Abstract
Fuzzy information in venture capital can be well expressed by neutrosophic numbers, and TODIM method is an effective tool for multi-attribute decision-making. The distance measure is an essential step in TODIM method. The keystone of this paper is to define several new distance measures, in particular the improved interval neutrosophic Euclidean distance, and these measures are applied in the TODIM method for multi-attribute decision-making. Firstly, the normalized generalized interval neutrosophic Hausdorff distance is defined and proved to be valid in this paper. Secondly, we define a weighted parameter interval neutrosophic distance and discuss whether different weight parameters affect the decision result based on TODIM method. Thirdly, considering the preference perspective of decision-makers in behavioral economics, we define the improved interval neutrosophic Euclidean distance with the known parameter of risk preference. Finally, an application example is given to compare the effects of different parameters on the result and discuss the feasibility of these two distance measures in TODIM method.
Highlights
It is well known that the attribute decision information in multi-attribute investment is uncertain, incomplete, and inconsistent
Euclidean distance and the normalized interval neutrosophic Hausdorff distance are usually used in the previous papers, and it is not discussed whether the parameter changes in the normalized generalized model of these formulas will affect the decision-making results
This paper first defines the normalized generalized interval neutrosophic Hausdorff distance and the weighted parameter interval neutrosophic distance, and discusses the change of parameters to draw a conclusion that the change of parameters has no effect on the decision-making results
Summary
It is well known that the attribute decision information in multi-attribute investment is uncertain, incomplete, and inconsistent. Tan et al [22] introduced an extended TOPSIS method based on new distance measures under IHF environment These sets supplement the non-membership degree to the FS, which can solve the incomplete information in decision-making, but cannot deal with the uncertain and inconsistent information. It defined simplified NS [26], multi-valued NS [27], quadripartitioned SVNS [28], complex NS [29] and others, INS can describe the MADM information and evaluate the impact of each attribute on the decision-making results through some corresponding methods very well These methods include TODIM [7,30,31,32,33], TOPSIS [22,34,35,36,37,38], VIKOR [39], EDAS(Evaluation Based on Distance from Average Solution) [40], PROMETHEE [41], ELECTRE [42] and so on. An example is used to verify its rationality and feasibility
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