Parameter analysis for sigmoid and hyperbolic transfer functions of fuzzy cognitive maps

Themistoklis Koutsellis, Georgios Xexakis, Konstantinos Koasidis (), Alexandros Nikas and Haris Doukas
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Themistoklis Koutsellis: National Technical University of Athens
Georgios Xexakis: HOLISTIC P.C.
Konstantinos Koasidis: National Technical University of Athens
Alexandros Nikas: National Technical University of Athens
Haris Doukas: National Technical University of Athens

Operational Research, 2022, vol. 22, issue 5, No 33, 5733-5763

Abstract: Abstract Fuzzy cognitive maps (FCM) have recently gained ground in many engineering applications, mainly because they allow stakeholder engagement in reduced-form complex systems representation and modelling. They provide a pictorial form of systems, consisting of nodes (concepts) and node interconnections (weights), and perform system simulations for various input combinations. Due to their simplicity and quasi-quantitative nature, they can be easily used with and by non-experts. However, these features come with the price of ambiguity in output: recent literature indicates that changes in selected FCM parameters yield considerably different outcomes. Furthermore, it is not a priori known whether an FCM simulation would reach a fixed, unique final state (fixed point). There are cases where infinite, chaotic, or cyclic behaviour (non-convergence) hinders the inference process, and literature shows that the primary culprit lies in a parameter determining the steepness of the most common transfer functions, which determine the state vector of the system during FCM simulations. To address ambiguity in FCM outcomes, we propose a certain range for the value of this parameter, $${\uplambda }$$ λ , which is dependent on the FCM layout, for the case of the log-sigmoid and hyperbolic tangent transfer functions. The analysis of this paper is illustrated through a novel software application, In-Cognitive, which allows non-experts to define the FCM layout via a Graphical User Interface and then perform FCM simulations given various inputs. The proposed methodology and developed software are validated against a real-world energy policy-related problem in Greece, drawn from the literature.

Keywords: Fuzzy cognitive maps; Mental modelling; Transfer function; Parameter selection; Decision making; Participatory modelling; 90C70 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s12351-022-00717-x

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