Abstract
AbstractIn the present paper, we propose a new approach on ‘distributed systems’: the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations met in various fields (such as computer science, economics and decision theory). We investigate questions associated to the numerical representability of order structures, relating concepts of economics and computing to each other. The concept of ‘quasi-finite partial orders’ is introduced as a finite family of chains with a communication between them. The representability of this kind of structure is studied, achieving a construction method for a finite (continuous) Richter–Peleg multi-utility representation.
Funder
Ministerio de Ciencia e Innovación
Universidad Pública de Navarra
Publisher
Springer Science and Business Media LLC
Reference41 articles.
1. Alcantud, J.C.R., Bosi, G., Zuanon, M.: Richter-Peleg multi-utility representations of preorders. Theory Decis. 80, 443–450 (2016)
2. Aleskerov, F., Bouyssou, D., Monjardet, B.: Utility maximization, choice and preference, 2nd edn. Springer, Berlin (2007)
3. Bosi, G., Estevan, A.: Continuous Representations of Preferences by Means of Two Continuous Functions. J. Optim. Theory Appl. 185, 700–710 (2020)
4. Bosi, G., Herden, G.: On continuous multi-utility representations of semi-closed and closed preorders. Math. Social Sci. 79, 20–29 (2016)
5. Bosi, G., Candeal, J.C., Induráin, E.: Continuous representability of interval orders and biorders. J. Math. Phychol. 51, 122–125 (2007)