This survey makes a review of the most recent applications and trends on fuzzy cognitive maps (FCMs) over the past decade. FCMs are inference networks, using cyclic digraphs, for knowledge representation and reasoning. Over the past decade, FCMs have gained considerable research interest and are widely used to analyze causal complex systems, which have originated from the combination of fuzzy logic and neural networks. FCMs have been applied in diverse application domains, such as computer science, engineering, environmental sciences, behavioral sciences, medicine, business, information systems, and information technology. Their dynamic characteristics and learning capabilities make them essential for a number of tasks such as modeling, analysis, decision making, forecast, etc. Overall, this paper summarizes the current state of knowledge of the topic of FCMs. It creates an understanding of the topic for the reader by discussing the findings presented in recent research papers. A survey on FCM studies concentrated on FCM applications on diverse scientific areas, where the FCMs emerged with a high degree of applicability, has also been done during the past ten years.

A Review of Fuzzy Cognitive Maps Research During the Last Decade

This study presents a survey on the most recent learning approaches and algorithms that are related to fuzzy cognitive maps (FCMs). FCMs are cognition fuzzy influence graphs, which are based on fuzzy logic and neural network aspects that inherit their main advantages. They gained momentum due to their dynamic characteristics and learning capabilities. These capabilities make them essential for modeling and decision-making tasks as they improve the performance of these tasks. An efficient number of learning algorithms for FCMs, by modifying the FCM weight matrix, have been developed in order to update the initial knowledge of human experts and/or include any knowledge from historical data in order to produce learned weights. The proposed learning techniques have mainly been concentrated on three directions: on the production of weight matrices on the basis of historical data, on adaptation of the cause-effect relationships of the FCM on the basis of experts' intervention, and on the production of weight matrices by combining experts' knowledge and data. The learning techniques could be categorized into three groups on the basis of the learning paradigm: Hebbian-based, population-based, and hybrid, which subsequently combine the main aspects of Hebbian-based- and population-based-type learning algorithms. These types of learning algorithms are the most efficient and widely used to train the FCMs, according to the existing literature. A survey on recent advances on learning methodologies and algorithms for FCMs that present their dynamic capabilities and application characteristics in diverse scientific fields is established here.

Learning Algorithms for Fuzzy Cognitive Maps—A Review Study

Fuzzy cognitive maps (FCMs) keep growing in popularity within the scientific community. However, despite substantial advances in the theory and applications of FCMs, there is a lack of an up-to-date, comprehensive presentation of the state-of-the-art in this domain. In this review study we are filling that gap. First, we present basic FCM concepts and analyze their static and dynamic properties, and next we elaborate on existing algorithms used for learning the FCM structure. Second, we provide a goal-driven overview of numerous theoretical developments recently reported in this area. Moreover, we consider the application of FCMs to time series forecasting and classification. Finally, in order to support the readers in their own research, we provide an overview of the existing software tools enabling the implementation of both existing FCM schemes as well as prospective theoretical and/or practical contributions.

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A review on methods and software for fuzzy cognitive maps

This paper is a statistical analysis of hybrid expert system approaches and their applications but more specifically connectionist and neuro-fuzzy system oriented articles are considered. The current survey of hybrid expert systems is based on the classification of articles from 1988 to 2010. Present analysis includes 91 articles from related academic journals, conference proceedings and literature reviews. Our results show an increase in the number of recent publications which is an indication of gaining popularity on the part of hybrid expert systems. This increase in the articles is mainly in neuro-fuzzy and rough neural expert systems' areas. We also observe that many new industrial applications are developed using hybrid expert systems recently.

Review: Hybrid expert systems: A survey of current approaches and applications

Fuzzy neural networks and neuro-fuzzy networks: A review the main techniques and applications used in the literature

The fuzzy cognitive map (FCM) has gradually emerged as a powerful paradigm for knowledge representation and a simulation mechanism that is applicable to numerous research and application fields. However, since efficient methods to determine the states of the investigated system and to quantify causalities that are the very foundations of FCM theory are lacking, constructing FCMs for complex causal systems greatly depends on expert knowledge. The manually developed models have a substantial shortcoming due to the model subjectivity and difficulties with assessing its reliability. In this paper, we proposed a fuzzy neural network to enhance the learning ability of FCMs. Our approach incorporates the inference mechanism of conventional FCMs with the determination of membership functions, as well as the quantification of causalities. In this manner, FCM models of the investigated systems can automatically be constructed from data and, therefore, operate with less human intervention. In the employed fuzzy neural network, the concept of mutual subsethood is used to describe the causalities, which provides more transparent interpretation for causalities in FCMs. The effectiveness of the proposed approach in handling the prediction of time series is demonstrated through many numerical simulations.

F. Catthoor

Papers

Implementation of Fuzzy Cognitive Maps Based on Fuzzy Neural Network and Application in Prediction of Time Series