Ranking of Downstream Fish Passage Designs for a Hydroelectric Project under Spherical Fuzzy Bipolar Soft Framework

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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
16 Downloads (Pure)


Nowadays, several real-world decision-making problems concerning falling economies,
power crises, depleting resources, etc., require efficient decision-making. To solve such problems,
researchers proposed several hybrid models by combining the spherical fuzzy sets with other theories,
such as spherical fuzzy soft sets, which is an efficient tool to deal with the uncertainties concerning
positive, neutral, and negative memberships in the soft environment. However, all the existing
hybridizations of spherical fuzzy sets fail to deal with information symmetrically in a bipolar soft
environment. Accordingly, this paper presents a novel hybrid model called spherical fuzzy bipolar
soft sets (SFBSSs) by fusing spherical fuzzy sets and bipolar soft sets, considering the opposite sets of
parameters in symmetry. An example considering the selection of a chief management officer (CMO)
for a multi-national company illustrates the proposed model in detail. In addition, some symmetric
properties and algebraic operations of the initiated model, including subset, complement, relative null
SFBSSs, relative absolute SFBSSs, extended union, extended intersection, restricted union, restricted
intersection, AND, and OR operations, are discussed and illustrated via numerical examples. Further,
some fundamental results, namely, commutativity, associativity, distribution, and De Morgan’s laws
are presented for SFBSSs. Moreover, by considering the massive impact of hydropower in combating
the energy crisis and possible dangers to fish migration, a multi-attribute decision-making problem
concerning the ranking of downstream fish passage designs for a hydroelectric project is modeled and
solved under the developed algorithm based on SFBSSs. Finally, a comparative analysis discusses the
supremacy of the initiated model over its building blocks
Original languageEnglish
Article number2141
Number of pages30
Issue number14
Publication statusPublished - 13 Oct 2022


  • bipolar soft sets
  • spherical fuzzy sets
  • spherical fuzzy bipolar soft sets
  • hydropower
  • algorithm
  • decision-making


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