A novel score function and accuracy function for real-life multi-criteria decision-making problems under neutrosophic environment

Abstract

 The purpose of this work is to understand the ranking order of the neutrosophic sets,
where the uncertain or ambiguous information/data is stored in the terms of three independent variables i.e., degree of truthfulness, degree of indeterminacy, and degree of falseness. There exist many ranking tools in decision-making (DM) like score function (SF) and accuracy function (AF) that help to rank the single-valued neutrosophic set (SVNS) and the interval-valued neutrosophic set (IVNS) to make a better choice among all the available alternatives. An intensive study about all the existing score functions and an accuracy function reveals that the existing ranking method for SVNS and IVNS in DM problems holds for certain kinds of neutrosophic information and has its limitations. To validate these observations some well-defined examples are chosen, illustrating that the existing score functions and accuracy functions are like special cases for certain kinds of neutrosophic data. Since nothing in this world is an ultimate truth, hence this existing gap is a real motivation to come up with a more efficient SF and AF that would rank SVNS and IVNS in the real-life problems to make a better selection among all the available alternatives in DM problems in an efficient way. Hence, a new SF and AF have been proposed and multi-criteria decision-making
(MCDM) method is developed based on these proposed SF and AF. Furthermore, a real-life problem from our immediate surroundings is taken and solved successfully, and also a comparative analysis of the solutions for the existing problems is made in detail