Fuzzy Cognitive Maps Advances in Theory, Methodologies, Tools and Ap
The theory of cognitive maps was developed in 1976. Its main aim was the representation of (causal) relationships among “concepts” also known as “factors” or “nodes”. Concepts could be assigned values. Causal relationships between two concepts could be of
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A New Intuitionitic Fuzzy Cognitive Maps Building Method Ioan Despi
GuYin Song
Kankana Chakrabarty
School of Science and Technology University of New england Armidale-2351, NSW, Australia
School of Science and Technology University of New england Armidale-2351, NSW, Australia
School of Science and Technology University of New england Armidale-2351, NSW, Australia
Abstract—When modeling complex systems, conventional methodologies are recognized to be limited. Because of their fuzzy feedback structure of causality, Fuzzy Cognitive Maps (FCMs) have been seen as a promising alternative in multiple domains as a support for decision making and systems modeling. In an attempt to improve this framework, we extend it by considering both determinacy and indeterminacy of experts when assigning weights to causal relations between concepts such that a new initutionistic fuzzy method for constructing FCMs is considered. The proposed method largely improves the accuracy of evaluating weights of edges in the FCM models and avoids subjectiveness and indeterminacy while experts are designing the models.
I. I NTRODUCTION Fuzzy Cognitive Maps (FCMs) are a very simple, convenient tool for analyzing dynamic systems and supporting decision making. Together with this, they are highly powerful and effectively applied to various domains, such as medical treatment, control engineering, political decision making and military affairs [1]. They were proposed by Bart Kosko [2] in 1986 as a soft computing technique for simulating complex systems. On the other hand, in 1983, Atanassov [3] proposed Initutionistic Fuzzy Sets as a generalization of Fuzzy Sets concept introduced by Zadeh [4] in 1965. Given an universe of discourse 𝑋, one can define fuzzy sets based on membership functions 𝜇𝐴 : 𝑋 → [0, 1], that is sets with ‘vague boundary’ when compared with crip sets (𝜇𝐴 : 𝑋 → {0, 1}). In FCM terminology, a given system is seen as a collection of interrelated concepts with cause-effect relationships among them [5]. The concepts are represented as nodes and the interrelationships are depicted as weighted arcs denoting the strength of influence. This can be expressed by linguistic hedges (fuzzy terms), such as ‘very weak’, ‘weak’, ‘acceptable’, ‘strong’ or ‘very strong’, etc. How much a concept 𝐶1 causes 𝐶2 is indicated by the weight of a directed edge from node 𝐶1 to 𝐶2 [1]. The weight is a positive fuzzy number for direct influence or a negative fuzzy number for reversed influence. Of course, there is no arc and we will consider a zero weight if there is no causality between two concepts. Being extremely intuitive and simple to understand, the FCM method is relatively easy to apply for displaying structured systems, where the hidden pattern can be calculated by computing with connection matrices instead of complex IF/THEN rules [6]. It is highly flexible in simulating and
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controlling systems, convenient when data is unsupervised [7] and appropriate for fuzzy reasoning [8]. However, FCMs show some defici
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