Optimization of fuzzy classification knowledge bases using improving transformations - Rakytyanska, Hanna (Eastern-European Journal of Enterprise Technologies, 2017)
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.