Some Novel Geometric Aggregation Operators of Spherical Cubic Fuzzy Information with Application

Zafar Ullah,Rukhshanda Anjum,Huma Bashir,Suheer Al-Hadhrami,Abdul Ghaffar,Mabrook Al-Rakhami,Kifayat Ullah

doi:10.1155/2021/3774353

Abstract

Technology is quickly evolving and becoming part of our lives. Life has become better and easier due to the technologies. Although it has lots of benefits, it also brings serious risks and threats, known as cyberattacks, which are neutralized by cybersecurities. Since spherical fuzzy sets (SFSs) and interval-valued SFS (IVSFS) are an excellent tool in coping with uncertainty and fuzziness, the current study discusses the idea of spherical cubic FSs (SCFSs). These sets are characterized by three mappings known as membership degree, neutral degree, and nonmembership degree. Each of these degrees is spherical cubic fuzzy numbers (SCFNs) such that the summation of their squares does not exceed one. The score function and accuracy function are presented for the comparison of SCFNs. Moreover, the spherical cubic fuzzy weighted geometric (SCFWG) operators and SCF ordered weighted geometric (SCFOWG) operators are established for determining the distance between two SCFNs. Furthermore, some operational rules of the proposed operators are analyzed and multiattribute decision-making (MADM) approach based on these operators is presented. These methods are applied to make the best decision on the basis of risks factors as a numerical illustration. Additionally, the comparison of the proposed method with the existing methods is carried out; since the proposed methods and operators are the generalizations of existing methods, they provide more general, exact, and accurate results. Finally, for the legitimacy, practicality, and usefulness of the decision-making processes, a detailed illustration is given.

Highlights

Multiple-attribute decision-making (MADM) means that, from the restricted alternatives set according to multiple attribute, the best alternative is selected that could be called cognitive processing
MADM is a key subdivision of the theory of decision-making (DM), commonly used in human activities [1]. e fuzzy knowledge usually is of two forms: qualitative and quantitative. e quantitative fuzzy knowledge is determined by fuzzy set (FS) [2], intuitionistic FS (IFS) [3], Pythagorean FS (PyFS) [4], and so forth
If the membership, representing the support of an Security and Communication Networks expert, is 0.8 and nonmembership representing the opposition, is 0.6, surely, this information cannot be represented by IFS, but it can be effectively described by PyFS

Summary

Introduction

Multiple-attribute decision-making (MADM) means that, from the restricted alternatives set according to multiple attribute, the best alternative is selected that could be called cognitive processing. (􏽢ţ), μ􏽥UA􏽥􏽥Q2 (􏽢ţ)], [η􏽥LA􏽥􏽥Q2 (􏽢ţ), η􏽥UA􏽥􏽥Q2 (􏽢ţ)], [θ􏽥LA􏽥􏽥Q2 (􏽢ţ), θ􏽥UA􏽥􏽥Q2 (􏽢ţ)]) be the set comprised of IVSFNs; IVSF weighted geometric (IVSFWG) operator is defined as follows:. Supposing Ţ􏽢 be a universal set, a spherical cubic FS (SCFS) Q􏽥 􏽥C is defined as follows: Q􏽥 C􏽥 􏼨􏼪􏽢ţ, ΓQ􏽥􏽥C(􏽢ţ), ΥQ􏽥􏽥C(􏽢ţ), ΛQ􏽥􏽥C(􏽢ţ)􏼫 ∣ 􏽢ţ ∈ Ţ􏽢 􏼩,. ⎧⎨ ⎩􏼪[a−Q􏽥􏽥C , a+Q􏽥􏽥C 􏼕, μ􏽥Q􏽥􏽥C􏼫, be SCFS; the score function of Q􏽥 C􏽥 is defined as follows: Score􏼐Q􏽥 􏽥C􏼑. N) be weighted geometric (SCFOWG) operator is a mapping SCFOWG: SCFNn ⟶ SCFN defined as follows: SCFOWG􏼒Q􏽥 􏽥C1, Q􏽥 C􏽥2, Q􏽥 C􏽥3, . Let i be a set comprised of SCFNs; SCF hybrid ordered weighted geometric (SCFHOWG) operator is a mapping SCFHOWG: SCFNn ⟶ SCFN defined as follows: SCFHOWG􏼒Q􏽥 C􏽥1, Q􏽥 C􏽥2, Q􏽥 C􏽥3, . Step 4: e best alternative is selected by the ranking of all the alternatives

Numerical Illustration

Conclusion