Lattice Generalizations of the Concept of Fuzzy Numbers and Zadeh's Extension Principle
This work addresses theoretical extensions in fuzzy logic for applications like expert systems, but it appears incremental as it builds on existing fuzzy number concepts.
The paper generalizes fuzzy numbers to lattice-based membership functions and corrects Zadeh's extension principle for this case, also proposing an analogue of mean value and applying it to cognitive maps with expert assessments.
The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements, more precisely, a lattice, when a membership function also takes values in a partially ordered set (a lattice). Zadeh's extension principle for determining the degree of membership of a function of fuzzy numbers is corrected for this generalization. An analogue of the concept of mean value is also suggested. The use of partially ordered values in cognitive maps with comparison of expert assessments is considered.