A study of the strong Allee effect with fuzzy parameters for its application in economics

作者：Corominas Coll Dolors; Carles Ferrer Comalat Joan; Linares Mustaros Salvador; Bertran Xavier

来源：Kybernetes, 2017, 46(1): 191-206.

DOI：10.1108/K-06-2016-0154

• Allee effect
• Fuzzy number
• Generalization of Hukuhara difference
• Hukuhara difference
• Level sets
• Standard difference

Purpose - The purpose of this study is to present a detailed quantitative and qualitative fuzzy approach to the Allee effect that permits dealing with uncertainty.
Design/methodology/approach - The Allee effect is related to those aspects of population dynamics that are connected with a decrease in individual fitness when the population size diminishes to very low levels. It allows to model the evolution of certain sectors or clusters which, due to their low population density, may have problems of survival. In uncertain environments, an estimate of the effect's parameters can be performed in the form of fuzzy numbers, which means that this study is using the methodology of fuzzy arithmetic.
Findings - This study reveals that fuzziness changes the behavior of the set of solutions when the strong Allee effect is studied under uncertainty from the point of view of standard difference or generalization of the Hukuhara difference.
Originality/value - The value and originality of the work consists in offering a set of tools for studying the evolution of a group of firms subject to an Allee effect in uncertain environments.

• 出版日期2017