By Elpiniki I. Papageorgiou
Fuzzy Cognitive Maps (FCM) represent cognitive types within the type of fuzzy directed graphs together with uncomplicated parts: the nodes, which essentially correspond to “concepts” bearing various states of activation counting on the information they signify, and the “edges” denoting the causal results that every resource node workouts at the receiving suggestion expressed via weights. Weights take values within the period [-1,1], which denotes the optimistic, unfavorable or impartial causal courting among innovations. An FCM will be more often than not acquired via linguistic phrases, inherent to fuzzy structures, yet with a constitution just like the neural networks, which enables information processing, and has features for education and adaptation.
During the final 10 years, an exponential progress of released papers in FCMs was once exhibiting nice impression strength. diversified FCM constructions and studying schemes were constructed, whereas a number of experiences document their use in lots of contexts with hugely profitable modeling effects.
The objective of this ebook is to fill the prevailing hole within the literature referring to basics, versions, extensions and studying algorithms for FCMs in wisdom engineering. It comprehensively covers the state of the art FCM modeling and studying equipment, with algorithms, codes and software program instruments, and gives a collection of functions that reveal their numerous usages in technologies and engineering.
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Extra resources for Fuzzy Cognitive Maps for Applied Sciences and Engineering: From Fundamentals to Extensions and Learning Algorithms
IFS is a generalization of conventional fuzzy sets since the IFS membership is a fuzzy logical value rather than a single truth value. Fig. 4 A relation between a couple of nodes (x1 and x2 ) in iFCM-II. Each node has an impact weight and a hesitancy weight 10 E. I. Papageorgiou and J. L. Salmeron iFCM-I proposal just considers the hesitancy of the influence between a couple of concepts. On the other hand, iFCM-II introduced hesitancy in the determination of concept values . The hesitancy of the element x of a fuzzy set A is defined as follows (7) π A (x) = 1 − μ A (x) − γ A (x) The iFCM-I iterative reasoning process is computed as follows n ci (t + 1) = f (2 · ci (t + 1)) + μ ((2 · c j (t + 1)) · ζ ji · w ji · (1 − wπji )) (8) i=1 μ where ci ∈ [0, 1], i = 1, .
IFCM proposal is effective with numeric, reproducible examples, on process control and decision support. iFCMs include the Intuitionistic Fuzzy Sets (IFS) to handle the experts’ hesitancy in their judgements. It improves conventional FCM through the intuitionistic theory so that it models the degree of hesitancy in the relations defined by the experts (Fig. 4). The experts propose the cause-effect relations between two concepts, and the degree to which the expert hesitates to express that relation.
This is acceptable due to the operation of the evolutionary approaches for optimization tasks. 24 E. I. Papageorgiou and J. L. Salmeron Summarizing, population-based methods outperform Hebbian-based in terms of model error. The evolutionary learning algorithms use fitness functions for design and optimization tasks, thus defining the problem constraints more efficiently in learning approach. 8 Conclusions and Future Directions FCM-based methods and computational learning algorithms have emerged attention throughout recent years for modeling and decision support tasks.
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