Aggregation Operators Review - Mathematical Properties and Behavioral Measures

Abstract

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, selfdistributivity, 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.

Some Construction Methods of Aggregation Operators in Decision Making Problems: An Overview

“…Using discussed constructing methods in previous sections as the underlying formula, we can provide some more new classes of aggregation operators based on the given technique in (18). For example, combining formulas given by (7) and 20, we can get a weighted version of Example 11 as below:…”

“…Xu and Da [4] fulfilled the first overview of the aggregation operators in 2003 by reviewing the existing main aggregation operators. Authors in [5][6][7] focused on properties and classification of aggregation functions. Furthermore, Grabisch et al [8] have made a review on averaging aggregation operators.…”

Some Construction Methods of Aggregation Operators in Decision-Making Problems: An Overview

“…Xu and Da [21] fulfilled the first overview of the aggregation operators in 2003 by reviewing the existing main aggregation operators. The authors of [22][23][24] focused on properties and classification of aggregation functions. Grabisch et al [25] made a review only on averaging aggregation operators.…”