Aggregation functions on bounded lattices. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Karaçal, Funda; Mesiar, Radko
• Is Part Of: International journal of general systems. Volume 46:Issue 1(2017)
• Page Start: 37
• Page End: 51
• Publication Date: 2017-01-02
• Subjects: Aggregation -- bounded lattice -- lattice polynomial; System theory -- Periodicals; 003
• DOI: 10.1080/03081079.2017.1291634
• Languages: English
• ISSNs: 0308-1079

Abstract

Abstract : In this paper, we show that the setA n ( 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 thatn ≠ 0, we obtain thatL m form ∈ [ n ] can be embedded into the latticeA n ( 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.