Aggregation functions on bounded lattices


KARAÇAL F. , Mesiar R.

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol.46, no.1, pp.37-51, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 1
  • Publication Date: 2017
  • Doi Number: 10.1080/03081079.2017.1291634
  • Title of Journal : INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
  • Page Numbers: pp.37-51

Abstract

In this paper, we show that the set An(L) of all n-ary aggregation functions on a complete lattice L is a complete lattice and we study some properties of this lattice. If L is a bounded lattice and n is a natural number such that n not equal 0, we obtain that Lm for m is an element of[n] can be embedded into the lattice An(L). We generate aggregation functions from monotone functions. We introduce the concept of internal product of aggregation functions. We give some examples of aggregation functions on bounded lattices.