Uncertainty Propagation in Fuzzy Grey Cognitive Maps With Hebbian-Like Learning Algorithms

Abstract

This paper is focused on an innovative fuzzy cognitive maps extension called fuzzy grey cognitive maps (FGCMs). FGCMs are a mixture of fuzzy cognitive maps and grey systems theory. These have become a useful framework for facing problems with high uncertainty, under discrete small and incomplete datasets. This paper deals with the problem of uncertainty propagation in FGCM dynamics with Hebbian learning. In addition, this paper applies differential Hebbian learning (DHL) and balanced DHL to FGCMs for the first time. We analyze the uncertainty propagation in eight different scenarios in a classical chemical control problem. The results give insight into the propagation of the uncertainty or greyness in the iterations of the FGCMs. The results show that the nonlinear Hebbian learning is the choice with less uncertainty in steady final grey states for Hebbian learning algorithms.

Методы И Модели Поддержки Принятия Решений При Управлении Инновационными Проектами В Производственно-Экономических Системах

“…В качестве возможных путей решения данной проблемы различными авторами были предложены специальные конструкции (расширения) НКК, связанные с представлением силы связей НКК в виде некоторых интервальных оценок. К числу подобных структур НКК относятся такие разновидности НКК, как уже упоминавшиеся серые НКК (Grey FCM) [132], а также интервально-значные НКК (Interval-Valued FCM) [133], грубые НКК (Rough FCM) [134], интуиционистские НКК (Intuitionistic FCM) [135].…”

“…Имеется в виду, что эксперт зачастую затрудняется определить значения функции принадлежности Учитывая более высокую сложность модели iFCM-II по сравнению с моделью iFCM-I, выберем для дальнейшего анализа более простой вариант интуиционистской НКК -когнитивную карту iFCM-I, уравнения состояния которой принимают в данном случае следующий вид [132]:…”

Fuzzy cognitive maps in systems risk analysis: a comprehensive review

“…Each relationship between the concepts C i and C j have a weight of W ij (the weight between ith node and jth node), which might be positive, negative, or neutral (indicates that two concepts under consideration have no relationship) [36,128]. Based on the FCM developed by Kosko [76], the relationship between concepts is changed from the state {0,1} or {− 1,0,1} to a set of states by a number in the interval [0,1] or [− 1,1] or fuzzy linguistic terms [129,130,135].…”

Fuzzy cognitive map based approach for determining the risk of ischemic stroke

“…It has various applications in the scientific and industrial fields, such as expansion of the decision making in support systems, political and military sciences, software engineering, information systems, business, modelling, pattern recognition, robotics, computer science, management, forecasting, expert systems, management, and so on [7][8][9][10][11]. In addition, FCM is considered as a modern and extremely efficient method for diagnosis of diseases.…”