ICLA imperialist competitive learning algorithm for fuzzy cognitive map: Application to water demand forecasting

In this paper, we develop a new Fuzzy Cognitive Map (FCM) learning method using the imperialistic competitive learning algorithm (ICLA). An FCM seems like a fuzzy signed directed graph with feedback, and models complex systems as a collection of concepts and causal relations between concepts. Conventional FCMs are mainly constructed by human experts who have experience in the specific problem domain. However, large problems need automated methods. We develop an automated method for FCM construction inspired by the socio-political behavior of countries as imperialists with colonies. In the real world imperialists extend their territories and change the socio attributes of their colonies. The ICLA is an evolutionary algorithm and simulates this behavior. We explain the algorithm for FCM learning and demonstrate its performance advantages through synthetic and real data of water demand. The results of the new algorithm were compared to that of a genetic algorithm, which is the most commonly used and well-known FCM learning algorithm.

I. Introduction

A Fuzzy Cognitive Map (FCM) is a directed weighted network with feedback loops [19]. This network type is used to model and analyze the behavior of dynamic and complex systems. This modeling technique creates a network which consists of all possible causal relationships between components of the system modeled. Nodes in this network are components of the system and arrows in this network represent the direction of relationship between nodes. Each relationship is associated with a weighted arrow which indicates the strength of relationship between two nodes [13].