Selective majority additive ordered weighting averaging operator

Abstract

Usually, in order to summarize various opinions about a particular situation (mainly product or service valuation on Internet) a process called aggregation is used. This process basically consists of determining the appropriate value to represent the majority's opinion and many strategies and operators can be used for this purpose. Simple arithmetic mean is widely used to resume several opinions in a single value, but this value is generally not representative or it is affected by the extreme values. An alternative to aggregate opinions are the Ordered Weighting Averaging (OWA) operators. Nevertheless, they have distribution problems when applied to aggregates with cardinalities. These problems may be solved by using Majority Additive OWA (MA-OWA) operator, a sort of arithmetic mean of arithmetic means. MA-OWA operator works adequately but, in some cases, discards the minority's opinion, specifically when it does not coincide with the largest cardinality value. In order to generalize the usage of MA-OWA operator, the rest of opinions are taken into account using a Cardinality Relevance Factor. This paper introduces a Selective Majority Additive OWA (SMA-OWA) which manages the significance of all opinions varying the Cardinality Relevance Factor. Mathematical extension of SMA-OWA, its properties and some illustrative examples are presented in this article.