How to implement MCDM tools and continuous logic into neural computation?: Towards better interpretability of neural networks

摘要

The theories of multi-criteria decision-making (MCDM) and fuzzy logic both aim to model human thinking. In MCDM, aggregation processes and preference modeling play the central role. This paper suggests a consistent framework for modeling human thinking by using the tools of both fields: fuzzy logical operators as well as aggregation and preference operators. In this framework, aggregation, preference, and the logical operators are described by the same unary generator function. Similarly to the implication being defined as a composition of the disjunction and the negation operator, preference operators were introduced as a composition of the aggregative operator and the negation operator. After a profound examination of the main properties of the preference operator, our main goal is the implementation into neural networks. We show how preference can be modeled by a perceptron, and illustrate the results in practical neural applications.