Multiple-Attribute Group Decision-Making Method under a Neutrosophic Number Environment

Abstract As a neutrosophic number, which consists of a determinate part and an indeterminate part, can more easily and better express incomplete and indeterminate information that exists commonly in real situations, the main purposes of this paper are to provide a neutrosophic number tool for group decision-making problems with indeterminate information under a neutrosophic number environment and to develop a de-neutrosophication method and a possibility degree ranking method for neutrosophic numbers from the probability viewpoint as a methodological support for group decision-making problems. In group decision-making problems with neutrosophic numbers, through the de-neutrosophication and possibility degree ranking order of neutrosophic numbers, the ranking order of alternatives is performed well as the possibility degree ranking method has the intuitive meaning from the probability viewpoint, and then the best one(s) can be determined as well. Finally, two illustrative examples show the applications and effectiveness of the proposed method.

[1]  Florentin Smarandache,et al.  Introduction to Neutrosophic Statistics , 2014, ArXiv.

[2]  uan-juan Penga,et al.  An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets , 2014 .

[3]  Jun Ye,et al.  Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making , 2014, J. Intell. Fuzzy Syst..

[4]  Jun Ye,et al.  Clustering Methods Using Distance-Based Similarity Measures of Single-Valued Neutrosophic Sets , 2014, J. Intell. Syst..

[5]  Z. S. Xu,et al.  The uncertain OWA operator , 2002, Int. J. Intell. Syst..

[6]  Jun Ye,et al.  A novel image thresholding algorithm based on neutrosophic similarity score , 2014 .

[7]  Jiuying Dong,et al.  A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making , 2014, J. Comput. Syst. Sci..

[8]  Florentin Smarandache,et al.  Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability , 2013, ArXiv.

[9]  Peide Liu,et al.  The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making , 2015, Neural Computing and Applications.

[10]  Jun Ye,et al.  Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses , 2015, Artif. Intell. Medicine.

[11]  Jun Ye,et al.  Single valued neutrosophic cross-entropy for multicriteria decision making problems , 2014 .