Multi-Valued Cognitive Maps: Calculations with Linguistic Variables without Using Numbers
This work addresses uncertainty modeling for experts in decision-making systems, but it appears incremental as it builds upon fuzzy cognitive maps.
The paper tackles the problem of handling uncertainty in cognitive maps by introducing multi-valued cognitive maps with partially-ordered linguistic variables, eliminating the need for fuzzification/defuzzification and allowing more subtle uncertainty distinctions than fuzzy methods, with results including a proof of convergence and a computational example.
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.