Average distances are widely used in many fields for calculating the distances between two sets of elements. This paper presents several new average distances by using the ordered weighted average, the probability and the weighted average. First, the work presents the probabilistic ordered weighted averaging weighted average distance (POWAWAD) operator. POWAWAD is a new aggregation operator that uses distance measures in a unified framework between the probability, the weighted average and the ordered weighted average (OWA) operator that considers the degree of importance that each concept has in the aggregation. The POWAWAD operator includes a wide range of particular cases including the maximum distance, the minimum distance, the normalized Hamming distance, the weighted Hamming distance and the ordered weighted average distance (OWAD). The article also presents further generalizations by using generalized and quasi-arithmetic means forming the generalized probabilistic ordered weighted averaging weighted average distance (GPOWAWAD) operator and the quasi-POWAWAD operator. The study ends analysing the applicability of this new approach in the calculation of the average fixed assets. Particularly, the work focuses on measuring the average distances between the ideal percentage of fixed assets that the companies of a specific country should have versus the real percentage of fixed assets they have. The illustrative example focuses on the Asian market.
Distance measures Aggregation operators OWA operator Average fixed asset Group decision-making
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We would like to thank the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the Distinguished Scientist Fellowship Programme from King Saud University (Saudi Arabia) and the Chilean Government through the Fondecyt Regular Programme (Project Number 1160286) is gratefully acknowledged.
Compliance with ethical standards
This article does not contain any studies with human participants performed by any of the authors.
Conflict of interest
The authors declare that they have no conflict of interests.
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