,
Intuitionistic Fuzzy Metric Space,
Hausdorff Intuitionistic Fuzzy Metric.

##### 2343 IFS on the Multi-Fuzzy Fractal Space

**Authors:**
Nadia M. G. AL-Sa'idi,
Muhammad Rushdan Md. Sd.,
Adil M. Ahmed

**Abstract:**

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

**Keywords:**
Fuzzy metric space,
Fuzzy fractal space,
Multi fuzzy
fractal space.

##### 2342 A New Class F2 (M, 0, N)L„ p)F of The Double Difference Sequences of Fuzzy Numbers

**Authors:**
N. Subramanian,
C. Murugesan

**Abstract:**

The double difference sequence space I2 (M, of fuzzy numbers for both 1 < p < oo and 0 < p < 1, is introduced. Some general properties of this sequence space are studied. Some inclusion relations involving this sequence space are obtained.

**Keywords:**
Orlicz function,
solid space,
metric space,
completeness

##### 2341 A New Class χ2 (M, A,) of the Double Difference Sequences of Fuzzy Numbers

**Authors:**
N.Subramanian,
U.K.Misra

**Abstract:**

The aim of this paper is to introduce and study a new concept of strong double χ2 (M,A, Δ) of fuzzy numbers and also some properties of the resulting sequence spaces of fuzzy numbers were examined.

**Keywords:**
Modulus function,
fuzzy number,
metric space.

##### 2340 On Fuzzy Weakly-Closed Sets

**Authors:**
J. Mahanta,
P.K. Das

**Abstract:**

A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.

**Keywords:**
Fuzzy weakly-closed set,
fuzzy weakly-closed
space,
fuzzy weakly-compactness,
MSC: 54A40,
54D30.

##### 2339 A New Concept for Deriving the Expected Value of Fuzzy Random Variables

**Authors:**
Liang-Hsuan Chen,
Chia-Jung Chang

**Abstract:**

Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

**Keywords:**
Fuzzy random variables,
Distance measure,
Expected value.

##### 2338 Method of Moments Applied to a Cuboidal Cavity Resonator: Effect of Gravitational Field Produced by a Black Hole

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

This paper deals with the formulation of Maxwell-s equations in a cavity resonator in the presence of the gravitational field produced by a blackhole. The metric of space-time due to the blackhole is the Schwarzchild metric. Conventionally, this is expressed in spherical polar coordinates. In order to adapt this metric to our problem, we have considered this metric in a small region close to the blackhole and expressed this metric in a cartesian system locally.

**Keywords:**
Method of moments,
General theory of relativity,
Electromagnetism,
Metric tensor,
schwarzchild metric,
Wave Equation.

##### 2337 An Iterated Function System for Reich Contraction in Complete b Metric Space

**Authors:**
R. Uthayakumar,
G. Arockia Prabakar

**Abstract:**

In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.

**Keywords:**
Fractals,
Iterated Function System,
Compact set,
Reich
Contraction,
Well posedness.

##### 2336 A Comparative Analysis of Fuzzy, Neuro-Fuzzy and Fuzzy-GA Based Approaches for Software Reusability Evaluation

**Authors:**
Parvinder Singh Sandhu,
Dalwinder Singh Salaria,
Hardeep Singh

**Abstract:**

**Keywords:**
Software Reusability,
Software Metrics,
Neural
Networks,
Genetic Algorithm,
Fuzzy Logic.

##### 2335 On λ− Summable of Orlicz Space of Gai Sequences of Fuzzy Numbers

**Authors:**
N.Subramanian,
S.Krishnamoorthy,
S. Balasubramanian

**Abstract:**

**Keywords:**
Fuzzy numbers,
statistical convergence,
Orlicz space,
gai sequence.

##### 2334 Fixed Point Theorems for Set Valued Mappings in Partially Ordered Metric Spaces

**Authors:**
Ismat Beg,
Asma Rashid Butt

**Abstract:**

Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0 x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.

**Keywords:**
Fixed point,
partially ordered set,
metric space,
set
valued mapping.

##### 2333 On λ− Summable of Orlicz Space of Entire Sequences of Fuzzy Numbers

**Authors:**
N. Subramanian,
U. K. Misra,
M. S. Panda

**Abstract:**

**Keywords:**
Fuzzy numbers,
statistical convergence,
Orlicz space,
entire sequence.

##### 2332 On Some Subspaces of Entire Sequence Space of Fuzzy Numbers

**Authors:**
T. Balasubramanian,
A. Pandiarani

**Abstract:**

In this paper we introduce some subspaces of fuzzy entire sequence space. Some general properties of these sequence spaces are discussed. Also some inclusion relation involving the spaces are obtained. Mathematics Subject Classification: 40A05, 40D25.

**Keywords:**
Fuzzy Numbers,
Entire sequences,
completeness,
Fuzzy entire sequences

##### 2331 The Orlicz Space of the Entire Sequence Fuzzy Numbers Defined by Infinite Matrices

**Authors:**
N.Subramanian,
C.Murugesan

**Abstract:**

This paper is devoted to the study of the general properties of Orlicz space of entire sequence of fuzzy numbers by using infinite matrices.

**Keywords:**
Fuzzy numbers,
infinite matrix,
Orlicz space,
entiresequence.

##### 2330 A Reusability Evaluation Model for OO-Based Software Components

**Authors:**
Parvinder S. Sandhu,
Hardeep Singh

**Abstract:**

**Keywords:**
CK-Metric,
ID3,
Neuro-fuzzy,
Reusability.

##### 2329 Tensorial Transformations of Double Gai Sequence Spaces

**Authors:**
N.Subramanian,
U.K.Misra

**Abstract:**

The precise form of tensorial transformations acting on a given collection of infinite matrices into another ; for such classical ideas connected with the summability field of double gai sequence spaces. In this paper the results are impose conditions on the tensor g so that it becomes a tensorial transformations from the metric space χ2 to the metric space C

**Keywords:**
tensorial transformations,
double gai sequences ,
double analytic,
dual.

##### 2328 Unsupervised Image Segmentation Based on Fuzzy Connectedness with Sale Space Theory

**Authors:**
Yuanjie Zheng,
Jie Yang,
Yue Zhou

**Abstract:**

**Keywords:**
Image segmentation,
unsupervised imagesegmentation,
fuzzy connectedness,
scale space.

##### 2327 On The Comparison of Fuzzy Logic and State Space Averaging based Sliding Control Methods Applied onan Arc Welding Machine

**Authors:**
İres İskender,
Ahmet Karaarslan

**Abstract:**

**Keywords:**
Fuzzy logic,
arc welding,
sliding state space control,
PWM,
current control.

##### 2326 Fuzzy Metric Approach for Fuzzy Time Series Forecasting based on Frequency Density Based Partitioning

**Authors:**
Tahseen Ahmed Jilani,
Syed Muhammad Aqil Burney,
C. Ardil

**Abstract:**

In the last 15 years, a number of methods have been proposed for forecasting based on fuzzy time series. Most of the fuzzy time series methods are presented for forecasting of enrollments at the University of Alabama. However, the forecasting accuracy rates of the existing methods are not good enough. In this paper, we compared our proposed new method of fuzzy time series forecasting with existing methods. Our method is based on frequency density based partitioning of the historical enrollment data. The proposed method belongs to the kth order and time-variant methods. The proposed method can get the best forecasting accuracy rate for forecasting enrollments than the existing methods.

**Keywords:**
Fuzzy logical groups,
fuzzified enrollments,
fuzzysets,
fuzzy time series.

##### 2325 New Class of Chaotic Mappings in Symbol Space

**Authors:**
Inese Bula

**Abstract:**

Symbolic dynamics studies dynamical systems on the basis of the symbol sequences obtained for a suitable partition of the state space. This approach exploits the property that system dynamics reduce to a shift operation in symbol space. This shift operator is a chaotic mapping. In this article we show that in the symbol space exist other chaotic mappings.

**Keywords:**
Infinite symbol space,
prefix metric,
chaotic mapping,
generator function,
jump mapping.

##### 2324 A New Quantile Based Fuzzy Time Series Forecasting Model

**Authors:**
Tahseen A. Jilani,
Aqil S. Burney,
C. Ardil

**Abstract:**

Time series models have been used to make predictions of academic enrollments, weather, road accident, casualties and stock prices, etc. Based on the concepts of quartile regression models, we have developed a simple time variant quantile based fuzzy time series forecasting method. The proposed method bases the forecast using prediction of future trend of the data. In place of actual quantiles of the data at each point, we have converted the statistical concept into fuzzy concept by using fuzzy quantiles using fuzzy membership function ensemble. We have given a fuzzy metric to use the trend forecast and calculate the future value. The proposed model is applied for TAIFEX forecasting. It is shown that proposed method work best as compared to other models when compared with respect to model complexity and forecasting accuracy.

**Keywords:**
Quantile Regression,
Fuzzy time series,
fuzzy logicalrelationship groups,
heuristic trend prediction.

##### 2323 Determination of Adequate Fuzzy Inequalities for their Usage in Fuzzy Query Languages

**Authors:**
Marcel Shirvanian,
Wolfram Lippe

**Abstract:**

**Keywords:**
Fuzzy Databases,
Fuzzy Inequalities,
Fuzzy QueryLanguages,
Fuzzy Ranking.

##### 2322 Best Proximity Point Theorems for MT-K and MT-C Rational Cyclic Contractions in Metric Spaces

**Authors:**
M. R. Yadav,
A. K. Sharma,
B. S. Thakur

**Abstract:**

The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.

**Keywords:**
Cyclic contraction,
rational cyclic contraction,
best proximity point and complete metric space.

##### 2321 Graphs with Metric Dimension Two-A Characterization

**Authors:**
Sudhakara G,
Hemanth Kumar A.R

**Abstract:**

In this paper, we define distance partition of vertex set of a graph G with reference to a vertex in it and with the help of the same, a graph with metric dimension two (i.e. β (G) = 2 ) is characterized. In the process, we develop a polynomial time algorithm that verifies if the metric dimension of a given graph G is two. The same algorithm explores all metric bases of graph G whenever β (G) = 2 . We also find a bound for cardinality of any distance partite set with reference to a given vertex, when ever β (G) = 2 . Also, in a graph G with β (G) = 2 , a bound for cardinality of any distance partite set as well as a bound for number of vertices in any sub graph H of G is obtained in terms of diam H .

**Keywords:**
Metric basis,
Distance partition,
Metric dimension.

##### 2320 Intuitionistic Fuzzy Points in Semigroups

**Authors:**
Sujit Kumar Sardar Manasi Mandal Samit Kumar Majumder

**Abstract:**

**Keywords:**
Semigroup,
Regular(intra-regular) semigroup,
Intuitionistic fuzzy point,
Intuitionistic fuzzy subsemigroup,
Intuitionistic fuzzy ideal,
Intuitionistic fuzzy interior ideal,
Intuitionistic fuzzy semiprime ideal,
Intuitionistic fuzzy prime ideal.

##### 2319 Action Functional of the Electomagnetic Field: Effect of Gravitation

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

**Keywords:**
General theory of relativity,
electromagnetism,
metric tensor,
Maxwells equations,
test functions,
finite element method.

##### 2318 Fuzzy Clustering Analysis in Real Estate Companies in China

**Authors:**
Jianfeng Li,
Feng Jin,
Xiaoyu Yang

**Abstract:**

This paper applies fuzzy clustering algorithm in classifying real estate companies in China according to some general financial indexes, such as income per share, share accumulation fund, net profit margins, weighted net assets yield and shareholders' equity. By constructing and normalizing initial partition matrix, getting fuzzy similar matrix with Minkowski metric and gaining the transitive closure, the dynamic fuzzy clustering analysis for real estate companies is shown clearly that different clustered result change gradually with the threshold reducing, and then, it-s shown there is the similar relationship with the prices of those companies in stock market. In this way, it-s great valuable in contrasting the real estate companies- financial condition in order to grasp some good chances of investment, and so on.

**Keywords:**
Fuzzy clustering algorithm,
data mining,
real estate company,
financial analysis.

##### 2317 Heuristic Search Algorithms for Tuning PUMA 560 Fuzzy PID Controller

**Authors:**
Sufian Ashraf Mazhari,
Surendra Kumar

**Abstract:**

**Keywords:**
Controller tuning,
Fuzzy Control,
Genetic
Algorithm,
Heuristic search,
Robot control.