Three-term relation neuro-fuzzy cognitive maps

Abstract

In this paper, we propose a novel approach to modeling using fuzzy cognitive maps, which we refer to as the Three-Term Relation Neuro-Fuzzy Cognitive Map or simply the TTR NFCM. The proposed method is mostly suited to model complex nonlinear technical systems with dynamic internal characteristics. With this method we aim to solve some of the most critical problems of the conventional fuzzy cognitive maps. We target two of these problems by hybridization with artificial neural networks. First of them is a linear nature of relations between the concepts. The second is a lack of mutual dependence between the relations connecting to the same concept. Finally, we tackle a problem of relation dynamics using an inspiration from the control engineering. While focusing on bringing these advanced additional methods to the design of cognitive maps, we also aim to keep the degree of dependency on expert knowledge on the same level as with the conventional fuzzy cognitive maps. We achieve this by utilizing the machine learning methods. However, since the proposed method is heavily dependent on automated data-driven learning, it is suitable mainly for systems which are well observable and can produce sufficient training datasets.

A proposal for Multi-Purpose Fuzzy Cognitive Maps library for complex system modeling

“…The library is not limited only to the basic FCMs. It can also apply derived methods, such as recently proposed Three-Term Relation Neuro-Fuzzy Cognitive Maps (TTR-NFCM) [11]. The proposed library also supports various methods for relation expression (nonlinear relations, dynamic, relations, function relations, neural relations, etc.).…”

“…Despite JFCM is being considered a competent and efficient library, it does not provide support for advanced cognitive map designs such as nonlinear, dynamic relations, conditional relations or relations represented by neural networks [11]. However, such advanced designs are important for modeling relations between elements of complex systems, since it is difficult to model nonlinear systems with linear models (such as FCM) only [2].…”

“…• Definition of casual relations between concepts, including support for advanced approaches, such as the nonlinear, conditional and dynamic relations [12], possibly utilizing neural networks [11].…”

“…• simple linear weight with singleton value, • nonlinear analytic function (useful for modeling physical phenomena where relation are well known), • Three-Term Relation (TTR) [11] with three linear weights, one for proportional, derivative and average component, • time-window relation [11] with number of weights equivalent to the size of the time window.…”

“…Additionally, the relations can be represented as small multilayer feed-forward neural networks [11]. However, in this case it is necessary to use supervised learning methods, which are further described in the next section.…”