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

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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 (α, β, γ) -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.

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APA

Reig-Mullor, J., & Salas-Molina, F. (2022). Non-linear Neutrosophic Numbers and Its Application to Multiple Criteria Performance Assessment. International Journal of Fuzzy Systems. https://doi.org/10.1007/s40815-022-01295-y

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