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Algebraic and Einstein weighted operators of neutrosophic enthalpy values for multi-criteria decision making in neutrosophic multi-valued set settings


In fuzzy set theory, the aggregation is the process that combines input fuzzy sets into a single output fuzzy set. In this manner, an aggregation operator is an important tool in the fuzzy set theory and its applications. The purpose of this study is to present some algebraic operators among neutrosophic enthalpy values and to provide some aggregation operators with the help of general t-norms and t-conorms which produce a new theoretical base in the fuzzy environment. An enthalpy value is the information energy expressed by the complement of the Shannon’s entropy and a neutrosophic enthalpy set is characterized with a truth, an indeterminacy and a falsity function defined on a universal set to \([0,1]^{2}\). The first component of each function is the average of the truth, the indeterminacy and the falsity sequence of a neutrosophic multi-valued set, respectively, and the second component of each function is the fuzzy complement of the normalized Shannon’s entropy of the truth, the indeterminacy and the falsity of the same neutrosophic multi-valued set, respectively. Therefore, a neutrosophic enthalpy set contains both the level of the mean of the data and the degree of uncertainty of the data via enthalpy. Then, by using Algebraic and Einstein t-norms and t-conorms we give a multi-criteria decision making method based on these aggregation operators and a score function. This method is applied to a multi-criteria decision making problem with neutrosophic enthalpy set information and the comparison analysis is given with the existing methods to show the efficiency and sensitivity of the proposed method.

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The authors are grateful to the Referees for carefully reading the manuscript and for offering substantial comments and suggestions which enabled them to improve the paper.

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Correspondence to Jun Ye.

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Ye, J., Türkarslan, E., Ünver, M. et al. Algebraic and Einstein weighted operators of neutrosophic enthalpy values for multi-criteria decision making in neutrosophic multi-valued set settings. Granul. Comput. 7, 479–487 (2022).

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  • Neutrosophic enthalpy set
  • Shannon’s entropy
  • Aggregation operator
  • Multi-criteria decision making