Nanotechnology Prioritization Through Complex Fermatean Neutrosophic Super-Hypersoft Structures

Dua Sajid; Anns Uzair; Aiman Ishtiaq; Rashid Jan; Muhammad Talha Azhar; Qamar Noureen

doi:10.67334/cds31202646

Authors

Dua Sajid Department of Chemistry, Government Graduate College Attock, University of Punjab, Attock 43600, Punjab, Pakistan Author https://orcid.org/0009-0003-5485-8934
Anns Uzair Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Punjab, Pakistan Author https://orcid.org/0009-0007-3703-0384
Aiman Ishtiaq Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Punjab, Pakistan Author https://orcid.org/0009-0005-1538-2907
Rashid Jan Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia Author https://orcid.org/0000-0001-9709-7045
Muhammad Talha Azhar Department of Economics, Thal University, Bhakkar 30000, Punjab, Pakistan Author https://orcid.org/0009-0000-0890-2787
Qamar Noureen Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan Author https://orcid.org/0009-0001-9772-3066

DOI:

https://doi.org/10.67334/cds31202646

Keywords:

Decision Making, Complex Fermatean Neutrosophic Hypersoft Theory, Nano-technology, Super-HyperSoft Sets, Fuzzy Algebra

Abstract

Selecting appropriate nanoparticle formulations for specific applications is a challenging decision-making problem due to uncertainty and the presence of multiple conflicting criteria. Green-synthesized silver nanoparticles (AgNPs) have attracted considerable attention because of their potential applications in various fields, including agriculture and healthcare. However, identifying the most suitable AgNP formulation requires a systematic evaluation of several criteria and their associated subcriteria. To address this problem, this study introduces complex Fermatean neutrosophic hypersoft sets and complex Fermatean neutrosophic super-hypersoft sets as mathematical frameworks for representing uncertainty in decision-making problems. The fundamental algebraic operations of the proposed structures, including equality, subset relations, union, and intersection, are defined and discussed. Based on these operations, a decision-making application is presented to evaluate green-synthesized silver nanoparticle formulations under uncertain conditions. Numerical examples are provided to illustrate the application of the proposed framework and demonstrate its ability to represent complex and ambiguous evaluation information. The proposed approach offers a mathematical framework for addressing uncertainty and conflicting evaluation criteria, thereby supporting the selection of suitable nanoparticle formulations for different applications.

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References

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