A multi-objective optimization-based granular neural networks under the principle of justifiable granularity

Abstract

The optimal allocation of information granularity is the key to build a granular neural network model with good interpretability. The existing granular neural networks adopt the single-objective optimization to realize the granularity allocation, with the result that the single granularity allocation cannot support the diverse perspective analysis by model. Under the principle of justifiable granularity, the information granularity allocation should take into account the two mutually exclusive indexes of coverage and specificity. By employing a multi-objective optimization algorithm based on the Pareto optimality concept to achieve optimized allocation of information granularity, a granular neural network based on the NSGA-II multi-objective optimization under the principle of justifiable granularity is proposed. The presented method allocates specific information granularity levels to input variables using NSGA-II optimization, which can not only get the multiple sets of input variable granularity combinations but also facilitate the granulated output of the model. Experimental results on artificial and UCI datasets demonstrate that the proposed modeling method of granular neural network allows for reliable predictions through granulated output analysis. Additionally, it enables the identification of key input variables influencing the output through granulated input analysis, thus satisfying the need for multidimensional problem analysis from various granular perspectives.