Search results for: fuzzy data
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8092

Search results for: fuzzy data

8032 A Fuzzy Linear Regression Model Based on Dissemblance Index

Authors: Shih-Pin Chen, Shih-Syuan You

Abstract:

Fuzzy regression models are useful for investigating the relationship between explanatory variables and responses in fuzzy environments. To overcome the deficiencies of previous models and increase the explanatory power of fuzzy data, the graded mean integration (GMI) representation is applied to determine representative crisp regression coefficients. A fuzzy regression model is constructed based on the modified dissemblance index (MDI), which can precisely measure the actual total error. Compared with previous studies based on the proposed MDI and distance criterion, the results from commonly used test examples show that the proposed fuzzy linear regression model has higher explanatory power and forecasting accuracy.

Keywords: Dissemblance index, fuzzy linear regression, graded mean integration, mathematical programming.

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8031 Neuro-Fuzzy System for Equalization Channel Distortion

Authors: Rahib H. Abiyev

Abstract:

In this paper the application of neuro-fuzzy system for equalization of channel distortion is considered. The structure and operation algorithm of neuro-fuzzy equalizer are described. The use of neuro-fuzzy equalizer in digital signal transmission allows to decrease training time of parameters and decrease the complexity of the network. The simulation of neuro-fuzzy equalizer is performed. The obtained result satisfies the efficiency of application of neurofuzzy technology in channel equalization.

Keywords: Neuro-fuzzy system, noise equalization, neuro-fuzzy equalizer, neural system.

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8030 Using Fuzzy Numbers in Heavy Aggregation Operators

Authors: José M. Merigó, Montserrat Casanovas

Abstract:

We consider different types of aggregation operators such as the heavy ordered weighted averaging (HOWA) operator and the fuzzy ordered weighted averaging (FOWA) operator. We introduce a new extension of the OWA operator called the fuzzy heavy ordered weighted averaging (FHOWA) operator. The main characteristic of this aggregation operator is that it deals with uncertain information represented in the form of fuzzy numbers (FN) in the HOWA operator. We develop the basic concepts of this operator and study some of its properties. We also develop a wide range of families of FHOWA operators such as the fuzzy push up allocation, the fuzzy push down allocation, the fuzzy median allocation and the fuzzy uniform allocation.

Keywords: Aggregation operators, Fuzzy numbers, Fuzzy OWAoperator, Heavy OWA operator.

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8029 Evaluation of Fuzzy ARTMAP with DBSCAN in VLSI Application

Authors: K. A. Sumithradevi, Vijayalakshmi. M. N., Annamma Abraham., Dr. Vasanta

Abstract:

The various applications of VLSI circuits in highperformance computing, telecommunications, and consumer electronics has been expanding progressively, and at a very hasty pace. This paper describes a new model for partitioning a circuit using DBSCAN and fuzzy ARTMAP neural network. The first step is concerned with feature extraction, where we had make use DBSCAN algorithm. The second step is the classification and is composed of a fuzzy ARTMAP neural network. The performance of both approaches is compared using benchmark data provided by MCNC standard cell placement benchmark netlists. Analysis of the investigational results proved that the fuzzy ARTMAP with DBSCAN model achieves greater performance then only fuzzy ARTMAP in recognizing sub-circuits with lowest amount of interconnections between them The recognition rate using fuzzy ARTMAP with DBSCAN is 97.7% compared to only fuzzy ARTMAP.

Keywords: VLSI, Circuit partitioning, DBSCAN, fuzzyARTMAP.

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8028 Complex Fuzzy Evolution Equation with Nonlocal Conditions

Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

Abstract:

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups.

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8027 Solving Fuzzy Multi-Objective Linear Programming Problems with Fuzzy Decision Variables

Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

Abstract:

In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: Fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem.

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8026 Fuzzy Uncertainty Theory for Stealth Fighter Aircraft Selection in Entropic Fuzzy TOPSIS Decision Analysis Process

Authors: C. Ardil

Abstract:

The purpose of this paper is to present fuzzy TOPSIS in an entropic fuzzy environment. Due to the ambiguous concepts often represented in decision data, exact values are insufficient to model real-life situations. In this paper, the rating of each alternative is defined in fuzzy linguistic terms, which can be expressed with triangular fuzzy numbers. The weight of each criterion is then derived from the decision matrix using the entropy weighting method. Next, a vertex method is proposed to calculate the distance between two triangular fuzzy numbers. According to the TOPSIS concept, a closeness coefficient is defined to determine the ranking order of all alternatives by simultaneously calculating the distances to both the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS). Finally, an illustrative example of selecting stealth fighter aircraft is shown at the end of this article to highlight the procedure of the proposed method. Correlation analysis and validation analysis using TOPSIS, WSM, and WPM methods were performed to compare the ranking order of the alternatives.

Keywords: stealth fighter aircraft selection, fuzzy uncertainty theory (FUT), fuzzy entropic decision (FED), fuzzy linguistic variables, triangular fuzzy numbers, multiple criteria decision making analysis, MCDMA, TOPSIS, WSM, WPM

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8025 Optimizing of Fuzzy C-Means Clustering Algorithm Using GA

Authors: Mohanad Alata, Mohammad Molhim, Abdullah Ramini

Abstract:

Fuzzy C-means Clustering algorithm (FCM) is a method that is frequently used in pattern recognition. It has the advantage of giving good modeling results in many cases, although, it is not capable of specifying the number of clusters by itself. In FCM algorithm most researchers fix weighting exponent (m) to a conventional value of 2 which might not be the appropriate for all applications. Consequently, the main objective of this paper is to use the subtractive clustering algorithm to provide the optimal number of clusters needed by FCM algorithm by optimizing the parameters of the subtractive clustering algorithm by an iterative search approach and then to find an optimal weighting exponent (m) for the FCM algorithm. In order to get an optimal number of clusters, the iterative search approach is used to find the optimal single-output Sugenotype Fuzzy Inference System (FIS) model by optimizing the parameters of the subtractive clustering algorithm that give minimum least square error between the actual data and the Sugeno fuzzy model. Once the number of clusters is optimized, then two approaches are proposed to optimize the weighting exponent (m) in the FCM algorithm, namely, the iterative search approach and the genetic algorithms. The above mentioned approach is tested on the generated data from the original function and optimal fuzzy models are obtained with minimum error between the real data and the obtained fuzzy models.

Keywords: Fuzzy clustering, Fuzzy C-Means, Genetic Algorithm, Sugeno fuzzy systems.

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8024 Discovery of Production Rules with Fuzzy Hierarchy

Authors: Fadl M. Ba-Alwi, Kamal K. Bharadwaj

Abstract:

In this paper a novel algorithm is proposed that integrates the process of fuzzy hierarchy generation and rule discovery for automated discovery of Production Rules with Fuzzy Hierarchy (PRFH) in large databases.A concept of frequency matrix (Freq) introduced to summarize large database that helps in minimizing the number of database accesses, identification and removal of irrelevant attribute values and weak classes during the fuzzy hierarchy generation.Experimental results have established the effectiveness of the proposed algorithm.

Keywords: Data Mining, Degree of subsumption, Freq matrix, Fuzzy hierarchy.

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8023 S-Fuzzy Left h-Ideal of Hemirings

Authors: D.R Prince Williams

Abstract:

The notion of S-fuzzy left h-ideals in a hemiring is introduced and it's basic properties are investigated.We also study the homomorphic image and preimage of S-fuzzy left h-ideal of hemirings.Using a collection of left h-ideals of a hemiring, S-fuzzy left h-ideal of hemirings are established.The notion of a finite-valued S-fuzzy left h-ideal is introduced,and its characterization is given.S-fuzzy relations on hemirings are discussed.The notion of direct product and S-product are introduced and some properties of the direct product and S-product of S-fuzzy left h-ideal of hemiring are also discussed.

Keywords: hemiring, left h-ideal, anti fuzzy h-ideal, S-fuzzy left hideal, t-conorm , homomorphism.

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8022 A Fuzzy Nonlinear Regression Model for Interval Type-2 Fuzzy Sets

Authors: O. Poleshchuk, E.Komarov

Abstract:

This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: Interval type-2 fuzzy sets, fuzzy regression, weighted interval.

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8021 A Comparison of Fuzzy Clustering Algorithms to Cluster Web Messages

Authors: Sara El Manar El Bouanani, Ismail Kassou

Abstract:

Our objective in this paper is to propose an approach capable of clustering web messages. The clustering is carried out by assigning, with a certain probability, texts written by the same web user to the same cluster based on Stylometric features and using fuzzy clustering algorithms. Focus in the present work is on comparing the most popular algorithms in fuzzy clustering theory namely, Fuzzy C-means, Possibilistic C-means and Fuzzy Possibilistic C-Means.

Keywords: Authorship detection, fuzzy clustering, profiling, stylometric features.

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8020 A Novel Fuzzy Logic Based Controller to Adjust the Brightness of the Television Screen with Respect to Surrounding Light

Authors: A. V. Sai Balasubramanian, N. Ravi Shankar, S. Subbaraman, R. Rengaraj

Abstract:

One of the major cause of eye strain and other problems caused while watching television is the relative illumination between the screen and its surrounding. This can be overcome by adjusting the brightness of the screen with respect to the surrounding light. A controller based on fuzzy logic is proposed in this paper. The fuzzy controller takes in the intensity of light surrounding the screen and the present brightness of the screen as input. The output of the fuzzy controller is the grid voltage corresponding to the required brightness. This voltage is given to CRT and brightness is controller dynamically. For the given test system data, different de-fuzzifier methods have been implemented and the results are compared. In order to validate the effectiveness of the proposed approach, a fuzzy controller has been designed by obtaining a test data from a real time system. The simulations are performed in MATLAB and are verified with standard system data. The proposed approach can be implemented for real time applications.

Keywords: Fuzzy controller, Grid voltage

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8019 Fuzzy Estimation of Parameters in Statistical Models

Authors: A. Falsafain, S. M. Taheri, M. Mashinchi

Abstract:

Using a set of confidence intervals, we develop a common approach, to construct a fuzzy set as an estimator for unknown parameters in statistical models. We investigate a method to derive the explicit and unique membership function of such fuzzy estimators. The proposed method has been used to derive the fuzzy estimators of the parameters of a Normal distribution and some functions of parameters of two Normal distributions, as well as the parameters of the Exponential and Poisson distributions.

Keywords: Confidence interval. Fuzzy number. Fuzzy estimation.

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8018 Automated Knowledge Engineering

Authors: Sandeep Chandana, Rene V. Mayorga, Christine W. Chan

Abstract:

This article outlines conceptualization and implementation of an intelligent system capable of extracting knowledge from databases. Use of hybridized features of both the Rough and Fuzzy Set theory render the developed system flexibility in dealing with discreet as well as continuous datasets. A raw data set provided to the system, is initially transformed in a computer legible format followed by pruning of the data set. The refined data set is then processed through various Rough Set operators which enable discovery of parameter relationships and interdependencies. The discovered knowledge is automatically transformed into a rule base expressed in Fuzzy terms. Two exemplary cancer repository datasets (for Breast and Lung Cancer) have been used to test and implement the proposed framework.

Keywords: Knowledge Extraction, Fuzzy Sets, Rough Sets, Neuro–Fuzzy Systems, Databases

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8017 Change Detector Combination in Remotely Sensed Images Using Fuzzy Integral

Authors: H. Nemmour, Y. Chibani

Abstract:

Decision fusion is one of hot research topics in classification area, which aims to achieve the best possible performance for the task at hand. In this paper, we investigate the usefulness of this concept to improve change detection accuracy in remote sensing. Thereby, outputs of two fuzzy change detectors based respectively on simultaneous and comparative analysis of multitemporal data are fused by using fuzzy integral operators. This method fuses the objective evidences produced by the change detectors with respect to fuzzy measures that express the difference of performance between them. The proposed fusion framework is evaluated in comparison with some ordinary fuzzy aggregation operators. Experiments carried out on two SPOT images showed that the fuzzy integral was the best performing. It improves the change detection accuracy while attempting to equalize the accuracy rate in both change and no change classes.

Keywords: change detection, decision fusion, fuzzy logic, remote sensing.

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8016 Discovery of Fuzzy Censored Production Rules from Large Set of Discovered Fuzzy if then Rules

Authors: Tamanna Siddiqui, M. Afshar Alam

Abstract:

Censored Production Rule is an extension of standard production rule, which is concerned with problems of reasoning with incomplete information, subject to resource constraints and problem of reasoning efficiently with exceptions. A CPR has a form: IF A (Condition) THEN B (Action) UNLESS C (Censor), Where C is the exception condition. Fuzzy CPR are obtained by augmenting ordinary fuzzy production rule “If X is A then Y is B with an exception condition and are written in the form “If X is A then Y is B Unless Z is C. Such rules are employed in situation in which the fuzzy conditional statement “If X is A then Y is B" holds frequently and the exception condition “Z is C" holds rarely. Thus “If X is A then Y is B" part of the fuzzy CPR express important information while the unless part acts only as a switch that changes the polarity of “Y is B" to “Y is not B" when the assertion “Z is C" holds. The proposed approach is an attempt to discover fuzzy censored production rules from set of discovered fuzzy if then rules in the form: A(X) ÔçÆ B(Y) || C(Z).

Keywords: Uncertainty Quantification, Fuzzy if then rules, Fuzzy Censored Production Rules, Learning algorithm.

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8015 Support Vector Fuzzy Based Neural Networks For Exchange Rate Modeling

Authors: Prof. Chokri SLIM

Abstract:

A Novel fuzzy neural network combining with support vector learning mechanism called support-vector-based fuzzy neural networks (SVBFNN) is proposed. The SVBFNN combine the capability of minimizing the empirical risk (training error) and expected risk (testing error) of support vector learning in high dimensional data spaces and the efficient human-like reasoning of FNN.

Keywords: Neural network, fuzzy inference, machine learning, fuzzy modeling and rule extraction, support vector regression.

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8014 Fuzzy T-Neighborhood Groups Acting on Sets

Authors: Hazem. A. Khorshed, Mostafa A. El Gendy, Amer. Abd El-Razik

Abstract:

In this paper, The T-G-action topology on a set acted on by a fuzzy T-neighborhood (T-neighborhood, for short) group is defined as a final T-neighborhood topology with respect to a set of maps. We mainly prove that this topology is a T-regular Tneighborhood topology.

Keywords: Fuzzy set, Fuzzy topology, Triangular norm, Separation axioms.

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8013 More on Gaussian Quadratures for Fuzzy Functions

Authors: Shu-Xin Miao

Abstract:

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.

Keywords: Guassian quadrature rules, fuzzy number, fuzzy integral, fuzzy solution.

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8012 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.

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8011 Characterizations of Ordered Semigroups by (∈,∈ ∨q)-Fuzzy Ideals

Authors: Jian Tang

Abstract:

Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S. Finally, characterizations of regular ordered semigroups and intra-regular ordered semigroups by means of the lower part of (∈ ,∈ ∨q)-fuzzy left ideals, (∈,∈ ∨q)-fuzzy right ideals and (∈,∈ ∨q)- fuzzy (generalized) bi-ideals are given.

Keywords: Ordered semigroup, regular ordered semigroup, intraregular ordered semigroup, (∈, ∈ ∨q)-fuzzy left (right) ideal of an ordered semigroup, (∈, ∈ ∨q)-fuzzy (generalized) bi-ideal of an ordered semigroup.

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8010 Prioritization Method in the Fuzzy Analytic Network Process by Fuzzy Preferences Programming Method

Authors: Tarifa S. Almulhim, Ludmil Mikhailov, Dong-Ling Xu

Abstract:

In this paper, a method for deriving a group priority vector in the Fuzzy Analytic Network Process (FANP) is proposed. By introducing importance weights of multiple decision makers (DMs) based on their experiences, the Fuzzy Preferences Programming Method (FPP) is extended to a fuzzy group prioritization problem in the FANP. Additionally, fuzzy pair-wise comparison judgments are presented rather than exact numerical assessments in order to model the uncertainty and imprecision in the DMs- judgments and then transform the fuzzy group prioritization problem into a fuzzy non-linear programming optimization problem which maximize the group satisfaction. Unlike the known fuzzy prioritization techniques, the new method proposed in this paper can easily derive crisp weights from incomplete and inconsistency fuzzy set of comparison judgments and does not require additional aggregation producers. Detailed numerical examples are used to illustrate the implement of our approach and compare with the latest fuzzy prioritization method.

Keywords: Fuzzy Analytic Network Process (FANP), Fuzzy Non-linear Programming, Fuzzy Preferences Programming Method (FPP), Multiple Criteria Decision-Making (MCDM), Triangular Fuzzy Number.

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8009 Fuzzy Decision Making via Multiple Attribute

Authors: Behnaz Zohouri, Mahdi Zowghiand, Mohsen haghighi

Abstract:

In this paper, a method for decision making in fuzzy environment is presented.A new subjective and objective integrated approach is introduced that used to assign weight attributes in fuzzy multiple attribute decision making (FMADM) problems and alternatives and fmally ranked by proposed method.

Keywords: Multiple Attribute Decision Making, Triangular fuzzy numbers, ranking index, Fuzzy Entropy.

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8008 Isomorphism on Fuzzy Graphs

Authors: A.Nagoor Gani, J.Malarvizhi

Abstract:

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed.

Keywords: complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.

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8007 An Adaptive Fuzzy Clustering Approach for the Network Management

Authors: Amal Elmzabi, Mostafa Bellafkih, Mohammed Ramdani

Abstract:

The Chiu-s method which generates a Takagi-Sugeno Fuzzy Inference System (FIS) is a method of fuzzy rules extraction. The rules output is a linear function of inputs. In addition, these rules are not explicit for the expert. In this paper, we develop a method which generates Mamdani FIS, where the rules output is fuzzy. The method proceeds in two steps: first, it uses the subtractive clustering principle to estimate both the number of clusters and the initial locations of a cluster centers. Each obtained cluster corresponds to a Mamdani fuzzy rule. Then, it optimizes the fuzzy model parameters by applying a genetic algorithm. This method is illustrated on a traffic network management application. We suggest also a Mamdani fuzzy rules generation method, where the expert wants to classify the output variables in some fuzzy predefined classes.

Keywords: Fuzzy entropy, fuzzy inference systems, genetic algorithms, network management, subtractive clustering.

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8006 An Interval Type-2 Dual Fuzzy Polynomial Equations and Ranking Method of Fuzzy Numbers

Authors: Nurhakimah Ab. Rahman, Lazim Abdullah

Abstract:

According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.

Keywords: Dual fuzzy polynomial equations, Interval type-2, Ranking method, Value.

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8005 An Overview of the Application of Fuzzy Inference System for the Automation of Breast Cancer Grading with Spectral Data

Authors: Shabbar Naqvi, Jonathan M. Garibaldi

Abstract:

Breast cancer is one of the most frequent occurring cancers in women throughout the world including U.K. The grading of this cancer plays a vital role in the prognosis of the disease. In this paper we present an overview of the use of advanced computational method of fuzzy inference system as a tool for the automation of breast cancer grading. A new spectral data set obtained from Fourier Transform Infrared Spectroscopy (FTIR) of cancer patients has been used for this study. The future work outlines the potential areas of fuzzy systems that can be used for the automation of breast cancer grading.

Keywords: Breast cancer, FTIR, fuzzy inference system, principal component analysis

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8004 An Innovative Fuzzy Decision Making Based Genetic Algorithm

Authors: M. A. Sharbafi, M. Shakiba Herfeh, Caro Lucas, A. Mohammadi Nejad

Abstract:

Several researchers have proposed methods about combination of Genetic Algorithm (GA) and Fuzzy Logic (the use of GA to obtain fuzzy rules and application of fuzzy logic in optimization of GA). In this paper, we suggest a new method in which fuzzy decision making is used to improve the performance of genetic algorithm. In the suggested method, we determine the alleles that enhance the fitness of chromosomes and try to insert them to the next generation. In this algorithm we try to present an innovative vaccination in the process of reproduction in genetic algorithm, with considering the trade off between exploration and exploitation.

Keywords: Genetic Algorithm, Fuzzy Decision Making.

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8003 Dependent Weighted Aggregation Operators of Hesitant Fuzzy Numbers

Authors: Jing Liu

Abstract:

In this paper, motivated by the ideas of dependent weighted aggregation operators, we develop some new hesitant fuzzy dependent weighted aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy numbers rather than exact numbers, or intervals. In fact, we propose three hesitant fuzzy dependent weighted averaging(HFDWA) operators, and three hesitant fuzzy dependent weighted geometric(HFDWG) operators based on different weight vectors, and the most prominent characteristic of these operators is that the associated weights only depend on the aggregated hesitant fuzzy numbers and can relieve the influence of unfair hesitant fuzzy numbers on the aggregated results by assigning low weights to those “false” and “biased” ones. Some examples are given to illustrated the efficiency of the proposed operators.

Keywords: Hesitant fuzzy numbers, hesitant fuzzy dependent weighted averaging(HFDWA) operators, hesitant fuzzy dependent weighted geometric(HFDWG) operators.

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