Preference Operators

Abstract

The theories of multi-criteria decision-making (MCDM) and fuzzy logic both seek to model human thinking. In MCDM, aggregation processes and preference modeling play the central role. This chapter presents a consistent framework for modeling human thinking 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. Similar to the implication being defined as a composition of the disjunction and the negation operator, preference operators that describe to what extent x is preferable to y, are introduced as a composition of the aggregative operator and the negation operator. Although these operators have many properties in common with implications, we show that there is a subtle but important difference. After a profound examination of the main properties of the preference operator, our main goal is the implementation of this operator into neural networks.