On Fuzziness in Algebraic System of Aggregates

Abstract

In this paper, we present fuzzy data processing based on the Algebraic System of Aggregates (ASA) which operates with complex data structures called aggregates. An aggregate is a tuple of arbitrary tuples whose elements can be both crisp and fuzzy values. There are three categories of operations on aggregates in ASA: logical operations, ordering operations, and arithmetical operations. In this paper, we define the fuzzy case of ordering and logical operations. ASA has a practical value for data processing in various tasks where an object (process, phenomenon) of study needs to be defined through multiple measurable characteristics of its behavior changing in the course of time. In some cases, such characteristics cannot measured but only estimated with certain accuracy and thus, they are represented as fuzzy values. Application of ASA for processing of imprecise biomedical data is discussed in the paper as well.