Interval order relationships based on automorphisms and their application to interval optimization

Author(s)

Costa, T. M. ; Chalco-Cano, Y. ; Osuna-Gomez, R. ; Lodwick, W. A.

• Document type: Journal article
• Source: INFORMATION SCIENCES; v. 615, p. 12-pg., 2022-10-21.

Abstract

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 u-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 u-interval optimization problem is equivalent to a biobjective optimization problem. Some optimality conditions for the phi-interval optimization problems are obtained. The method, concepts and results presented herein are illustrated by several examples.(C) 2022 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 21/03269-7 - 3D Structure determination of proteins and nanostructured materials with uncertain data via optimization
• Grantee: Luiz Leduíno de Salles Neto
• Support Opportunities: Regular Research Grants