Decision support modeling for multiple criteria assessments using a likelihood-based consensus ranking method under Pythagorean fuzzy uncertainty

Ting Yu Chen*

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

9 Scopus citations


This paper intends to exploit point operator-oriented likelihood measures to constitute a likelihood-based consensus ranking model aimed at conducting multiple criteria decision making encompassing complex uncertain evaluations with Pythagorean fuzzy sets. This paper takes advantage of Pythagorean fuzzy point operators and the scalar functions of upper and lower estimations to formulate a point operator-oriented likelihood measure for preference intensity. On this basis, this paper propounds the notion of penalty weights to characterize dominated relations for acquiring the measurement of comprehensive disagreement and constituting a likelihood-based consensus ranking model. The primary contributions of this study are fourfold. Firstly, two useful point operators are initiated for upper and lower estimations towards Pythagorean membership grades. Secondly, an effective likelihood measure is exploited for determining outranking relations of Pythagorean fuzzy information. Thirdly, a pragmatic concept of penalty weights is proposed for characterizing the dominated relations among alternatives and measuring degrees of comprehensive disagreement. Fourthly, a functional likelihood-based consensus ranking model is constructed for implementing a multiple criteria evaluation with Pythagorean fuzzy uncertainty. Furthermore, a real-life application relating to a financing problem is presented to provide a justification for the practicability of the proposed methodology. This paper executes an analysis of parameters sensitivity and comparative studies for showing more theoretical insights.

Original languageEnglish
Pages (from-to)4879-4939
Number of pages61
JournalArtificial Intelligence Review
Issue number6
StatePublished - 08 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature B.V.


  • Consensus ranking model
  • Measurement of comprehensive disagreement
  • Multiple criteria decision making
  • Point operator-oriented likelihood measure
  • Pythagorean fuzzy set


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