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 Journal Statistic

 Journal Numbers Count: 27 Total Articles Count: 222

 Accepted Paper No.853

A FUZZY VERSION OF HAHN-BANACH EXTENSION

THEOREM

L. ZEDAM

Abstract. In this paper, a fuzzy version of the analytic form of Hahn-Banach extension theorem is given. As application, the Hahn-Banach theorem for r- fuzzy bounded linear functionals on r-fuzzy normed linear spaces is obtained.

 Accepted Paper No.1104

A new method for solving fuzzy differential equations

Amit Kumar, Sneh Lata

To the best of our knowledge till now there are only two analytical methods for finding the exact solution of fuzzy differential equations. In this paper, the shortcoming of one of these existing methods is pointed out. To overcome the shortcoming of the existing method, a new method, named as Mehar's method, is proposed for solving fuzzy differential equations. To show the advantage of Mehar's method over existing method the fuzzy Kolmogorov's differential equations, developed by using fuzzy Markov model of piston manufacturing system, are solved by using the existing and Mehar's method and it is shown that the results, obtained by using the existing method, may or may not be fuzzy number while the results, obtained by using Mehar's method, are always fuzzy number.

 Accepted Paper No.1201

FIXED POINT THEORY FOR CYCLIC φ-CONTRACTIONS IN FUZZY METRIC SPACES

YONG-HONG SHEN, DONG QIU AND WEI CHEN

In this paper, the notion of cyclic φ-contraction in fuzzy metric spaces is introduced and a fixed point theorem for this type of mapping isestablished. Meantime, an example is provided to illustrate this theorem. The main result shows that a self-mapping on a G-complete fuzzy metric space has a unique fixed point if it satisfied  yclic φ-contraction. Afterwards, some results in connection with the fixed point are given.

 Accepted Paper No.981

REVISION OF SIGN DISTANCE METHOD FOR RANKING OF
FUZZY NUMBERS

S. ABBASBANDY, R. NURAEI AND M. GHANBARI

Recently, Abbasbandy and Asady have been proposed a modification of the distance based approach, namely \sign distance method". However, in this paper, it is shown that this method has some drawbacks, i.e., the result is not consistent with human intuition for special cases and this method can- not always logically infer ranking order of the images of the fuzzy numbers. In this paper, we present a revised method which can avoid these problems for ranking fuzzy numbers. Also, we present several properties for revised sign distance method while the original method does not have some of them.

 Accepted Paper No.906

ON FUZZY CONVEX LATTICE-ORDERED SUBGROUPS

MAHMOOD BAKHSHI

Abstract. In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered msubgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore, the Fundamental Homomorphism Theorem is established. Finally, it is proved that the class of all fuzzy convex lattice-ordered subgroups of a lattice-ordered group G forms a complete Heyting sublattice of

the lattice of fuzzy subgroups of G.

 Accepted Paper No.1062

OPTIMAL CONTROL OF FUZZY LINEAR CONTROLLED

SYSTEM WITH FUZZY INITIAL CONDITIONS

M. NAJARIYAN, M. H. FARAHI

Abstract. In this article we found the solution of fuzzy linear controlled system with fuzzy initial conditions by using α-cuts and presentation of numbers in a more compact form by moving to the field of complex numbers. Next, a fuzzy optimal control problem for a fuzzy system is considered to optimize the expected value of a fuzzy objective function. Based on Pontryagin Maximum Principle, a constructive equation for the problem is presented. In the last section, three examples are used to show that the method in effective to solve fuzzy and fuzzy optimal linear controlled systems.

 Accepted Paper No.1266

FUZZY EQUATIONAL CLASSES ARE FUZZY VARIETIES

B. BUDIMIROVIC, V. BUDIMIROVIC, B. SESELJA, A. TEPAVCEVIC

In the framework of fuzzy algebras with fuzzy equalities and a complete lattice as a structure of membership values, we investigate fuzzy equational classes. They consist of special fuzzy algebras fulfilling same fuzzy identities, defined with respect to fuzzy equalities. We introduce basic notions and the corresponding operators of universal algebra: construction of fuzzy subalgebras, homomorphisms and direct products. We prove that every fuzzy equational class is closed under these three operators, which means that such a class is a fuzzy variety.

 Accepted Paper No.1143

HURST EXPONENTS FOR NON-PRECISE DATA

M. ALVO AND F. THEBERGE

We provide a framework for the study of statistical quantities related to the Hurst phenomenon when the  data are non-precise with finite support.

 Accepted Paper No.955

EXISTENCE OF EXTREMAL SOLUTIONS FOR IMPULSIVE

DELAY FUZZY INTEGRODIFFERENTIAL EQUATIONS IN

n-DIMENSIONAL FUZZY VECTOR SPACE

Y. C. KWUN, J. S. KIM, J. S. HWANG AND J. H. PARK

Abstract. In this paper, we study the existence of extremal solutions for impulsive delay fuzzy   ntegrodifferential equations in n-dimensional fuzzy vector space, by using monotone method. We show that obtained result is an extension of the result of Rodr´ıguez-L´opez [8] to impulsive delay fuzzy integrodifferential equations in n-dimensional fuzzy vector space.

 Accepted Paper No.1057

BILEVEL LINEAR PROGRAMMING WITH FUZZY

PARAMETERS

F. HAMIDI AND H. MISHMAST NEHI

Abstract. Bilevel linear programming is a decision making problem with a two-level decentralized organization. The “leader” is in the upper level and the “follower”, in the lower. Making a decision at one level affects that at the other one. In this paper, bilevel linear programming with inexact parameters has been studied and a method is proposed to solve a fuzzy bilevel linear programming using interval bilevel linear programming.

 Accepted Paper No.1028

MEET-CONTINUITY ON L-DIRECTED COMPLETE POSETS

SHUHUA SU, QINGGUO LI AND LANKUN GUO

Abstract. In this paper, the definition of meet-continuity on L-directed com- plete posets (for short, L-dcpos) is introduced. As a generalization of meet- continuity on crisp dcpos, meet-continuity on L-dcpos, based in the generalized Scott topology, is characterized. In particular, it is shown that every continu- ous L-dcpo is meet-continuous and L-continuous retracts of meet-continuous  L-dcpos are also meet-continuous. Then, some topological properties of meet- continuity on L-dcpos are discussed. It is shown that meet-continuity on L- dcpos is a topological invariant with respect to the generalized Scott topology, and meet-continuity on L-dcpos is hereditary with respect to generalized Scott closed subsets.

 Accepted Paper No.1026

A NEW SIMILARITY MEASURE BETWEEN TYPE-2 FUZZY
NUMBERS AND FUZZY RISK ANALYSIS

D. STEPHEN DINAGAR AND A. ANBALAGAN

Abstract. In this paper, we present a revised similarity measure based on Chen-and-Chen’s similarity measure for fuzzy risk analysis. The revised similarity measure uses the corrected formulae to calculate the centre of gravity points, therefore it is more effective than the Chen-and-Chen’s method. The revised similarity measure can overcome the drawbacks of the existing methods. We have also proposed a new similarity measure between type-2 fuzzy numbers and a method for handling fuzzy risk analysis problem.

 Accepted Paper No.1135

ON INTERRELATIONSHIPS BETWEEN FUZZY METRIC

STRUCTURES

A. ROLDAN, J. MARTINEZ-MORENO, C. ROLDAN

Abstract.
Considering the increasing interest in fuzzy theory and possible
applications, the concept of fuzzy  metric space concept has been introduced by several authors from different perspectives. This paper interprets the theory in terms of metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology. We study interrelationships between this theory and other fuzzy theories such as intuitionistic fuzzy metric spaces, Kramosil and Michalek's spaces, Kaleva and Seikkala's spaces, probabilistic metric spaces, probabilistic metric co-spaces, Menger spaces and intuitionistic probabilistic metric spaces,  determining their position in the framework of theses different theories.

 Accepted Paper No.1117

REPRESENTATION THEOREMS OF L-SUBSETS AND

L-FAMILIES ON COMPLETE RESIDUATED LATTICE

HUI HAN, JINMING FANG

Abstract. In this paper, our purpose is twofold. Firstly, the tensor and
residuum operations on L-nested systems are introduced under the condition of complete residuated lattice. Then we show that L-nested systems form a complete residuated lattice, which is precisely the classical isomorphic object of complete residuated power set lattice. Thus the new representation theorem of

L-subsets on complete residuated lattice is obtained. Secondly, we introduce the concepts of L- amily and the system of L-subsets, then with the tool of the system of L-subsets, we obtain the representation theorem of intersectionpreserving L-families on complete residuated lattice.

 Accepted Paper No.1158

RANDOM FUZZY SETS: A MATHEMATICAL TOOL
TO DEVELOP STATISTICAL FUZZY DATA ANALYSIS

A. BLANCO-FERN´ANDEZ, M.R. CASALS, A. COLUBI, N. CORRAL, M. GARC´IA-B´ARZANA, M.A. GIL, G. GONZ´ALEZ-RODR´IGUEZ, M.T. L´OPEZ, M.A. LUBIANO, M. MONTENEGRO, A.B. RAMOS-GUAJARDO, S. DE LA ROSA DE S´AA, B. SINOVA

Abstract. Data obtained in association with many real-life random experiments from different fields cannot be perfectly/exactly quantified. Often the underlying imprecision can be suitably described in terms of fuzzy numbers/ values. For these random experiments, the scale of fuzzy numbers/values enables to capture more variability and subjectivity than that of categorical data, and more accuracy and expressiveness than that of numerical/vectorial data. On the other hand, random fuzzy numbers/sets model the random mechanisms generating experimental fuzzy data, and they are soundly formalized within the probabilistic setting.

This paper aims to review a significant part of the recent literature concerning the statistical data analysis with fuzzy data and being developed around the concept of random fuzzy numbers/sets.

 Accepted Paper No.1255

AGE REPLACEMENT POLICY IN UNCERTAIN

ENVIRONMENT

KAI YAO, DAN A. RALESCU

Abstract.
Age replacement policy is concerned with finding an optional time to minimize the cost, at which time the unit is replaced even if it does not fail. So far, age replacement policy involving random age has been proposed. This paper will assume the age of the unit is an uncertain variable, and find the

optimal time to replace the unit.

 Accepted Paper No.1007

LINEAR OBJECTIVE FUNCTION OPTIMIZATION WITH THE
MAX-PRODUCT FUZZY RELATION INEQUALITY
CONSTRAINTS

ALI ABBASI MOLAI

Abstract. In this paper, an optimization problem with a linear objective function subject to a consistent finite system of fuzzy relation inequalities us- ing the max-product composition is studied. Since its feasible domain is non- convex, traditional linear programming methods cannot be applied to solve it. We study this problem and capture some special characteristics of its feasi- ble domain and optimal solutions. Some procedures are proposed to reduce and decompose the original problem into several sub-problems with smaller dimensions. Combining the procedures, a new algorithm is proposed to solve the original problem. An example is also provided to show the eciency of the algorithm.

 Accepted Paper No.1164

ON LACUNARY STATISTICAL LIMIT AND CLUSTER POINTS
OF SEQUENCES OF FUZZY NUMBERS

PANKAJ KUMAR, S. S. BHATIA, VIJAY KUMAR

For any lacunary sequence $\theta = (k_{r})$, we define the concepts of $S_{\theta}-$limit point and $S_ \theta}-$cluster point of a sequence of fuzzy numbers $X = (X_{k})$. We introduce the new sets  \Lambda^{F}_{S_{\theta}}(X)$,$\Gamma^{F}_{S_{\theta}}(X)$and prove some inclusion relaions between these and the sets$\Lambda^{F}_{S}(X)$,$\Gamma^{F}_{S}(X)$introduced in ~\cite{Ayt:Slpsfn} by Aytar [S. ytar, Statistical limit points of sequences of fuzzy numbers, Inform. Sci. 165 (2004) 129-138]. Later, we ind restriction on the lacunary sequence$\theta = (k_{r})$for which the sets$\Lambda^{F}_{S_{\theta}} X)$and$\Gamma^{F}_{S_{\theta}}(X)$respectively coincides with the sets$\Lambda^{F}_{S}(X)$and \Gamma^{F}_{S}(X)$.

 Accepted Paper No.1110

A NOTE ON THE RELATIONSHIP BETWEEN HUTTON'S
QUASI-UNIFORMITIES AND SHI'S QUASI-UNIFORMITIES

YUELI YUE

This note studies the relationship between Hutton's quasi-uniformities and Shi's quasi-uniformities. It is shown that when L satis es \multiple choice principle" for co-prime elements, the category of Hutton's quasi-uniform spaces is a bireective full subcategory of the category of Shi's quasi-uniform spaces. Especially, If the remote-neighborhood mapping defined by Shi preserves arbitrary joins, then the two categories are isomorphic to each other

 Accepted Paper No.1144

AN EMPIRICAL COMPARISON BETWEEN GRADE OF

MEMBERSHIP AND PRINCIPAL COMPONENT ANALYSIS

A. SULEMAN

Abstract.
It is the purpose of this paper to contribute to the discussion ini- tiated by Wachter about the  arallelism between principal component (PC) and a typological grade of membership (GoM) analysis. The  uthor tested empirically the close relationship between both analysis in a low dimensional framework  omprising up to nine dichotomous variables and two typologies. Our contribution to the subject is also  mpirical. It relies on a dataset from a survey which was especially designed to study the reward of skills in  he banking sector in Portugal. The statistical data comprise thirty polythomous variables and were  ecomposed in four typologies using an optimality crite- rion. The empirical evidence shows a high   rrelation  etween the first PC scores and individual GoM scores. No correlation with the remaining PCs was found, however. In addtion to that, the first PC also proved efiective to rank individuals by skill following   e particularity of data distribution meanwhile unveiled in GoM analysis.

 Accepted Paper No.1011

ON APPROXIMATE CAUCHY EQUATION IN FELBIN'S TYPE

FUZZY NORMED LINEAR SPACES

Abstract. In this paper we study the Hyers-Ulam-Rassias stability of Cauchy equations in Felbin's type fuzzy normed linear spaces. As a result we give an example of a fuzzy normed linear space such that the fuzzy version of the stability problem remains true, while it fails to be correct in classical analysis.

This shows how the category of fuzzy normed linear spaces di_ers from the classical normed linear spaces in general..

 Accepted Paper No. 1100

ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND

ATTACHMENTS

ANNA FRASCELLA, COSIMO GUIDO, SERGEY A. SOLOVYOV

Abstract. The paper continues the study of the authors on relationships between topological systems of S. Vickers and attachments of C. Guido. We extend topological systems to algebraically-topological systems. A particular instance of the latter, called attachment system, incorporates the notion of attachment, thus, making it categorically redundant in mathematics. We show that attachment systems are equipped with an internal topology, which is similar to the topology induced by locales. In particular, we provide an attachment system analogue of the well-known categorical equivalence between sober topological spaces and spatial locales.

 Accepted Paper No.1169

APPLICATION OF PREFERENCE RANKING ORGANIZATION
METHOD FOR ENRICHMENT EVALUATION METHOD IN
ENERGY PLANNING - REGIONAL LEVEL

ALI KHATAMI FIROUZABADI AND ELHAM GHAZIMATIN

Abstract. Nowadays energy is one of the most essential needs of human being and it can be considered as the basic prerequisite of social and economic development. Hence, many of the correlations and legislations of a country are affected by it. Since Iran has huge source of gas and oil, it has turned to a fossil fuel oriented county. But as oil and gas sources are non-renewable ones and cannot be replaced, its essential for any country to focus on Renewable Energy Sources (RES). So today is the time of studying and investing on RES to be able to exploit them in the time of oil and gas crisis. In the past, the choice among alternative sources was based on cost minimization, but ranking the RES options is a complex task. The objective of this paper is determining the best renewable energy alternative for Sistan & Baluchestan province of Iran by using interval Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method. In the application of the proposed methodology the most appropriate renewable energy alternative is determined fuel cell and biomass for the mentioned province.

 Accepted Paper No.1200

UNIVERSAL TRIPLE I METHOD FOR FUZZY REASONING
AND FUZZY CONTROLLER

Y. M. TANG, F. J. REN

Abstract. As a generalization of the triple I method, the universal triple I method is investigated from the viewpoints of both fuzzy reasoning and fuzzy controller. The universal triple I principle is put forward, which improves the previous triple I principle. Then, unified form of universal triple I method is established based on the (0,1)-implication or R-implication. Moreover, the reversibility property of universal triple I method is analyzed from expansion, reduction and other type operators, which demonstrate that its reversibility property seems fine, especially for the case employing the (0,1)-implication. Lastly, we analyze the response ability of fuzzy controllers based on universal triple I method, then the practicability of triple I method is improved.

 Accepted Paper No. 1151

REGION MERGING STRATEGY FOR BRAIN MRI

SEGMENTATION USING DEMPSTER-SHAFER THEORY

J. GHASEMI, M. R. KARAMI MOLLAEI, R. GHADERI, AND S. A. HOJJATOLESLAMI

Abstract. Detection of brain tissues using magnetic resonance imaging (MRI) is an active and challenging research area in computational neuroscience. Brain MRI artifacts lead to an uncertainty in pixel values. Therefore, brain MRI segmentation is a complicated concern which is tackled by a novel data fusion approach. The proposed algorithm has two main steps. In the rst step the brain MRI is divided to some main and ancillary cluster which is done using Fuzzy c-mean (FCM). In the second one, the considering ancillary clusters are merged with main clusters employing Dempster-Shafer Theory. The proposed method was validated on simulated brain images from the commonly used BrainWeb dataset. The results of the proposed method are evaluated by using Dice and Tanimoto coecients which demonstrate well performance and robustness of this algorithm.

 Accepted Paper No.989

ON FUZZY NEIGHBORHOOD BASED CLUSTERING

ALGORITHM WITH LOW COMPLEXITY

G. ULUTAGAY & E. NASIBOV

Abstract.
The main purpose of this paper is to achieve improvement in the speed of Fuzzy Joint Points (FJP)  lgorithm. Since FJP approach is a basis for fuzzy neighborhood based clustering algorithms such as Noise-Robust FJP (NRFJP) and Fuzzy Neighborhood DBSCAN (FN-DBSCAN), improving FJP algorithm  ould an important achievement in terms of these FJP-based meth- ods. Although FJP has many advantages  uch as robustness, auto detection of the optimal number of clusters by using cluster validity,   dependency  rom scale, etc., it is a little bit slow. In order to eliminate this disadvantage, by im- proving the FJP algorithm, we propose a novel Modified FJP algorithm, which theoretically runs approximately n / log2 n times faster  nd which is less com- plex than the FJP algorithm. We evaluated the performance of the Modified FJP  lgorithm both analytically and experimentally.

 Accepted Paper No. 1186

PRESERVATION THEOREMS IN
LUKASIEWICZ MODEL THEORY

S.M. BAGHERI, M. MONIRI

Abstract. We present some model theoretic results for Lukasiewicz predicate logic by using the methods of continuous model theory developed by Chang and Keisler. We prove compactness theorem with respect to the class of all structures taking values in the Lukasiewicz BL-algebra. We also prove some appropriate preservation theorems concerning universal and inductive theories. Finally, Skolemization and Morleyization in this framework are discussed and some natural examples of fuzzy theories are presented.

 Accepted Paper No.1254

A NOTE ON STRATIFIED LM-FILTERS

GUNTHER JAGER

Abstract. We develop a theory of stratified LM-filters which generalizes the theory of stratified L-filters. Our stratification condition explicitly depends on a suitable mapping between the lattices L and M. If L and M are identical and the mapping is the identity mapping, then we obtain the theory of stratified  L-filters. Based on the stratified LM-filters, a general theory of lattice-valued convergence spaces can be developed.

 Accepted Paper No. 1152

ANOMALY DETECTION IN CLUSTER-BASED MOBILE AD
HOC NETWORKS

M. RAHMANIMANESH AND S. JALILI

Abstract. In this paper, an anomaly detection method in cluster-based mobile ad hoc networks with ad hoc on demand distance vector (AODV) routing protocol is proposed. In the method, the required features for describing the normal behavior of AODV are de ned via step by step analysis of AODV and independent of any attack. In order to learn the normal behavior of AODV, a fuzzy averaging method is used for combining one-class support vector machine (OCSVM), mixture of Gaussians (MoG), and self-organizing maps (SOM) one-class classi ers and the combined model is utilized to partially detect the attacks in cluster members. The votes of cluster members are periodically transmitted to the cluster head and nal decision on attack detec- tion is carried out in the cluster head. In the proposed method, an adaptive ordered weighted averaging (OWA) operator is used for aggregating the votes of cluster members in the cluster head. Since the network topology, traffic, and environmental conditions of a MANET as well as the number of nodes in each cluster dynamically change, the mere use of a xed quanti er-based weight generation approach for OWA operator is not efficient. We propose a condition-based weight generation method for OWA operator in which the number of cluster members that participate in decision making may be varying in time and OWA weights are calculated periodically and dynamically based on the conditions of the network. Simulation results demonstrate the e ec- tiveness of the proposed method in detecting rushing, RouteError fabrication, and wormhole attacks.

 Accepted Paper No. 1042

I2-CONVERGENCE OF DOUBLE SEQUENCES
OF FUZZY NUMBERS

ERDINC. DUNDAR AND OZER TALO

Abstract. In this paper, we introduce and study the concepts of I2-convergence, I*2 -convergence for double sequences of fuzzy real numbers, where I2 denotes the ideal of subsets of N. Also, we study some properties and relations of them.

 Accepted Paper No. 997

NEW RESULTS ON THE EXISTING FUZZY DISTANCE
MEASURES

S. ABBASBANDY, S. SALAHSHOUR

Abstract. In this paper, we investigate the properties of some recently proposed fuzzy distance measures. We find out some shortcomings for these distances and then the obtained results are illustrated by solving several examples and compared with the other fuzzy distances.