Abstract
This paper investigates some Frank aggregation operators of interval-valued neutrosophic numbers (IVNNs) and applies to multi-attribute group decision-making (MAGDM) problems. First, the Frank t-conorm and t-norm are extended to interval-valued neutrosophic environment. Some new operational laws for IVNNs are defined and their related properties are investigated. Based on these new operational laws, some new aggregation operators for IVNNs are developed including the interval-valued neutrosophic Frank weighted averaging (IVNFWA) operator and the interval-valued neutrosophic Frank weighted geometric (IVNFWG) operator. Then some desirable properties and special cases of these new operators are further discussed. To solve the MAGDM with IVNNs, the weights of decision makers (DMs) are determined by using extended technique for order preference by similarity to ideal solution (TOPSIS) method based on cross-entropy. Additionally, attribute weights are determined based on the similarity degrees between alternatives and the absolute ideal solutions. Further, two new decision-making approaches for MAGDM with IVNNs are put forward by means of the IVNFWA and IVNFWG operators, respectively. Finally, a case study of selecting an agricultural socialization service provider is analyzed to illustrate the practicality and effectiveness of the developed two approaches.
Highlights
Multi-attribute decision-making (MADM) and multiattribute group decision-making (MAGDM) have been extensively used in real-life decision-making problems
For MAGDM with interval-valued neutrosophic numbers (IVNNs), the weights of decision makers (DMs) are determined by using extended TOPSIS method based on cross-entropy
Thereby, two new decision-making approaches for MAGDM with IVNNs are proposed by the interval-valued neutrosophic Frank weighted averaging (IVNFWA) and interval-valued neutrosophic Frank weighted geometric (IVNFWG) operators, respectively
Summary
Multi-attribute decision-making (MADM) and multiattribute group decision-making (MAGDM) have been extensively used in real-life decision-making problems. Numerous research results on MADM and MAGDM with IVN information have been reported These results can be roughly divided into two categories: aggregation operators and decision-making methods. There is not yet an operator which can provide desirable generality and flexibility in aggregation of criterion values This reality motivates us to extend the Frank t-conorm and t-norm to IVN environment due to the fact that Frank t-norm and t-conorm can make information fusion more flexible and robust with the aid of parameter. Thereby, two new decision-making approaches for MAGDM with IVNNs are proposed by the IVNFWA and IVNFWG operators, respectively. This paper determines the attribute weights and DMs’ weights based on the decision information, which is more in line with the actual situation of decision-making.
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