Order based hierarchies on hesitant fuzzy approximation space
- 9 Downloads
Granular computing which focuses on everyday and commonly used concepts and notions is a new field of multi-disciplinary study in dealing with theories, methodologies and techniques. As an important role in granular computing, hierarchy has attracted considerable attention. We are usually hesitant and irresolute for one thing when making decisions, which leads to a set of possible membership degrees. However, the existing hierarchies focus on crisp environment or fuzzy environment in which each element of the set has only one membership degree. To fill this gap, we research the hierarchies on hesitant fuzzy information granulations whose information granule has at least one membership degree of one object to the reference set. Firstly, we put forward new orders on hesitant fuzzy sets to characterize the hierarchies on hesitant fuzzy sets, the relationships of these orders are also researched. Moreover, we characterize the hierarchies on hesitant fuzzy information granulations from the viewpoint of granular computing. And then, new orders are presented to characterize the hierarchies on hesitant fuzzy information granulations. The order based hierarchies on hesitant fuzzy approximation space provide us with a more comprehensible perspective for the study of granular computing. Finally, two examples are given. One example is employed to compare the differences among the proposed orders on hesitant fuzzy sets, the other example is illustrated to show the orders on hesitant fuzzy sets that can be applied to hesitant fuzzy multi-attribute decision making. The results show that the orders proposed in this paper are effective to characterize the hierarchies on hesitant fuzzy approximation space.
KeywordsGranular computing Hesitant fuzzy approximation space Hesitant fuzzy relation Hesitant fuzzy set Hierarchy
This work is supported by the Macau Science and Technology Development Fund (No. 081/2015/A3), National Natural Science Foundation of China (Nos. 71471060 and 61572242).
- 6.Feng XQ, Tan QY, Wei CP (2017) Hesitant fuzzy linguisitc multi-criteria decision making based on possibility theory. Int J Mach Learn Cybern. https://doi.org/10.1007/s1304201706597
- 8.Hobbs JR (1985) Granularity. In: Proceedings of the 9th Intational Joint Conference on Artificial Intelligence, pp 432–435Google Scholar
- 11.Kang XP, Miao DQ, Lin GP, Liu Y (2017) Relation granulation and algebraic structure based on concept lattice in complex information systems. Int J Mach Learn Cybern. https://doi.org/10.1007/s1304201706980
- 18.Priestley HA (2002) Ordered sets and complete lattices: a primer for computer science. In: Backhouse R et al (eds) Algebraic and coalgebraic methods in the mathematics of program construction, vol 2297. LNCS, pp 21–78Google Scholar
- 21.Qian YH, Dang CY, Liang JY, Wu WZ (2012) Partial ordering of information granulations: a further investigation. Expert Syst 29(1):3–24Google Scholar
- 24.Sang BB, Guo YT, Shi DR, Xu WH (2017) Decision-theoretic rough set model of multi-source decision systems. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-017-0729-x
- 27.Song JJ, Yang XB, Qi Y, Yu HL, Song XN, Yang JY (2014) Characterizing hierarchies on covering-based multigranulation spaces. In: Miao D et al (eds) The 9th International Conference on Rough Sets and Knowledge Technology, vol 8818. LNAI, pp 467–478Google Scholar
- 41.Xu YJ, Rui D, Wang HM (2015) Dual hesitant fuzzy interaction operators and their application to group decision making. J Ind Prod Eng 32(4):273–290Google Scholar
- 45.Yan L, Yan S (2016) Granular computing and attribute reduction based on a new discernibility function. Int J Simul Syst Sci Technol 17(33):1–10Google Scholar
- 55.Zhang HY, Yang SY (2015) Inclusion measure for typical hesitant fuzzy sets, the relative similarity measure and fuzzy entropy. Soft Comput 20:1–11Google Scholar