Aggregation Operators on Bounded Partially Ordered Sets, Aggregative Spaces and Their Duality

Demirci M.

15th International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Montpellier, France, 15 - 19 July 2014, vol.442, pp.457-465 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 442
  • Doi Number: 10.1007/978-3-319-08795-5_47
  • City: Montpellier
  • Country: France
  • Page Numbers: pp.457-465
  • Keywords: Aggregation operator, Aggregative space, Q-space, Generalized topological space, Category theory, Adjoint situation, Duality, Spatiality, Sobriety, TRIANGULAR NORMS, LATTICES
  • Akdeniz University Affiliated: Yes

Abstract

The present paper introduces aggregative spaces and their category AGS, and then establishes a dual adjunction between AGS and the category Agop of aggregation operators on bounded partially ordered sets. Spatial aggregation operators and sober aggregative spaces, enabling us to restrict the dual adjunction between AGS and Agop to a dual equivalence between the full subcategory of Agop consisting of spatial aggregation operators and the full subcategory of AGS consisting of sober aggregative spaces, will also be subjects of this paper.