On WA Expressions of Induced OWA Operators and Inducing Function Based Orness With Application in Evaluation

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Abstract
Induced OWA operators are important extensions of OWA operators and can suit more different decision environments. However, when practitioners perform Induced OWA operators, they frequently do not considered the tied values in inducing information, therein lay the problem of possible non-uniqueness of aggregation results. From a novel perspective that can easily remove this flaw, this study uses a systematical frame to better redefine Induced OWA operators, which not only covers all the spirits of original definition of Induced OWA operator but also extends it to some wider understandings and usages. One significant feature related to this frame is that we can express Induced OWA operators fully in terms of Weighted Averaging operators, making the usages and expressions of Induced OWA operators much more flexible and stricter. In detail, we propose several new definitions such as Positioning Transformation, permutation based orness and inducing function based orness. As an example of flexibly formulating complex preferences under the proposed concepts, a novel Investigators-Consultants-Decision maker (ICD) two-stage IOWA evaluation model is clearly proposed and illustrated.
Funding Information
  • Scientific Research Start-up Foundation (184080H202B165)
  • Science and Technology Assistance Agency (APVV-17-0066)
  • Czech IT4 Innovations Excellence in Sciences (LQ1602)
  • Natural Science Foundation of Jiangsu Province (BK20190695)

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