# Influence of fuzzy norms and other heuristics on Mixed fuzzy rule formation

Save this PDF as:

Size: px
Start display at page:

Download "Influence of fuzzy norms and other heuristics on Mixed fuzzy rule formation"

## Transcription

2 196 T.R. Gabriel, M.R. Berthold / Internat. J. Approx. Reason. 35 (2004) correct class, its core-region is extended in order to cover the new pattern (cover). Secondly, if the new pattern is not yet covered, a new fuzzy rule of the correct class is introduced (commit). The new example is assigned to its core, whereas the support-region is initialized infinite, that is, the new fuzzy rule covers the entire domain. Lastly, if a new pattern is incorrectly covered by an existing fuzzy rule, the fuzzy point s support-region is reduced so that the conflict is avoided (shrink). This heuristic for conflict avoidance aims to minimize the loss in volume [1]. In Section 2 three different heuristics to determine the loss in volume are compared in more detail. As discussed in [1], the algorithm terminates after only few iterations over the set of example patterns. The resulting set of fuzzy rules can then be used to classify new patterns by computing the overall fuzzy membership degree. The accumulated membership degrees over all input dimensions and across multiple rules are calculated using fuzzy t-norm resp. t-conorm. Again, [1] does not discuss different fuzzy norms, thus we present some choices in Section 3 in more detail and show how they can affect the classification accuracy. 2. Shrink heuristics As mentioned above, the training procedure relies on a heuristic which affects the strategy to avoid conflicts. We have several different choices for this conflict avoidance heuristic. One common approach is to shrink the fuzzy rule in dimension i (1 6 i 6 n) that minimizes the loss in volume: i min ¼ arg min i¼1;...;n fv i g: The loss in volume V i of a fuzzy rule R (using trapezoid membership functions with parameters ha; b; c; di where ða; bþ and ðc; dþ bound the supportregion, and ½b; cš the fuzzy rule s core-region) is then: V i ¼ ð~x; RÞ Y n j¼1;j6¼i d j ð~x; RÞ; where di ðþ (1 6 i 6 n) is the distance between example pattern ~x and the border (core- or support-region) of a fuzzy rule R in dimension i, and dj ðþ (1 6 j 6 n) indicates the distance to fuzzy rule R in dimension j. Later in this section, these two functions are defined more precisely. Furthermore, the loss in volume is normalized with respect to the overall volume: V norm i ¼ ð~x; RÞ Q n dj j¼1;j6¼i Q n j¼1 ð~x; RÞ d j ð~x; RÞ ¼ ð~x; RÞd i ð~x; RÞ:

3 T.R. Gabriel, M.R. Berthold / Internat. J. Approx. Reason. 35 (2004) That is, the computation of this loss in volume can be simplified because only the shrunken dimension has to be considered. However, the losses in volume in the core- and support-region still have to be treated separately. If the conflict occurs in the support-region (a < x < b _ c < x < d), the volume loss function di ðþ between the outer left resp. right (marked by the initial vector v i ) border of the support- and core-region is: ð~x; RÞ ¼ x i a i ; x i 6 v i ; d i x i ; otherwise: The function ðþ weighting the loss in volume still needs to be defined. We introduce three alternative shrink heuristics: Rule-based shrink: weights the loss in volume with respect to the entire fuzzy rule spread: ð~x; RÞ ¼d i a i : Anchor-based shrink: weights the loss in volume with respect to the distance between the initial vector (anchor) and the border of the fuzzy rule s supportregion: ð~x; RÞ ¼ v i a i ; x i 6 v i ; d i v i ; otherwise: Area-based shrink: weights the loss in volume with respect to the distance between the border of the fuzzy rule s support- and core-region: ð~x; RÞ ¼ b i a i ; x i 6 v i ; d i c i ; otherwise: If the conflict is part of the core-region (b 6 x 6 c), the function di ðþ is: ð~x; RÞ ¼ x i b i ; x i 6 v i ; c i x i ; otherwise; and we have two choices in order to compute the function ðþ. Rule-/ shrink: weights the loss in volume with respect to the spread of the fuzzy rule s core-region: ð~x; RÞ ¼c i b i : Anchor-based shrink: weights the loss in volume with respect to the distance between the border of the core-region and the fuzzy rule s anchor (initial vector):

4 198 T.R. Gabriel, M.R. Berthold / Internat. J. Approx. Reason. 35 (2004) ð~x; RÞ ¼ v i b i ; x i 6 v i ; c i v i ; otherwise: For our tests these three shrink heuristics are used for evaluation. The next section discusses the results on benchmark data sets in more detail. 3. Fuzzy norms The algorithm described in [1] constructs a set of fuzzy rules that can be used to classify new example instances of unknown class. The one-dimensional rule antecedents are combined using a fuzzy t-norm and the degrees of fulfillment of all rules of one class are combined using a t-conorm, resulting in a final degree of membership for each class. The choice of these norms have a noticeable influence on the classification outcome. The most popular choice for these fuzzy norms was introduced by Zadeh in [5]: >ðlðxþ; lðyþþ ¼ minflðxþ; lðyþg;?ðlðxþ; lðyþþ ¼ maxflðxþ; lðyþg; where lðþ is the degree of membership of a fuzzy rule, >ðþ (t-norm) the fuzzy operator for the conjunction, and? ðþ (t-conorm) the operator for the disjunction. This so-called minimum/maximum norm represents the most optimistic resp. most pessimistic choice for these operators. Other common choices are the product norm: >ðlðxþ; lðyþþ ¼ lðxþlðyþ;?ðlðxþ; lðyþþ ¼ lðxþþlðyþ lðxþlðyþ; and the Łukasiewicz norm [2]: >ðlðxþ; lðyþþ ¼ maxf0; lðxþþlðyþ 1g;?ðlðxÞ; lðyþþ ¼ minf1; lðxþþlðyþg: In [4] an entire family of fuzzy norms called Yager norm is defined as: > x ðlðxþ; lðyþþ ¼ 1 min n n 1; ½ð1 lðxþþ x þð1 lðyþþ x x Š 1 o o ;? x ðlðxþ; lðyþþ ¼ min 1; ½lðxÞ x þ lðyþ x x Š 1 ; x 2Š0; 1½: The definitions above are probably the most well-known choices for fuzzy t- norms and t-conorms. We focus our experiments using the Yager norm with x ¼ 2 1 and x ¼ 2, in addition to the minimum/maximum, product, and

5 T.R. Gabriel, M.R. Berthold / Internat. J. Approx. Reason. 35 (2004) Table 1 Used data sets along with the number of features, classes, train, and test data Data set # features # classes # train data # test data Diabetes fold Aust. Cred fold Vehicle fold Segment fold Shuttle SatImage DNA Letter Łukasiewicz norm in order to evaluate their influence on the classification performance using the same benchmark data sets as in [1]. 4. Experimental results The evaluation of the proposed methodology is conducted using eight data sets from the StatLog-Project [3]. 1 Table 1 shows the properties of the used data sets. All sets are divided into train and test data (see last two columns). On the first four data sets we perform n-fold cross validation following [3] due to the small number of examples (the last column shows the number of folds). As mentioned before, the classification accuracy is compared using five different fuzzy norms minimum/maximum, product, Yager 1=2, Łukasiewicz, and Yager 2 and also three shrink heuristics for conflict avoidance rule-, anchor-, and shrink. Tables 2 4 summarize the error rates in percent for each data set. The tables are grouped by shrink heuristic first and fuzzy norm second to compare the parameters influences individually. Fig. 1 shows a graphical summary grouped by shrink heuristics. It is obvious to see that most strategies only have a weak influence on the model s generalization performance for the different choices of fuzzy norms. The Yager 1=2 norm is the outlier in this case, always providing results which are substantially worse than the others. Better results can be achieved using the minimum/ maximum as well as product norm. In addition, these two norms seem to be more stable on the data sets used here. The Yager 2 norm reaches similar results, the best in the anchor- and group. The Łukasiewicz norm achieves good results in comparison to the other fuzzy norms but always slightly worse than the error average. 1 The remaining 12 data sets are either not suitable for the underlying FRL algorithm (contain categorical variables) or were not available for download.

6 200 T.R. Gabriel, M.R. Berthold / Internat. J. Approx. Reason. 35 (2004) Table 2 Rule-based shrink heuristic along with fuzzy norms Data set Min/max Product Yager 1=2 Łuka Yager 2 Diabetes Aust. Cred Vehicle Segment Shuttle SatImage DNA Letter Table 3 Anchor-based shrink heuristic along with fuzzy norms Data set Min/max Product Yager 1=2 Łuka Yager 2 Diabetes Aust. Cred Vehicle Segment Shuttle SatImage DNA Letter Table 4 Area-based shrink heuristic along with fuzzy norms Data set Min/max Product Yager 1=2 Łuka Yager 2 Diabetes Aust. Cred Vehicle Segment Shuttle SatImage DNA Letter Fig. 2 summarizes the results for the three shrink heuristics grouped by fuzzy norms. The graphic shows that the choice of fuzzy norm only has a small influence on the performance of the generated model. But it is interesting to see that the shrink heuristic consistently delivers worse results than any of the other strategies. The anchor- and heuristics provide almost same results except for the Yager 1=2 norm (as already discussed before).

7 T.R. Gabriel, M.R. Berthold / Internat. J. Approx. Reason. 35 (2004) % 2.00% 1.00% 0.00% -1.00% -2.00% -3.00% min/max product Yager(p=1/2) Luka Yager(p=2) min/max product Yager(p=1/2) Luka Yager(p=2) min/max product Yager(p=1/2) Luka Yager(p=2) -4.00% -5.00% -6.00% Fig. 1. Deviation from the average error rate grouped by the three shrink heuristics rule-, anchor-, and. 3.00% 2.00% 1.00% 0.00% -1.00% -2.00% -3.00% -4.00% -5.00% -6.00% min/max product Yager(p=1/2) Luka Yager(p=2) Fig. 2. Deviation from the average error rate grouped by the five fuzzy norms minimum/maximum, product, Yager 1=2, Łukasiewicz, and Yager Conclusion In this addendum to [1], we showed how the choice of different fuzzy norms affects the generalization performance of the resulting rule systems considerably. We also demonstrated how various heuristics to adjust rules for conflict avoidance with new training instances affect the performance of the rule system. For most choices, the algorithm behaves well as long as Yager fuzzy norms and shrink heuristics are avoided. In general this addendum illustrates that the choice of conflict avoidance heuristic and fuzzy norm can affect the final classification performance of the resulting fuzzy rule model

8 202 T.R. Gabriel, M.R. Berthold / Internat. J. Approx. Reason. 35 (2004) substantially. However, if the most drastic choices are avoided, the outcome is reasonably independent of the task at hand. References [1] M.R. Berthold, Mixed fuzzy rule formation, Int. J. Approx. Reason. (IJAR) 32 (2003) [2] J. Łukasiewicz, Selected Works Studies in Logic and the Foundations of Mathematics, North- Holland, Amsterdam, [3] D. Michie, D.J. Spiegelhalter, C.C. Taylor (Eds.), Machine Learning, Neural and Statistical Classification, Ellis Horwood Limited, [4] R.R. Yager, S. Ovchinnikov, R.M. Tong, H.T. Ngugen (Eds.), Fuzzy Sets and Applications, Wiley, New York, [5] L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965)

### A vector quantization method for nearest neighbor classifier design

Pattern Recognition Letters 25 (2004) 725 731 www.elsevier.com/locate/patrec A vector quantization method for nearest neighbor classifier design Chen-Wen Yen a, *, Chieh-Neng Young a, Mark L. Nagurka b

### Complex object comparison in a fuzzy context

Information and Software Technology 45 (2003) 431 444 www.elsevier.com/locate/infsof Complex object comparison in a fuzzy context N. Marín*, J.M. Medina, O. Pons, D. Sánchez, M.A. Vila Intelligent Databases

### Keywords Fuzzy, Set Theory, KDD, Data Base, Transformed Database.

Volume 6, Issue 5, May 016 ISSN: 77 18X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: www.ijarcsse.com Fuzzy Logic in Online

### ISSN: Page 320

A NEW METHOD FOR ENCRYPTION USING FUZZY SET THEORY Dr.S.S.Dhenakaran, M.Sc., M.Phil., Ph.D, Associate Professor Dept of Computer Science & Engg Alagappa University Karaikudi N.Kavinilavu Research Scholar

### DEFUZZIFICATION METHOD FOR RANKING FUZZY NUMBERS BASED ON CENTER OF GRAVITY

Iranian Journal of Fuzzy Systems Vol. 9, No. 6, (2012) pp. 57-67 57 DEFUZZIFICATION METHOD FOR RANKING FUZZY NUMBERS BASED ON CENTER OF GRAVITY T. ALLAHVIRANLOO AND R. SANEIFARD Abstract. Ranking fuzzy

### Formal Model. Figure 1: The target concept T is a subset of the concept S = [0, 1]. The search agent needs to search S for a point in T.

Although this paper analyzes shaping with respect to its benefits on search problems, the reader should recognize that shaping is often intimately related to reinforcement learning. The objective in reinforcement

### Developing a heuristic algorithm for order production planning using network models under uncertainty conditions

Applied Mathematics and Computation 182 (2006) 1208 1218 www.elsevier.com/locate/amc Developing a heuristic algorithm for order production planning using network models under uncertainty conditions H.

### Univariate Margin Tree

Univariate Margin Tree Olcay Taner Yıldız Department of Computer Engineering, Işık University, TR-34980, Şile, Istanbul, Turkey, olcaytaner@isikun.edu.tr Abstract. In many pattern recognition applications,

### Comparing Fuzzy Graphs

Comparing Fuzzy Graphs Michael R. Berthold! and Klaus-Peter Huber 2 1 Department of EECS Computer Science Division University of California at Berkeley Berkeley, CA 94720, USA Email: bertholdclca. berkeley.

### Reichenbach Fuzzy Set of Transitivity

Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 9, Issue 1 (June 2014), pp. 295-310 Applications and Applied Mathematics: An International Journal (AAM) Reichenbach Fuzzy Set of

### Efficiency of k-means and K-Medoids Algorithms for Clustering Arbitrary Data Points

Efficiency of k-means and K-Medoids Algorithms for Clustering Arbitrary Data Points Dr. T. VELMURUGAN Associate professor, PG and Research Department of Computer Science, D.G.Vaishnav College, Chennai-600106,

### EVALUATION FUZZY NUMBERS BASED ON RMS

EVALUATION FUZZY NUMBERS BASED ON RMS *Adel Asgari Safdar Young Researchers and Elite Club, Baft Branch, Islamic Azad University, Baft, Iran *Author for Correspondence ABSTRACT We suggest a new approach

### Class Conditional Density Estimation Using Mixtures with Constrained Component Sharing

924 IEEE TRANSACTIONS ON ATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 25, NO. 7, JULY 2003 Class Conditional Density Estimation Using Mixtures with Constrained Component Sharing Michalis K. Titsias and

### Improved fuzzy partitions for fuzzy regression models q

International Journal of Approximate Reasoning 32 (2003) 85 102 www.elsevier.com/locate/ijar Improved fuzzy partitions for fuzzy regression models q Frank H oppner *, Frank Klawonn Department of Computer

### Hybrid Models Using Unsupervised Clustering for Prediction of Customer Churn

Hybrid Models Using Unsupervised Clustering for Prediction of Customer Churn Indranil Bose and Xi Chen Abstract In this paper, we use two-stage hybrid models consisting of unsupervised clustering techniques

### Integration Base Classifiers Based on Their Decision Boundary

Integration Base Classifiers Based on Their Decision Boundary Robert Burduk (B) Department of Systems and Computer Networks, Wroclaw University of Science and Technology, Wybrzeze Wyspianskiego 27, 50-370

### Why Do Nearest-Neighbour Algorithms Do So Well?

References Why Do Nearest-Neighbour Algorithms Do So Well? Brian D. Ripley Professor of Applied Statistics University of Oxford Ripley, B. D. (1996) Pattern Recognition and Neural Networks. CUP. ISBN 0-521-48086-7.

### Fuzzy Optimization of the Constructive Parameters of Laboratory Fermenters

This article was downloaded by: [Bulgarian Academy of Sciences] On: 07 April 2015, At: 00:04 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered

### A Fuzzy Logic Approach to Assembly Line Balancing

Mathware & Soft Computing 12 (2005), 57-74 A Fuzzy Logic Approach to Assembly Line Balancing D.J. Fonseca 1, C.L. Guest 1, M. Elam 1, and C.L. Karr 2 1 Department of Industrial Engineering 2 Department

### A Modified Fuzzy Min-Max Neural Network and Its Application to Fault Classification

A Modified Fuzzy Min-Max Neural Network and Its Application to Fault Classification Anas M. Quteishat and Chee Peng Lim School of Electrical & Electronic Engineering University of Science Malaysia Abstract

### DECISION-TREE-BASED MULTICLASS SUPPORT VECTOR MACHINES. Fumitake Takahashi, Shigeo Abe

DECISION-TREE-BASED MULTICLASS SUPPORT VECTOR MACHINES Fumitake Takahashi, Shigeo Abe Graduate School of Science and Technology, Kobe University, Kobe, Japan (E-mail: abe@eedept.kobe-u.ac.jp) ABSTRACT

### COSC 6397 Big Data Analytics. Fuzzy Clustering. Some slides based on a lecture by Prof. Shishir Shah. Edgar Gabriel Spring 2015.

COSC 6397 Big Data Analytics Fuzzy Clustering Some slides based on a lecture by Prof. Shishir Shah Edgar Gabriel Spring 215 Clustering Clustering is a technique for finding similarity groups in data, called

### Fuzzy Equivalence on Standard and Rough Neutrosophic Sets and Applications to Clustering Analysis

Fuzzy Equivalence on Standard and Rough Neutrosophic Sets and Applications to Clustering Analysis Nguyen Xuan Thao 1(&), Le Hoang Son, Bui Cong Cuong 3, Mumtaz Ali 4, and Luong Hong Lan 5 1 Vietnam National

### Available online at ScienceDirect. Procedia Computer Science 35 (2014 )

Available online at www.sciencedirect.com ScienceDirect Procedia Computer Science 35 (2014 ) 388 396 18 th International Conference on Knowledge-Based and Intelligent Information & Engineering Systems

### Performance analysis of a MLP weight initialization algorithm

Performance analysis of a MLP weight initialization algorithm Mohamed Karouia (1,2), Régis Lengellé (1) and Thierry Denœux (1) (1) Université de Compiègne U.R.A. CNRS 817 Heudiasyc BP 49 - F-2 Compiègne

### Efficient Tuning of SVM Hyperparameters Using Radius/Margin Bound and Iterative Algorithms

IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 13, NO. 5, SEPTEMBER 2002 1225 Efficient Tuning of SVM Hyperparameters Using Radius/Margin Bound and Iterative Algorithms S. Sathiya Keerthi Abstract This paper

### Multi prototype fuzzy pattern matching for handwritten character recognition

Multi prototype fuzzy pattern matching for handwritten character recognition MILIND E. RANE, DHABE P. S AND J. B. PATIL Dept. of Electronics and Computer, R.C. Patel Institute of Technology, Shirpur, Dist.

### CT79 SOFT COMPUTING ALCCS-FEB 2014

Q.1 a. Define Union, Intersection and complement operations of Fuzzy sets. For fuzzy sets A and B Figure Fuzzy sets A & B The union of two fuzzy sets A and B is a fuzzy set C, written as C=AUB or C=A OR

### Solution of m 3 or 3 n Rectangular Interval Games using Graphical Method

Australian Journal of Basic and Applied Sciences, 5(): 1-10, 2011 ISSN 1991-8178 Solution of m or n Rectangular Interval Games using Graphical Method Pradeep, M. and Renukadevi, S. Research Scholar in

### Using Analytic QP and Sparseness to Speed Training of Support Vector Machines

Using Analytic QP and Sparseness to Speed Training of Support Vector Machines John C. Platt Microsoft Research 1 Microsoft Way Redmond, WA 9805 jplatt@microsoft.com Abstract Training a Support Vector Machine

### ECM A Novel On-line, Evolving Clustering Method and Its Applications

ECM A Novel On-line, Evolving Clustering Method and Its Applications Qun Song 1 and Nikola Kasabov 2 1, 2 Department of Information Science, University of Otago P.O Box 56, Dunedin, New Zealand (E-mail:

### A new approach for solving cost minimization balanced transportation problem under uncertainty

J Transp Secur (214) 7:339 345 DOI 1.17/s12198-14-147-1 A new approach for solving cost minimization balanced transportation problem under uncertainty Sandeep Singh & Gourav Gupta Received: 21 July 214

### Real World Performance of Association Rule Algorithms

To appear in KDD 2001 Real World Performance of Association Rule Algorithms Zijian Zheng Blue Martini Software 2600 Campus Drive San Mateo, CA 94403, USA +1 650 356 4223 zijian@bluemartini.com Ron Kohavi

### XI International PhD Workshop OWD 2009, October Fuzzy Sets as Metasets

XI International PhD Workshop OWD 2009, 17 20 October 2009 Fuzzy Sets as Metasets Bartłomiej Starosta, Polsko-Japońska WyŜsza Szkoła Technik Komputerowych (24.01.2008, prof. Witold Kosiński, Polsko-Japońska

### COSC 6339 Big Data Analytics. Fuzzy Clustering. Some slides based on a lecture by Prof. Shishir Shah. Edgar Gabriel Spring 2017.

COSC 6339 Big Data Analytics Fuzzy Clustering Some slides based on a lecture by Prof. Shishir Shah Edgar Gabriel Spring 217 Clustering Clustering is a technique for finding similarity groups in data, called

### CLASSIFICATION WITH RADIAL BASIS AND PROBABILISTIC NEURAL NETWORKS

CLASSIFICATION WITH RADIAL BASIS AND PROBABILISTIC NEURAL NETWORKS CHAPTER 4 CLASSIFICATION WITH RADIAL BASIS AND PROBABILISTIC NEURAL NETWORKS 4.1 Introduction Optical character recognition is one of

### On the Use of Data Mining Tools for Data Preparation in Classification Problems

2012 IEEE/ACIS 11th International Conference on Computer and Information Science On the Use of Data Mining Tools for Data Preparation in Classification Problems Paulo M. Gonçalves Jr., Roberto S. M. Barros

### HALF&HALF BAGGING AND HARD BOUNDARY POINTS. Leo Breiman Statistics Department University of California Berkeley, CA

1 HALF&HALF BAGGING AND HARD BOUNDARY POINTS Leo Breiman Statistics Department University of California Berkeley, CA 94720 leo@stat.berkeley.edu Technical Report 534 Statistics Department September 1998

### Vague Congruence Relation Induced by VLI Ideals of Lattice Implication Algebras

American Journal of Mathematics and Statistics 2016, 6(3): 89-93 DOI: 10.5923/j.ajms.20160603.01 Vague Congruence Relation Induced by VLI Ideals of Lattice Implication Algebras T. Anitha 1,*, V. Amarendra

### Detecting Spam with Artificial Neural Networks

Detecting Spam with Artificial Neural Networks Andrew Edstrom University of Wisconsin - Madison Abstract This is my final project for CS 539. In this project, I demonstrate the suitability of neural networks

### A High Performance k-nn Classifier Using a Binary Correlation Matrix Memory

A High Performance k-nn Classifier Using a Binary Correlation Matrix Memory Ping Zhou zhoup@cs.york.ac.uk Jim Austin austin@cs.york.ac.uk Advanced Computer Architecture Group Department of Computer Science

### Comparing SOM neural network with Fuzzy c-means, K-means and traditional hierarchical clustering algorithms

European Journal of Operational Research 174 (2006) 1742 1759 Stochastics and Statistics Comparing SOM neural network with Fuzzy c-means, K-means and traditional hierarchical clustering algorithms Sueli

### Fuzzy Partitioning with FID3.1

Fuzzy Partitioning with FID3.1 Cezary Z. Janikow Dept. of Mathematics and Computer Science University of Missouri St. Louis St. Louis, Missouri 63121 janikow@umsl.edu Maciej Fajfer Institute of Computing

### APPROXIMATING THE MAXMIN AND MINMAX AREA TRIANGULATIONS USING ANGULAR CONSTRAINTS. J. Mark Keil, Tzvetalin S. Vassilev

Serdica J. Computing 4 00, 3 334 APPROXIMATING THE MAXMIN AND MINMAX AREA TRIANGULATIONS USING ANGULAR CONSTRAINTS J. Mark Keil, Tzvetalin S. Vassilev Abstract. We consider sets of points in the two-dimensional

### An evaluation approach to engineering design in QFD processes using fuzzy goal programming models

European Journal of Operational Research 7 (006) 0 48 Production Manufacturing and Logistics An evaluation approach to engineering design in QFD processes using fuzzy goal programming models Liang-Hsuan

### A Comparative Study of Locality Preserving Projection and Principle Component Analysis on Classification Performance Using Logistic Regression

Journal of Data Analysis and Information Processing, 2016, 4, 55-63 Published Online May 2016 in SciRes. http://www.scirp.org/journal/jdaip http://dx.doi.org/10.4236/jdaip.2016.42005 A Comparative Study

### Unknown Malicious Code Detection Based on Bayesian

Available online at www.sciencedirect.com Procedia Engineering 15 (2011) 3836 3842 Advanced in Control Engineering and Information Science Unknown Malicious Code Detection Based on Bayesian Yingxu Lai

### On the efficiency of domain-based COTS product selection method

Information and Software Technology 44 (2002) 703 715 www.elsevier.com/locate/infsof On the efficiency of domain-based COTS product selection method Karl R.P.H. Leung a, Hareton K.N. Leung b, * a Compuware

### DIFFERENCES BETWEEN THE METHOD OF MINI-MODELS AND THE K-NEAREST NEIGHBORS ON EXAMPLE OF MODELING OF UNEMPLOYMENT RATE IN POLAND

DIFFERENCES BETWEEN THE METHOD OF MINI-MODELS AND THE K-NEAREST NEIGHBORS ON EXAMPLE OF MODELING OF UNEMPLOYMENT RATE IN POLAND Andrzej Piegat a), b), Barbara Wąsikowska b), Marcin Korzeń a) a) Faculty

### Linear Discriminant Analysis in Ottoman Alphabet Character Recognition

Linear Discriminant Analysis in Ottoman Alphabet Character Recognition ZEYNEB KURT, H. IREM TURKMEN, M. ELIF KARSLIGIL Department of Computer Engineering, Yildiz Technical University, 34349 Besiktas /

### Traffic Signs Recognition using HP and HOG Descriptors Combined to MLP and SVM Classifiers

Traffic Signs Recognition using HP and HOG Descriptors Combined to MLP and SVM Classifiers A. Salhi, B. Minaoui, M. Fakir, H. Chakib, H. Grimech Faculty of science and Technology Sultan Moulay Slimane

### Occluded Facial Expression Tracking

Occluded Facial Expression Tracking Hugo Mercier 1, Julien Peyras 2, and Patrice Dalle 1 1 Institut de Recherche en Informatique de Toulouse 118, route de Narbonne, F-31062 Toulouse Cedex 9 2 Dipartimento

### An Efficient Method for Extracting Fuzzy Classification Rules from High Dimensional Data

Published in J. Advanced Computational Intelligence, Vol., No., 997 An Efficient Method for Extracting Fuzzy Classification Rules from High Dimensional Data Stephen L. Chiu Rockwell Science Center 049

### * The terms used for grading are: - bad - good

Hybrid Neuro-Fuzzy Systems or How to Combine German Mechanics with Italian Love by Professor Michael Negnevitsky University of Tasmania Introduction Contents Heterogeneous Hybrid Systems Diagnosis of myocardial

### Clustered SVD strategies in latent semantic indexing q

Information Processing and Management 41 (5) 151 163 www.elsevier.com/locate/infoproman Clustered SVD strategies in latent semantic indexing q Jing Gao, Jun Zhang * Laboratory for High Performance Scientific

### Deriving design aspects from canonical models

Deriving design aspects from canonical models Bedir Tekinerdogan & Mehmet Aksit University of Twente Department of Computer Science P.O. Box 217 7500 AE Enschede, The Netherlands e-mail: {bedir aksit}@cs.utwente.nl

### Efficient Case Based Feature Construction

Efficient Case Based Feature Construction Ingo Mierswa and Michael Wurst Artificial Intelligence Unit,Department of Computer Science, University of Dortmund, Germany {mierswa, wurst}@ls8.cs.uni-dortmund.de

### Learning and Generalization in Single Layer Perceptrons

Learning and Generalization in Single Layer Perceptrons Neural Computation : Lecture 4 John A. Bullinaria, 2015 1. What Can Perceptrons do? 2. Decision Boundaries The Two Dimensional Case 3. Decision Boundaries

### Model combination. Resampling techniques p.1/34

Model combination The winner-takes-all approach is intuitively the approach which should work the best. However recent results in machine learning show that the performance of the final model can be improved

### SOMSN: An Effective Self Organizing Map for Clustering of Social Networks

SOMSN: An Effective Self Organizing Map for Clustering of Social Networks Fatemeh Ghaemmaghami Research Scholar, CSE and IT Dept. Shiraz University, Shiraz, Iran Reza Manouchehri Sarhadi Research Scholar,

### fuzzylite a fuzzy logic control library in C++

fuzzylite a fuzzy logic control library in C++ Juan Rada-Vilela jcrada@fuzzylite.com Abstract Fuzzy Logic Controllers (FLCs) are software components found nowadays within well-known home appliances such

MetaData for Database Mining John Cleary, Geoffrey Holmes, Sally Jo Cunningham, and Ian H. Witten Department of Computer Science University of Waikato Hamilton, New Zealand. Abstract: At present, a machine

### How to Conduct a Heuristic Evaluation

Page 1 of 9 useit.com Papers and Essays Heuristic Evaluation How to conduct a heuristic evaluation How to Conduct a Heuristic Evaluation by Jakob Nielsen Heuristic evaluation (Nielsen and Molich, 1990;

### A heuristic approach to find the global optimum of function

Journal of Computational and Applied Mathematics 209 (2007) 160 166 www.elsevier.com/locate/cam A heuristic approach to find the global optimum of function M. Duran Toksarı Engineering Faculty, Industrial

### Image segmentation by three-level thresholding based on maximum fuzzy entropy and genetic algorithm

Pattern Recognition Letters 24 (2003) 3069 3078 www.elsevier.com/locate/patrec Image segmentation by three-level thresholding based on maximum fuzzy entropy and genetic algorithm Wen-Bing Tao *, Jin-Wen

### Using Analytic QP and Sparseness to Speed Training of Support Vector Machines

Using Analytic QP and Sparseness to Speed Training of Support Vector Machines John C. Platt Microsoft Research 1 Microsoft Way Redmond, WA 98052 jplatt@microsoft.com Abstract Training a Support Vector

### Hybrid Feature Selection for Modeling Intrusion Detection Systems

Hybrid Feature Selection for Modeling Intrusion Detection Systems Srilatha Chebrolu, Ajith Abraham and Johnson P Thomas Department of Computer Science, Oklahoma State University, USA ajith.abraham@ieee.org,

### Author's personal copy

European Journal of Operational Research 202 (2010) 138 142 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor Production,

### COMPENDIOUS LEXICOGRAPHIC METHOD FOR MULTI-OBJECTIVE OPTIMIZATION. Ivan P. Stanimirović. 1. Introduction

FACTA UNIVERSITATIS (NIŠ) Ser. Math. Inform. Vol. 27, No 1 (2012), 55 66 COMPENDIOUS LEXICOGRAPHIC METHOD FOR MULTI-OBJECTIVE OPTIMIZATION Ivan P. Stanimirović Abstract. A modification of the standard

### Combining Different Feature Weighting Methods for. Case Based Reasoning

School of Innovation, Design and Engineering Fusion Framework For Case Based Reasoning Combining Different Feature Weighting Methods for Case Based Reasoning Authors: Lu Ling and Li Bofeng Supervisor:

### What is Learning? CS 343: Artificial Intelligence Machine Learning. Raymond J. Mooney. Problem Solving / Planning / Control.

What is Learning? CS 343: Artificial Intelligence Machine Learning Herbert Simon: Learning is any process by which a system improves performance from experience. What is the task? Classification Problem

### A Comparative Study on Optimization Techniques for Solving Multi-objective Geometric Programming Problems

Applied Mathematical Sciences, Vol. 9, 205, no. 22, 077-085 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/ams.205.42029 A Comparative Study on Optimization Techniques for Solving Multi-objective

### Fast Branch & Bound Algorithm in Feature Selection

Fast Branch & Bound Algorithm in Feature Selection Petr Somol and Pavel Pudil Department of Pattern Recognition, Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic,

### 6. Concluding Remarks

[8] K. J. Supowit, The relative neighborhood graph with an application to minimum spanning trees, Tech. Rept., Department of Computer Science, University of Illinois, Urbana-Champaign, August 1980, also

### A running time analysis of an Ant Colony Optimization algorithm for shortest paths in directed acyclic graphs

Information Processing Letters 05 (2008) 88 92 www.elsevier.com/locate/ipl A running time analysis of an Ant Colony Optimization algorithm for shortest paths in directed acyclic graphs Nattapat Attiratanasunthron,

### Fast optimal task graph scheduling by means of an optimized parallel A -Algorithm

Fast optimal task graph scheduling by means of an optimized parallel A -Algorithm Udo Hönig and Wolfram Schiffmann FernUniversität Hagen, Lehrgebiet Rechnerarchitektur, 58084 Hagen, Germany {Udo.Hoenig,

### RANKING OF HEPTAGONAL FUZZY NUMBERS USING INCENTRE OF CENTROIDS

RANKING OF HEPTAGONAL FUZZY NUMBERS USING INCENTRE OF CENTROIDS Namarta 1, Dr Neha Ishesh Thakur, Dr Umesh Chandra Gupta 3 1 Research Scholar, UTU, Dehradun and Assistant Professor,Khalsa College Patiala

### A Proposed Model For Forecasting Stock Markets Based On Clustering Algorithm And Fuzzy Time Series

Journal of Multidisciplinary Engineering Science Studies (JMESS) A Proposed Model For Forecasting Stock Markets Based On Clustering Algorithm And Fuzzy Time Series Nghiem Van Tinh Thai Nguyen University

### SoftDoubleMinOver: A Simple Procedure for Maximum Margin Classification

SoftDoubleMinOver: A Simple Procedure for Maximum Margin Classification Thomas Martinetz, Kai Labusch, and Daniel Schneegaß Institute for Neuro- and Bioinformatics University of Lübeck D-23538 Lübeck,

### Design optimisation of industrial robots using the Modelica multi-physics modeling language

Design optimisation of industrial robots using the Modelica multi-physics modeling language A. Kazi, G. Merk, M. Otter, H. Fan, (ArifKazi, GuentherMerk)@kuka-roboter.de (Martin.Otter, Hui.Fan)@dlr.de KUKA

### A modified and fast Perceptron learning rule and its use for Tag Recommendations in Social Bookmarking Systems

A modified and fast Perceptron learning rule and its use for Tag Recommendations in Social Bookmarking Systems Anestis Gkanogiannis and Theodore Kalamboukis Department of Informatics Athens University

### Extensions of the multicriteria analysis with pairwise comparison under a fuzzy environment

International Journal of Approximate Reasoning 43 (2006) 268 285 www.elsevier.com/locate/ijar Extensions of the multicriteria analysis with pairwise comparison under a fuzzy environment Ming-Shin Kuo a,

### Cluster homogeneity as a semi-supervised principle for feature selection using mutual information

Cluster homogeneity as a semi-supervised principle for feature selection using mutual information Frederico Coelho 1 and Antonio Padua Braga 1 andmichelverleysen 2 1- Universidade Federal de Minas Gerais

### Boosting Sex Identification Performance

Boosting Sex Identification Performance Shumeet Baluja, 2 Henry Rowley shumeet@google.com har@google.com Google, Inc. 2 Carnegie Mellon University, Computer Science Department Abstract This paper presents

### Integrating Machine Learning in Parallel Heuristic Search

From: Proceedings of the Eleventh International FLAIRS Conference. Copyright 1998, AAAI (www.aaai.org). All rights reserved. Integrating Machine Learning in Parallel Heuristic Search R. Craig Varnell Stephen

### Using the Common Industry Format to Document the Context of Use

Human-Computer Interaction. Human-Centred Design Approaches, Methods, Tools, and Environments - 15th International Conference, HCI International 2013, Las Vegas, NV, USA, July 21-26, 2013, Proceedings,

### Subgoal Chaining and the Local Minimum Problem

Subgoal Chaining and the Local Minimum roblem Jonathan. Lewis (jonl@dcs.st-and.ac.uk), Michael K. Weir (mkw@dcs.st-and.ac.uk) Department of Computer Science, University of St. Andrews, St. Andrews, Fife

### HFCT: A Hybrid Fuzzy Clustering Method for Collaborative Tagging

007 International Conference on Convergence Information Technology HFCT: A Hybrid Fuzzy Clustering Method for Collaborative Tagging Lixin Han,, Guihai Chen Department of Computer Science and Engineering,

### Cost-sensitive C4.5 with post-pruning and competition

Cost-sensitive C4.5 with post-pruning and competition Zilong Xu, Fan Min, William Zhu Lab of Granular Computing, Zhangzhou Normal University, Zhangzhou 363, China Abstract Decision tree is an effective

### Tendency Mining in Dynamic Association Rules Based on SVM Classifier

Send Orders for Reprints to reprints@benthamscienceae The Open Mechanical Engineering Journal, 2014, 8, 303-307 303 Open Access Tendency Mining in Dynamic Association Rules Based on SVM Classifier Zhonglin

### Center for Automation and Autonomous Complex Systems. Computer Science Department, Tulane University. New Orleans, LA June 5, 1991.

Two-phase Backpropagation George M. Georgiou Cris Koutsougeras Center for Automation and Autonomous Complex Systems Computer Science Department, Tulane University New Orleans, LA 70118 June 5, 1991 Abstract

### FUZZY INFERENCE. Siti Zaiton Mohd Hashim, PhD

FUZZY INFERENCE Siti Zaiton Mohd Hashim, PhD Fuzzy Inference Introduction Mamdani-style inference Sugeno-style inference Building a fuzzy expert system 9/29/20 2 Introduction Fuzzy inference is the process

### Decision Management in the Insurance Industry: Standards and Tools

Decision Management in the Insurance Industry: Standards and Tools Kimon Batoulis 1, Alexey Nesterenko 2, Günther Repitsch 2, and Mathias Weske 1 1 Hasso Plattner Institute, University of Potsdam, Potsdam,

### E-Commerce - Bookstore with Recommendation System using Prediction

Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 6 (2017), pp. 2463-2470 Research India Publications http://www.ripublication.com E-Commerce - Bookstore with Recommendation

### Development of Technique for Healing Data Races based on Software Transactional Memory

, pp.482-487 http://dx.doi.org/10.14257/astl.2016.139.96 Development of Technique for Healing Data Races based on Software Transactional Memory Eu-Teum Choi 1,, Kun Su Yoon 2, Ok-Kyoon Ha 3, Yong-Kee Jun

### CART. Classification and Regression Trees. Rebecka Jörnsten. Mathematical Sciences University of Gothenburg and Chalmers University of Technology

CART Classification and Regression Trees Rebecka Jörnsten Mathematical Sciences University of Gothenburg and Chalmers University of Technology CART CART stands for Classification And Regression Trees.

### An Expert System for Plasma Cutting Process Quality Prediction and Optimal Parameter Suggestion

An Expert System for Plasma Cutting Process Quality Prediction and Optimal Parameter Suggestion Sam Y. S. Yang CSIRO Manufacturing Science and Technology, Australia Em: s.yang@cmst.csiro.au Keywords Abstract

### The Pseudo Gradient Search and a Penalty Technique Used in Classifications.

The Pseudo Gradient Search and a Penalty Technique Used in Classifications. Janyl Jumadinova Advisor: Zhenyuan Wang Department of Mathematics University of Nebraska at Omaha Omaha, NE, 68182, USA Abstract