Journal
APPLIED INTELLIGENCE
Volume 48, Issue 4, Pages 953-965Publisher
SPRINGER
DOI: 10.1007/s10489-017-1041-x
Keywords
Multi-attribute group decision making; Probabilistic hesitant fuzzy set; Frank t-conorm and t-norm; Information aggregation operators
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Funding
- Guizhou Province Department of Education Fund [KY[2015]34, KY[2016]088]
- Natural Science Foundation of the Jiangsu Higher Education Institutions of China [16KJB520001]
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Hesitant fuzzy sets were introduced by Torra to efficiently address situations in which the membership degree of an element in a set is expressed by several different values. However, there is a large shortcoming in hesitant fuzzy sets-the serious loss of information. Therefore, in this paper, we improve upon hesitant fuzzy sets by implementing a probabilistic hesitant fuzzy set (PHFS). Then, we introduce some new basic operations on the probabilistic hesitant fuzzy elements (PHFEs) using the Frank t-conorm and t-norm. Based on these proposed operations, we further develop probabilistic hesitant fuzzy weighted arithmetic and geometric aggregation operators. The desired properties and the relationships among them are investigated in detail. In addition, an approach to multi-attribute group decision making (MAGDM) is investigated on the basis of the new operators. Finally, a numerical example of public company efficiency evaluation is provided to illustrate the application and validity of the proposed approach.
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