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.