Research Article
A Multiattribute Decision-Making Framework: VIKOR
Method with Complex Spherical Fuzzy N-Soft Sets
Muhammad Akram ,
1
Maria Shabir,
1
Arooj Adeel ,
2
and Ahmad N. Al-Kenani
3
1
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
2
Department of Mathematics, University of Education, Bank Road Campus, Lahore, Pakistan
3
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia
Correspondence should be addressed to Muhammad Akram; m.akram@pucit.edu.pk
Received 3 July 2021; Revised 4 August 2021; Accepted 12 August 2021; Published 31 August 2021
Academic Editor: Naeem Jan
Copyright © 2021 Muhammad Akram et al. is is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
In this paper, we set forth a framework for solving a multiattribute group decision-making (MAGDM) problem, namely, the
selection of a firm for participation in a Saudi oil refinery project in Pakistan. is project will prove a key success factor for the
economic growth of Pakistan due to its enormous economic impact on the energy sector, industrial development, commerce,
transportation, and so on. is multiplicity justifies that several intricate components comprising both intrinsic and external
attributes should be adequately evaluated for the selection of such a firm, that is, the formulation of this question as a MAGDM
problem. Nonbinary evaluation with two-dimensional ambiguity and uncertainty in the parameters are general concerns in
modern literature, and they fit into this problem. Within this context, one of the most superior and amenable theories (complex
spherical fuzzy N-soft sets, henceforth CSFNS
f
Ss) shall be used to formulate a new comprehensive method, known as complex
spherical fuzzy N-soft-VIKOR (CSFNS
f
-VIKOR) method. According to the general spirit of the benchmark technique, the
normalized Euclidean distances and the weights of the attributes are jointly handled, and as consequence, two main features
(“maximum group utility” and “minimum individual regret”) are acquired. e coefficient strategy with reference to group utility
measure and individual regret measure of opponents are employed for the compromise measure. Armed with this novel tool, we
single out the most feasible firm according to the preference order of the alternatives examined by the decision-makers on the
subject of linear normalized weights of experts and attributes. Furthermore, a comparative analysis justifies the CSF-VIKOR
method, and some results prove its capabilities and validity. Moreover, a sensitivity test certifies the stability of the
proposed method.
1. Introduction
In 1998, the VIKOR approach was drafted by Opricovic [1]
as a multiattribute decision-making (MADM) method. In
the setting of civil engineering, this system attempted to find
a compromise solution based on two dominant principles
(group utility measure and individual regret of opponent),
where the compromise solution means a decision done by
generic involvement. Due to the paradigm of maximum
group utility and minimum individual regret, the feasible
solution closest to the best values and most distant from the
worst value is resolved by the recourse to the L
p
-metric as an
aggregation function, according to Opricovic. Opricovic and
Tzeng [2] extended the VIKOR theory for MADM for the
postearthquake reconstruction problem in Central Taiwan
and the selection of destination for the mountain climber,
respectively. Yazdani-Chamzini et al. [3] employed the
modified version of the VIKOR method along with the
combination of TOPSIS, MOORA, additive weighting, and
ratio assessment techniques in order to address a multi-
criteria decision-making (MCDM) problem relating to re-
newable energy resources.
People habitually live with real-life properties that are
not sufficiently precise and not fully objective, such as
“beautiful,” “tall,” or “experienced.” Many decision-related
problems must take into account such properties. To
Hindawi
Mathematical Problems in Engineering
Volume 2021, Article ID 1490807, 25 pages
https://doi.org/10.1155/2021/1490807