Abstract
Aggregating data is the main line of any discipline dealing with fusion of information from the knowledge-based systems to decision-making. The purpose of aggregation methods is to convert a list of objects, all belonging to a given set, into a single representative object of the same set usually by an n-ary function, so-called aggregation operator. As the useful aggregation functions for modeling real-life problems are limited, the basic problem is to construct a proper aggregation operator, usually a symmetric one, for each situation. During the last decades, a number of construction methods for aggregation functions have been developed to build new classes based on the existing well-known operators. There are three main construction methods in common use: transformation, composition, and convex combination. This paper compares these methods with respect to the type of aggregating problems that can be handled by each of them.
Highlights
The importance of aggregating in fusion of information, specially in decision-making problems, is, to get an overview of data for taking the final action
This paper aims to provide an overview of three key construction methods of aggregation functions, namely, transformation, composition, and convex combination, to compare them with respect to type of aggregating problems that can be handled by each of them
This study presents an overview of three constructing methods to aggregation functions, namely, transformation, composition, and convex combination, and their applications in group decision-making problems
Summary
The importance of aggregating in fusion of information, specially in decision-making problems, is, to get an overview of data for taking the final action. The non-decreasing function A : n∈N [0, 1]n → [0, 1] is usually considered as the standard definition of aggregation functions where the non-decreasing property of A shows increasing values of inputs increases the aggregated value. Group decision-making problems that refer to as multi-person or multi-observer decision situations, are one of the main application fields of aggregation functions theory. Such problems usually contain two key phases known as consensus and selection According to the final goal in different decision situations, over the past decades a number of methods have been applied to reach consensus in group decision-making problems.
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