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

TL;DR

This paper introduces multi-valued cognitive maps that operate with partially-ordered linguistic variables, enabling nuanced handling of expert uncertainty without relying on fuzzification or defuzzification.

Contribution

It extends fuzzy cognitive maps to multi-valued, partially-ordered linguistic variables, allowing more subtle uncertainty modeling and direct computation without fuzzification.

Findings

Proves convergence of multi-valued cognitive maps.

Demonstrates computation with a simple example.

Allows more nuanced uncertainty representation.

Abstract

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.