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On inclusion measures of intuitionistic and interval-valued intuitionistic fuzzy values and their applications to group decision making

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Abstract

Ranking intuitionistic fuzzy values (IFVs) and interval-valued intuitionistic fuzzy values (IVIFVs) is an important and necessary work in intuitionistic fuzzy group decision making. Since the set of all IFVs is a poset and inclusion measure indicates the degree to which a given element of a poset is contained in another one. This paper studies hybrid monotonic (HM) inclusion measures of IFVs and IVIFVs respectively and discuss their applications to group decision making. Firstly, HM inclusion measure is defined on the posets of all IFVs and IVIFVs respectively. Then HM inclusion measures are studied by constructive approach. Furthermore, the HM inclusion measures are employed to make intuitionistic and interval-valued intuitionistic fuzzy group decisions. Lastly, practical examples are provided to illustrate the developed approaches respectively.

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Acknowledgments

This work was supported by grants from the National Natural Science Foundation of China (Nos. 61005042 and 11071281), the Natural Science Foundation of Shaanxi Province (No. 2014JQ8348) and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Hong-Ying Zhang, Shu-Yun Yang & Zhi-Wei Yue

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  1. Hong-Ying Zhang
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Correspondence to Hong-Ying Zhang.

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Zhang, HY., Yang, SY. & Yue, ZW. On inclusion measures of intuitionistic and interval-valued intuitionistic fuzzy values and their applications to group decision making. Int. J. Mach. Learn. & Cyber. 7, 833–843 (2016). https://doi.org/10.1007/s13042-015-0410-1

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