In this study, a new two-stage learning based reduction approach for fuzzy cognitive maps (FCM) is introduced in order to reduce the number of concepts. FCM is a graphical modeling technique that follows a reasoning approach similar to the human reasoning and the decision-making process. The FCM model incorporates the available knowledge and expertise in the form of concepts and in the direction and strength of the interactions among concepts. One of the modeling problems of FCMs is that oversized FCM models suffer from interpretability problems. An oversized FCM may contain concepts that are semantically similar and affect the other concepts in a similar way. This new study introduces a two-stage model reduction approach, and both static and dynamic analyses are considered without losing essential information. In the first stage, the number of concepts is reduced by merging similar concepts into clusters, whereas in the second stage the transformation function parameters of concepts are optimized. In order to show the benefit of using the proposed reduction approach, two sets of studies are conducted. First, a huge set of synthetic FCMs are generated, and the results of these statistical analyses are presented via various tables and figures. Subsequently, suggestions to the decision makers are given. Second, experimental studies are also presented to show the decision parameters and procedure for the proposed approach. The results show that after using the concept reduction approach presented in this study, the interpretability of FCM increases with an acceptable amount of information loss in the output concepts.

Policy making, strategic planning and management in general are complex decision making tasks, where the formulation of a quantitative mathematical model may be difficult or impossible due to lack of numerical data and dependence on imprecise verbal expressions. For such systems, knowledge representation graphs and cognitive maps are most familiar and often used for modelling complexity and aiding decision making. Fuzzy Cognitive Maps (FCM), as graph-based cognitive models, have been successfully used for knowledge representation and reasoning. In modelling complex systems usually a large number of concepts need to be considered. However, it is often difficult in real applications to find the appropriate number of concepts. Using only a few concepts is not enough to represent the modelled system with the required precision, and increasing the number of concepts increases the complexity of the model quadratically; it is burdensome to work with for the experts. The contribution of this paper is two-fold: (i) to propose a new concept reduction approach for FCM and (ii) to apply it on developing less complex FCM for management and decision making. The behaviour of reduced models is analysed through a number of scenarios with respect to the original complex system. The main idea of the reduction is a clustering based on fuzzy tolerance relations. The new approach is focused on reducing complexity in the modelling process, which provides a more transparent and easy to use model for policy makers. The applicability of the proposed method is demonstrated via literature examples and a solid waste management case study that initiated this research. The results clearly show the advantageous characteristics of the proposed concept reduction method for FCM and its aid in policy making.