Algorithm for Optimization of Inverse Problem Modeling in Fuzzy Cognitive Maps

Alina Vladimirovna Petukhova, Anna Vladimirovna Kovalenko and Anna Vyacheslavovna Ovsyannikova ()
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Alina Vladimirovna Petukhova: COPELABS, Lusófona University, Campo Grande, 376, 1749-024 Lisbon, Portugal
Anna Vladimirovna Kovalenko: Department of Data Analysis and Artificial Intelligence, Kuban State University, Stavropolskaya St., 149, 350040 Krasnodar, Russia
Anna Vyacheslavovna Ovsyannikova: Department of Mathematicsl, Financial University under the Government of the Russian Federation, Leningradsky Prospekt, 49, 125993 Moscow, Russia

Mathematics, 2022, vol. 10, issue 19, 1-16

Abstract: Managerial decision-making is a complex process that has several problems. The more heterogeneous the system, the more immeasurable, non-numerical information it contains. To understand the cognitive processes involved, it is important to describe in detail their components, define the dependencies between components, and apply relevant algorithms for scenario modelling. Fuzzy cognitive maps (FCMs) is the popular approach for modeling a system’s behavior over time and defining its main properties. This work develops a new algorithm for scenario analysis in complex systems represented by FCMs to provide support for decision-making. The algorithm allows researchers to analyze system-development scenarios to obtain the required change to the system’s components that leads to the target state. The problem of determining a system’s initial state is most conspicuous when constructing a compound or unbalanced fuzzy maps. Currently, a brute force algorithm is used to calculate the steps needed to approach a target, but that takes exponential time. The paper describes a new algorithm to obtain the initial values of the controlled concepts in fuzzy cognitive maps using the theory of neutrosophic fuzzy equations. This approach reduces the time needed to find the optimal solution to a problem, and it allows inverse problems to be solved in the fuzzy cognitive maps as a part of the scenario-modeling framework.

Keywords: fuzzy cognitive maps; scenario modeling; reverse task; fuzzy relational equations; neutrosophic fuzzy equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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