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N-valued neutrosophic trapezoidal numbers with similarity measures and application to multi-criteria decision-making problems

Abstract

N-valued neutrosophic trapezoidal numbers (NVNT-numbers) are a special neutrosophic multi-sets on real number set based on neutrosophic sets. In the NVNT-numbers the occurrences are more than one with the possibility of the same or the different truth-membership function, indeterminacy-membership function and falsity-membership functions. In this paper, NVNT-numbers based on multi-criteria decision-making problems in which the ratings of alternatives are expressed with NVNT-numbers are defined. Firstly, some operational laws of NVNT-numbers by using t-norm and t-conorm are introduced. Then, some aggregation operators of NVNT-numbers including NVNT-numbers weighted geometric operator and NVNT-numbers weighted arithmetic operators are given. Also, a TOPSIS method for the ranking order of alternatives with NVNT-numbers is given according to the similarity of alternative with respect to the positive and negative ideal solution. Moreover, an illustrative example of multi-criteria decision-making in which the ratings of alternatives are expressed with NVNT-numbers is given to verify the developed TOPSIS method and to demonstrate its practicality and effectiveness. Finally, a comparative analysis is presented with illustrative example.

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Correspondence to İrfan Deli.

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Deli, İ., Uluçay, V. & Polat, Y. N-valued neutrosophic trapezoidal numbers with similarity measures and application to multi-criteria decision-making problems. J Ambient Intell Human Comput (2021). https://doi.org/10.1007/s12652-021-03294-7

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Keywords

  • Neutrosophic sets
  • Neutrosophic trapezoidal numbers
  • N-valued neutrosophic trapezoidal numbers
  • Similarity measures
  • Aggregation operators
  • Multi-criteria decision-making