Abstract
The method of fuzzy classification knowledge base optimization using improving transformations in the form of solutions of fuzzy relational equations is proposed. The logic-algorithmic models of improving transformations are developed, on the basis of which the genetic algorithm of fuzzy knowledge base optimization is proposed. Methods of rule generation and selection differ in computational complexity due to the redundancy of the initial model. The methods of candidate rule generation do not guarantee the optimum number of rules and optimum granularity of input variables. The selection process becomes more complicated with increasing number of criteria, in particular, when taking into account the rule length. Improving transformations are: transition to a composite model for selecting output classes and rules; transition to a relational model for selecting input terms. The min-max clustering problem is solved by generating composite rules in the form of interval solutions of the trend system of equations. The number of rules in a class is determined by the number of solutions, and the granularity is determined by intervals of values of input variables in rules. The set of minimum solutions provides the minimum rule length. Linguistic interpretation of the solutions obtained is reduced to solving the relational clustering problem. The level of detail and the density of coverage are determined by the “input terms – output classes” relational matrix, and the dimensions of hyperboxes are tuned using triangular membership functions. Improving transformations allow formalizing the process of fuzzy knowledge base generation and selection. Each improving transformation is related to the control variables (the number of terms, classes, rules) that affect the accuracy and complexity of the model. At the same time, consistent use of composite and relational improving transformations provides tuning process simplification.
Highlights
Fuzzy classification knowledge base design is carried out according to the criteria of accuracy, complexity, and interpretability
The level of detail and the density of coverage are determined by the “input terms – output classes” relational matrix, and the dimensions of hyperboxes are adjusted using triangular membership functions
The parameters of improving operators are the number of input terms, output classes, rules, and parameters of membership functions in logical conditions (10)–(12)
Summary
Fuzzy classification knowledge base design is carried out according to the criteria of accuracy, complexity, and interpretability. Improving transformations for a given granularity [4], when at the stage of generating the candidate rules it is possible to obtain the required number of input terms are called formalized. In this case, only the weights of rules are sufficient for selection. The considered approach differs in computational complexity due to the increasing number of rules Both at the stage of candidate rule generation and at the selection stage, the control variables are the membership function parameters in each rule. The problem of min-max clustering is solved by generating composite rules in the form of in-
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