Non-linear Neutrosophic Numbers and Its Application to Multiple Criteria Performance Assessment

Abstract

The concept of fuzzy set has been extended by neutrosophic fuzzy sets to represent sets whose elements have different degrees of membership characterized by a truth-membership function, an indeterminacy-membership function and a falsity-membership function. It is usually assumed that these functions are linear, hence excluding the possibility of non-linearity in many decision-making situations. From an alternative definition of non-linear neutrosophic numbers, we develop the concepts of (alpha ,beta ,gamma )-cuts, possibility mean, variance, skewness and a new possibility score function. These concepts are useful to deal with multiple criteria decision making problems. We illustrate the practical use of these concepts by means of a real case study in supply chain risk management in the motor industry. Due to the fact that neutrosophic sets have been used in several areas of decision-making, finance and economics, we argue that our proposal contributes to enhance the application of neutrosophic numbers.