Fuzzy Reasoning with Several Regularization Parameters

Abstract

In this paper, we propose a fuzzy reasoning method with plural regularization parameters. It is known that the annealing of the regularization term brings improvement of the generalization ability for the model by adding the regularization term to the error term in the cost function. In this study, we focus on the regularization parameter that is used to control the influence of the regularization term in relation to the error term. We consider the model that each parameter works on each rule by using not the regularization term as a unitary coefficient but as a matrix. Using the regularization parameters for each rule, a regularization parameter corresponds to one weight of the consequent part in a one-to-one relationship. Therefore we can know the influence of the weight to reasoning output. In the numerical simulations, the validity of the proposed method is discussed.