# Multi-Valued Cognitive Maps: Calculations with Linguistic Variables without Using Numbers

arXiv: https://arxiv.org/abs/2108.04760 · HTML: https://mlsanity.com/paper/2108.04760/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 31 references that are in the map.
- First posted on arXiv 10 Aug 2021.

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

- [Models of latent consensus](https://mlsanity.com/paper/1612.05201/) (2016)

## Built on by (most cited first, 2 of 2)

- [Lattice Generalizations of the Concept of Fuzzy Numbers and Zadeh's Extension Principle](https://mlsanity.com/paper/2208.06224/) (2022)
- [On the Convergence of Sigmoid and tanh Fuzzy General Grey Cognitive Maps](https://mlsanity.com/paper/2409.05565/) (2024)

## Abstract (arXiv)

A concept of multi-valued cognitive maps is introduced in this paper. The concept expands the fuzzy one. However, all variables and weights are not linearly ordered in the concept, but are only partially-ordered. Such an ap- proach allows us to operate in cognitive maps with partially-ordered linguis- tic variables directly, without vague fuzzification/defuzzification methods. Hence, we may consider more subtle differences in degrees of experts' uncer- tainty, than in the fuzzy case. We prove the convergence of such cognitive maps and give a simple computational example which demonstrates using such a partially-ordered uncertainty degree scale.