A commentary on “An improved score function for ranking
neutrosophic sets and its application to decision-making process”
Akanksha Singha112Corresponding
author & Current Address:
Lecturer, School of Sciences, Baddi University of Emerging Sciences
and Technologies,
Makhnumajra, Baddi district, Solan
Baddi, Himachal Pradesh, IN 173205
Email id: akanksha.singh@baddiuniv.ac.in
ORCID ID: 0000-0003-2189-4974
Phone no.: +91-98884146112, Shahid Ahmad
Bhata3
aSchool of Mathematics,
Thapar Institute of Engineering & Technology (Deemed to be University)
P.O. Box 32, Patiala, Pin -147004, Punjab, India
asingh3_phd16@thapar.edu1,
bhatshahid444@gmail.com3
Abstract: This work aims to study and observe all the existing score
functions that help to rank the single-valued neutrosophic set (SVNS) as
well as interval-valued neutrosophic set (IVNS) to make a better choice
among all the available alternatives in multi-criteria decision-making
(MCDM) problems. An intensive study about all these existing score
functions reveals that there holds some limitations in the method of
ranking order which is misleading the results in decision-making
problems. These observations about the existing score functions of the
SVNS and IVNS have been claimed with the help of well-defined examples,
illustrating an inefficiency of all these existing score functions.
Thus, to propose a valid score function for ranking SVNS and IVNS for
making a better selection among all the other available alternatives in
MCDM problems is still an open challenging research problem.
KEYWORDS - IVNS, MCDM, score function, SVNS
1. INTRODUCTION
In the real-life uncertainty is the only thing which is certain in life,
so the information available in the real-world cannot be crisp always.
This theory was incorporated by a deep thinker Zadeh who proposed a new
theory of sets i.e., fuzzy sets [27] which brought a huge revolution
in the area of new thinking world and mathematics. Fuzzy sets holds the
idea that in practical life the information available is not always
certain or crisp but beholds the hand of uncertainty together and the
study of this uncertainty would help a lot in the process of decision
making [28,29]. Later with the time some intriguing extensions of
fuzzy sets were developed like- intuitionistic fuzzy set (IFS) [2],
interval-valued intuitionistic fuzzy set (IVIFS) [3], Pythagorean
fuzzy set (PFS) [24-26], interval-valued Pythagorean fuzzy set
(IVPFS) [32], neutrosophic set [18-20], SVNS [23] and IVNS
[22] etc. In this note, a deep study have been made to analyze the
ranking order of some of the extensions of fuzzy sets like, IFS
[8,9,30], PFS [32], IVPFS [4-7,11,12,16,17,31], SVNS
[1,10,13-15,21] and IVNS [10,13]. After a rigorous study it has
been observed that there exist some restrictions in the existing methods
[10,13] for comparing SVNS and IVNS. Some well-defined
counter-examples are chosen where the uncertainty in the data is
expressed in the form of SVNS and IVNS to claim that the existing score
function defined to rank the SVNS and IVNS results incorrectly. The aim
of this note is to make researchers aware that, the shortcomings pointed
out by Nancy and Garg [10] in the existing methods [13] is also
occurring in the methods proposed by Nancy and Garg [10]. Therefore,
to propose the valid methods for the same is still an open challenging
research problem.