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Mathematics
Other literature type . 2022
License: CC BY
Full-Text: http://www.mdpi.com/2227-7390/10/7/1048/pdf
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Mathematics
Article . 2022 . Peer-reviewed
License: CC BY
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Mathematics
Article . 2022
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Bipolar Complex Fuzzy Soft Sets and Their Applications in Decision-Making

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 24 Mar 2022 English Publisher:MDPI AGJournal:Mathematics, volume 10, page 1,048 (eissn: 2227-7390, Copyright policy )
Authors: Tahir Mahmood; Ubaid Ur Rehman; Abdul Jaleel; Jabbar Ahmmad; Ronnason Chinram;

doi: 10.3390/math10071048

Bipolar Complex Fuzzy Soft Sets and Their Applications in Decision-Making

Abstract

This article introduces the notion of bipolar complex fuzzy soft set as a generalization of bipolar complex fuzzy set and soft set. Furthermore, this article contains elementary operations for bipolar complex fuzzy soft sets such as complement, union, intersection, extended intersection, and related properties. The OR and AND operations for bipolar complex fuzzy soft set are also initiated in this study. Moreover, this study contains the decision-making algorithm and real-life examples to display the success and usability of bipolar complex fuzzy soft sets. Finally, the comparative study of initiated notions with some prevailing ideas are also interpreted in this study.

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Keywords

bipolar complex fuzzy set, soft set; bipolar complex fuzzy set; bipolar complex fuzzy soft set; decision-making, QA1-939, soft set, bipolar complex fuzzy soft set, decision-making, Mathematics

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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 79
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Top 1%
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
79
Top 1%
Top 10%
Top 1%
gold