A characterization of reciprocal fuzzy preference structures and its compatibility with standard fuzzy preference structures
Fuzzy relations R : A² → [0, 1] are widely used in decision-making in order to represent degrees of preference between alternatives in A. Examining fuzzy relations, this paper first reflects on an inherent incompatibility inside the domain of reciprocal fuzzy preference relations and preference stru...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/104908 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/104908 |
| Access Level: | acceso abierto |
| Palabra clave: | Fuzzy preference relations Reciprocal relations Preference structures Preference semantics Teoría de la decisión 1209.04 Teoría y Proceso de decisión |
| Sumario: | Fuzzy relations R : A² → [0, 1] are widely used in decision-making in order to represent degrees of preference between alternatives in A. Examining fuzzy relations, this paper first reflects on an inherent incompatibility inside the domain of reciprocal fuzzy preference relations and preference structures. Aiming at clarifying the semantics of reciprocal fuzzy relations by means of that of weak fuzzy relations, a general frame is then proposed for studying the transformation between them, based on the notion of reciprocal functions. Next, we show that reciprocal relations can be naturally endowed with a preference structure of their own, containing two relations respectively showing a semantics of strict preference and lack of preference. Finally, we study the compatibility between these reciprocal preference structures and the standard preference structures of weak fuzzy preference relations by means of an axiomatic approach, leading to a system of functional equations that is shown to admit different solutions, allowing to explicitly assign one of the available semantics for reciprocal preference relations. |
|---|