Trapezoidal neutrosophic set and its application to multiple attribute decision-making

Based on the combination of trapezoidal fuzzy numbers and a single-valued neutrosophic set, this paper proposes a trapezoidal neutrosophic set, some operational rules, score and accuracy functions for trapezoidal neutrosophic numbers. Then, a trapezoidal neutrosophic number weighted arithmetic averaging (TNNWAA) operator and a trapezoidal neutrosophic number weighted geometric averaging (TNNWGA) operator are proposed to aggregate the trapezoidal neutrosophic information, and their properties are investigated. Furthermore, a multiple attribute decision-making method based on the TNNWAA and TNNWGA operators and the score and accuracy functions of a trapezoidal neutrosophic number is established to deal with the multiple attribute decision-making problems in which the evaluation values of alternatives on the attributes are represented by the form of trapezoidal neutrosophic numbers. Finally, an illustrative example about software selection is given to demonstrate the application and effectiveness of the developed method.