Aggregation Operators Review - Mathematical Properties and Behavioral Measures

Abstract

A problem that humans must face very often is that of having to add, melt or synthesize information, that is, combine together a series of data from various sources to reach a certain conclusion or make a certain decision. This involves the use of one or more aggregation operators capable to provide a collective preference relation. These operators must be chosen according to specific criteria taking into account the characteristic properties of each operator. Some conditions to be taken into account to identify them are the following: axiomatic strength, empirical setting, adaptability, numerical efficiency, compensation and compensation range, added behavior and scale level required of the membership functions. It is possible to establish a general list of possible mathematical properties whose verification might be desirable in certain cases: boundary conditions, continuity, not decreasing monotony, symmetry, idempotence, associativity, bisymmetry, self-distributivity, compensation, homogeneity, translativity, stability, φ-comparability, sensitivity and locally internal functions. For analyze the attitudinal character of the aggregation operator the following measures are studied: disjunction degree (orness), dispersion, balance and divergence. In this paper, a review of these issues is presented.Index Terms—Aggregation, aggregation operators, behavioral measures of aggregation operators, intersection operators, OWA operators.