# Lattice Generalizations of the Concept of Fuzzy Numbers and Zadeh's Extension Principle

arXiv: https://arxiv.org/abs/2208.06224 · HTML: https://mlsanity.com/paper/2208.06224/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 14 references that are in the map.
- First posted on arXiv 12 Aug 2022.

## Builds on (most cited first, 1 of 1)

- [Multi-Valued Cognitive Maps: Calculations with Linguistic Variables without Using Numbers](https://mlsanity.com/paper/2108.04760/) (2021)

## Abstract (arXiv)

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.