Logic Operators and Sibling Aggregators for Z-grades

Abstract

Trust in data is a crucial aspect of criterion-based flexible query answering and decision making. Inspired by Zadeh’s concept Z-number, we introduce the concept of a Z-grade and focus on some elementary aspects of aggregating Z-grades. A Z-grade, z, has two components, z= (s, c). The first component, s, is a satisfaction grade that can for example be used to express to what extent a given data element satisfies a given criterion. The second component, c, is a confidence grade that expresses how confident we can be about s. For example, in case we have less trust in the data element, this could result in a lower confidence in the outcome s of the criterion evaluation. Logical processing and aggregation of satisfaction grades are important aspects of criterion handling. When applied to Z-grades, the computation of the resulting confidence grade depends on the computation of the resulting satisfaction grade. For that purpose, novel logic operators and so-called sibling aggregators for Z-grades are proposed and studied in the paper.