An Innovative Hybrid Multi-Criteria Decision-Making Approach under Picture Fuzzy Information

Ghous Ali, Muhammad Zain Ul Abidin, Qin Xin, Ferdous M. O. Tawfiq

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These days, multi-criteria decision-making (MCDM) approaches play a vital role in making
decisions considering multiple criteria. Among these approaches, the picture fuzzy soft set model is
emerging as a powerful mathematical tool for handling various kinds of uncertainties in complex reallife MCDM situations because it is a combination of two efficient mathematical tools, namely, picture
fuzzy sets and soft sets. However, the picture fuzzy soft set model is deficient; that is, it fails to tackle
information symmetrically in a bipolar soft environment. To overcome this difficulty, in this paper,
a model named picture fuzzy bipolar soft sets (PRFBSSs, for short) is proposed, which is a natural
hybridization of two models, namely, picture fuzzy sets and bipolar soft sets. An example discussing
the selection of students for a scholarship is added to illustrate the initiated model. Some novel
properties of PRFBSSs such as sub-set, super-set, equality, complement, relative null and absolute
PRFBSSs, extended intersection and union, and restricted intersection and union are investigated.
Moreover, two fundamental operations of PRFBSSs, namely, the AND and OR operations, are studied.
Thereafter, some new results (De Morgan’s law, commutativity, associativity, and distributivity)
related to these proposed notions are investigated and explained through corresponding numerical
examples. An algorithm is developed to deal with uncertain information in the PRFBSS environment.
To show the efficacy and applicability of the initiated technique, a descriptive numerical example
regarding the selection of the best graphic designer is explored under PRFBSSs. In the end, concerning
both qualitative and quantitative perspectives a detailed comparative analysis of the initiated model with certain existing models is provided.
Original languageEnglish
Article number2434
Number of pages27
Issue number14
Publication statusPublished - 17 Nov 2022


  • picture fuzzy soft set
  • bipolarity
  • score function
  • Algorithm
  • multi-criteria decision-making


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