From quantitative to qualitative orness for lattice OWA operators

Abstract

This paper deals with OWA (ordered weighted average) operators defined on an arbitrary finite lattice endowed with a t-norm and a t-conorm. A qualitative orness measure for any OWA operator is suggested, based on its proximity to the OR operator that yields the maximum of the given data. In the particular case of a finite distributive lattice, considering the t-norm given by the meet and the t-conorm given by the join, this qualitative measure agrees with the value that some discrete Sugeno integral takes on the vector consisting of all the members of the lattice. Some applications of the qualitative orness of OWA operators to decision-making problems are shown. In addition, OWA operators defined on a finite product lattice are also applied in image processing. We analyze the effect of several OWA operators with respect to their orness.

Keywords:

• Qualitative aggregation
• OWA operator
• lattice
• orness
• decision making
• image processing

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been partially by MINECO, AEI/FEDER, UE under project TIN2016-77356-P.