A Generalized Family of Constant Orness Ordered Weighted Averaging Operators

In this article, we propose a novel beta binomial OWA operator (BBN-OWAO) based on the beta binomial distribution. The proposed biparametric operator can generate an unlimited number of weight vectors, irrespective of the total number of arguments to be aggregated, for a given level of optimism/pess...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2024-07, Vol.32 (7), p.4062-4073
Main Authors: Srivastava, Vikas, Singh, Amit K., Kishor, Amar, Pal, Nikhil R.
Format: Article
Language:English
Subjects:
Beta-binomial distribution
Binomial distribution
Dispersion
Entropy
Entropy (Information theory)
Fuzzy systems
Maximum entropy
Open wireless architecture
orness
OWA operator (OWAO)
player selection
Weight measurement
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Summary:In this article, we propose a novel beta binomial OWA operator (BBN-OWAO) based on the beta binomial distribution. The proposed biparametric operator can generate an unlimited number of weight vectors, irrespective of the total number of arguments to be aggregated, for a given level of optimism/pessimism (orness/andness). Our main objective is to develop a generalized family of constant-orness OWAO that encompasses nearly all constant-orness members. It generalizes well-known Broda-Kendall, Hurwicz, Binomial, Stancu, InHyp OWAOs, and many more. The BBN-OWAO allows decision makers to customize its parameters in accordance with their preferences. As a result, the BBN-OWAO enables decision makers to model a wide range of situations with greater flexibility. This study explores some additional interesting properties of the proposed operator, highlighting its capability to produce two consecutive identical weights. We also compute and demonstrate that the maximum entropy (Shannon) of the BBN-OWAO aligns very closely with the existing analytical results. Finally, we provide an example illustrating its practical application, demonstrated through a case study on player selection for a cricket team.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2024.3389977