scholarly journals A Study on the Behaviour of the Algorithm for Finding Relevant Attributes and Membership Functions

2009 ◽  
Vol 40 (1) ◽  
pp. 75-80
Author(s):  
Madara Gasparoviča ◽  
Ludmila Aleksejeva
Keyword(s):  
Fuzzy Classification ◽  
Primary Data ◽  
Optimal Size ◽  
Data Sets ◽  
Classification Rules ◽  
Membership Functions ◽  
Classification Problems ◽  
Data Set ◽  
Testing Data ◽  
Decision Tables

A Study on the Behaviour of the Algorithm for Finding Relevant Attributes and Membership FunctionsOne of the most recent approaches in machine learning is fuzzy rules usage for solving classification problems. This paper describes the algorithm for finding relevant attributes and searching for membership functions. Experimental results are used to clarify - which data sets can be used to automatically gain primary membership functions from primary data. This quality - gaining of membership functions - is one of the pros of the algorithm, because it eases resolution of classification task. The ability to use it with fuzzy data is one more merit. As a result, there are obtained reliable fuzzy classification rules to separate classes. By reconstructing primary membership functions also the number of IF-THEN rules gained from decision tables is reduced up to three times. Four experiments are conducted with different training and testing data set sizes. Conclusions are made about the optimal size of the training and testing data set that is necessary for achieving better results as well as about the data this algorithm is appropriate for. Finally, possible directions for further research are outlined.

Formulation of Fuzzyc-Means Clustering Using Calculus of Variations and Twofold Membership Clusters

2008 ◽  
Vol 12 (5) ◽  
pp. 454-460 ◽  
Author(s):  
Sadaaki Miyamoto ◽  
Keyword(s):  
Calculus Of Variations ◽  
Fuzzy Classification ◽  
Classification Rules ◽  
Membership Functions ◽  
Data Space ◽  
Possibilistic Clustering ◽  
Membership Matrix

A membership matrix of fuzzyc-means clustering is associated with corresponding fuzzy classification rules as membership functions defined on the whole data space. We directly derive such functions in fuzzyc-means and possibilistic clustering using the calculus of variations, generalizing ordinary fuzzyc-means and deriving new twofold membership clustering using this framework.

MODELING THE SYNTHESIS OF TAKAGI — SUGENO — KANG FUZZY CONTROLLERS IN SOME CONTROL SYSTEMS

2021 ◽  
Vol 7 (2) ◽  
pp. 147-169
Author(s):  
Irina V. Kulikova
Keyword(s):  
Genetic Algorithms ◽  
Control System ◽  
Fuzzy Controller ◽  
Industrial Society ◽  
Control Action ◽  
Effective Control ◽  
Control Parameters ◽  
Membership Functions ◽  
Fuzzy Controllers ◽  
Takagi Sugeno

Modern challenges in a post-industrial society require further development of management systems for complex technical and technological phenomena and processes. Effective control of an object is possible if a controller, or a fuzzy controller, correctly generates the required control action. Recently, fuzzy controllers have been very popular. Fuzzy logical statements in this case help considering various nonlinear relationships. The synthesis of the fuzzy controller parameters allows for more efficient operation of the control system. A possible option for obtaining the best set of parameters for a fuzzy controller is the use of genetic algorithms for its synthesis. The use of genetic algorithms for the fuzzy controllers synthesis can lead to the fact that the elements of its parameters array will change in such a way that an incorrect value of one or more elements will occur. This situation leads to impossibility of composing membership functions for the terms of the variables of the fuzzy controller. Incorrect value formation is excluded by constructing a limited functional dependency. This paper proposes a mathematical model of the parameters of the term-set of variables of a fuzzy controller of the Takagi — Sugeno — Kang type of the zero and first orders. The authors disclose the content of the conditions and conclusions of the rule base for the fuzzy controller of the above type. As a result of the simulation, some operations of the genetic algorithm are implemented using a random number generator. Graphical models of the membership functions of the input variables of the fuzzy controller of the type under consideration clearly illustrate the occurrence of all parameters in their range of possible values. A description of the control system operation with two control parameters and one control action at the specified values of the control parameters is presented.

Learning Fuzzy Classification Rules from Data

2001 ◽  
pp. 108-115 ◽  
Author(s):  
Hans Roubos ◽  
Magne Setnes ◽  
Janos Abonyi
Keyword(s):  
Fuzzy Classification ◽  
Classification Rules
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