Novel Distance Measures for Single-Valued Neutrosophic Fuzzy Sets and Their Applications to Multicriteria Group Decision-Making Problem

Abstract

Single-valued neutrosophic sets are a hybrid of fuzzy sets that are used to represent uncertain, imprecise, partial, and inconsistent information in the actual world. The focus of this research is to develop two novel distance measures for single-valued neutrosophic fuzzy sets (SVNFSs). We introduced two new distance measures named <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:msub><a:mrow><a:mi>d</a:mi></a:mrow><a:mrow><a:mi>η</a:mi></a:mrow></a:msub><a:mfenced open="(" close=")"><a:mrow><a:mi>G</a:mi><a:mo>,</a:mo><a:mi>Y</a:mi></a:mrow></a:mfenced></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M2"><e:msub><e:mrow><e:mi>d</e:mi></e:mrow><e:mrow><e:mi>ζ</e:mi></e:mrow></e:msub><e:mfenced open="(" close=")"><e:mrow><e:mi>G</e:mi><e:mo>,</e:mo><e:mi>Y</e:mi></e:mrow></e:mfenced></e:math> for SVNFSs and apply these measures to different examples and also compare them with existing measures to show the validity of our proposed measures. Our results are reliable and useful for decision-making problems. We also proposed an algorithm for multicriteria group decision-making. Based on this algorithm, we find the ranking matrices using proposed distance measures. We also give an example to demonstrate the notion and concept of our algorithm.