Multi-Attribute Decision-Making Method for the Assessment of Research Productivity Using Entropy Measures of Complex Fermatean Fuzzy Soft Sets

Ali Asghar; Khuram Ali Khan; Atiqe Ur Rahman

doi:10.26599/FIE.2024.9270048

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Article | Open Access

Multi-Attribute Decision-Making Method for the Assessment of Research Productivity Using Entropy Measures of Complex Fermatean Fuzzy Soft Sets

Ali Asghar^¹

, Khuram Ali Khan^¹

, Atiqe Ur Rahman^²

()

1Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

2Department of Mathematics, University of Management and Technology, Lahore 54000, Pakistan

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Abstract

The Fermatean fuzzy soft set (FFSS) is a natural extension of the intuitionistic fuzzy soft set (IFSS) and the Pythagorean fuzzy soft set (PyFSS). It retains the corresponding benefits of IFSS, PyFSS, and their extensions, including the ability to represent an entity from both favorable and adverse perspectives. It renders it feasible to mimic real-world situations where uncertainty is prevalent more precisely. It is possible to portray uncertain circumstances more effectively with the incorporated dimension of hesitation degree. The current study presents an innovative form of FFSS, known as complex Fermatean fuzzy soft set (cFRFSS), aiming at addressing the complexities related to data uncertainty and periodicity. The basic idea of cFRFSS, including set-theoretic operations and properties, is demonstrated numerically, and associated results are provided. To mitigate inconsistent information, modified entropy metrics for cFRFSS are put forward in the following section. Then, to assist university managers in assessing the research output of their faculty members within the institution, a robust method employing suggested cFRFSS-based entropy measures is offered. The suggested strategy’s adaptability is assessed by contrasting it with other strategies that have been previously put forth.

Keywords

Fermatean fuzzy soft set entropy measures research productivity optimization uncertainty

References

[1]

E. K. Zavadskas, Z. Turskis, and S. Kildienė, State of art surveys of overviews on mcdm/madm methods, Technol. Econ. Dev. Econ., vol. 20, no. 1, pp. 165–179, 2014.

Contributor	Theoretical model	Application
Liu et al.^[34]	FSS	No application section
Al-Qudah and Hassan^[35]	Complex multi-FSS	Evaluation of travel agencies
Kirisci^[36]	FFSS	Evaluation of cars and missile positions
Jiang et al.^[37]	IFSS	Evaluation of shirts
Athira et al.^[20]	PyFSS	Evaluation of apartments and pattern recognition
Selvachandran et al.^[38]	IFSS	Moderation of school-based assessment components of students
Han et al.^[39]	PyFSS	Evaluation of missile positions
Montes et al.^[40]	IFS	Evaluation of air-conditioning systems
Athira et al.^[41]	PyFSS	Evaluation of cars
Kumar and Bajaj^[42]	cPyFSS	Evaluation of cars

Criterion	Decision maker that suggests
Number of publications	${\overset{˘}{υ}}_{1}$ , ${\overset{˘}{υ}}_{2}$
Quality of publications	${\overset{˘}{υ}}_{2}$
Research grants secured as project leader	${\overset{˘}{υ}}_{1}$ , ${\overset{˘}{υ}}_{2}$ , ${\overset{˘}{υ}}_{3}$
Supervising postgraduate students	${\overset{˘}{υ}}_{1}$ , ${\overset{˘}{υ}}_{2}$ , ${\overset{˘}{υ}}_{4}$

Approach	Ranking
Proposed approach	${\ddot{Υ}}_{2} > {\ddot{Υ}}_{3} > {\ddot{Υ}}_{1}$
Entropy measures in Ref. [42]	${\ddot{Υ}}_{2} > {\ddot{Υ}}_{3} > {\ddot{Υ}}_{1}$
CFNWA operator	${\ddot{Υ}}_{2} > {\ddot{Υ}}_{3} > {\ddot{Υ}}_{1}$
CFNOWA operator	${\ddot{Υ}}_{2} > {\ddot{Υ}}_{1} > {\ddot{Υ}}_{3}$
CFNWG operator	${\ddot{Υ}}_{2} > {\ddot{Υ}}_{3} > {\ddot{Υ}}_{1}$
CFNOWG operator	${\ddot{Υ}}_{2} > {\ddot{Υ}}_{1} > {\ddot{Υ}}_{3}$