Interval order relationships based on automorphisms and their application to interval optimization
This paper presents a method to generate preference ordering relations on interval space based on a family of automorphisms on the bidimensional Euclidean space. This method generates a family of order relation with which many order relations presented in the literature can be obtained as particular...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/181631 |
| Acceso en línea: | https://hdl.handle.net/11441/181631 https://doi.org/10.1016/j.ins.2022.10.020 |
| Access Level: | acceso abierto |
| Palabra clave: | Preference order relations Decision under Uncertainty Interval optimization |
| Sumario: | This paper presents a method to generate preference ordering relations on interval space based on a family of automorphisms on the bidimensional Euclidean space. This method generates a family of order relation with which many order relations presented in the literature can be obtained as particular cases. This family of preference order relations is used to provide a formulation for a family of interval optimization problems that unifies those formulations whose solution concepts are a Pareto-type. The elements belonging to this family are called -interval optimization problems. An advantage of the proposed method is that decision makers can consider a suitable interval optimization problem, choosing an appropriate order relation, which is obtained by choosing an automorphism. Moreover, this paper shows that each -interval optimization problem is equivalent to a biobjective optimization problem. Some optimality conditions for the -interval optimization problems are obtained. The method, concepts and results presented herein are illustrated by several examples. |
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