Archimedean geometric Heronian mean aggregation operators based on dual hesitant fuzzy set and their application to mult
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METHODOLOGIES AND APPLICATION
Archimedean geometric Heronian mean aggregation operators based on dual hesitant fuzzy set and their application to multiple attribute decision making Jiongmei Mo1 · Han-Liang Huang1
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Fuzzy set, intuitionistic fuzzy set, hesitant fuzzy set can be regarded as a special case of dual hesitant fuzzy set. Therefore, dual hesitant fuzzy set is a more comprehensive set. Further, Archimedean t-norm and t-conorm provides generalized operational rules for dual hesitant fuzzy set. And geometric Heronian mean have advantages when considering the interrelationship of aggregation arguments. Thus, it is necessary to extend the geometric Heronian mean operator to the dual hesitant fuzzy environment based on Archimedean t-norm and t-conorm. Comprehensive above, in this paper, the dual hesitant fuzzy geometric Heronian mean operator and dual hesitant fuzzy geometric weighted Heronian mean operator based on Archimedean t-norm and t-conorm are developed. Their properties and special case are investigated. Moreover, a multiple attribute decision making method is proposed. The effectiveness of our method and the influence of parameters on multiple attribute decision making are studied by an example. The superiority of our method is illustrated by comparing with other existing methods. Keywords Dual hesitant fuzzy set · Archimedean t-norm and t-conorm · Geometric Heronian mean · Multiple attribute decision making
1 Introduction Intuitionistic fuzzy set (IFS) was first introduced by Atanassov (1986) and it is a generalization of fuzzy set (FS) (Zadeh 1965). On the basis of the FS, the non-membership function and hesitant membership function are added in IFS. Torra and Narukawa (2009) developed hesitant fuzzy set (HFS) to express the membership degree of elements as a set of possible values, which is a very useful tool for expressing people’s hesitation in our daily life. HFS has attracted more and more attention in multiple attribute decision making (MADM) (Xia and Xu 2011; Zhang and Wei 2013; Wei et al. 2017; Yu 2017; Tang et al. 2018), clustering (Chen
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Han-Liang Huang [email protected] Jiongmei Mo [email protected]
1
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, People’s Republic of China
et al. 2013; Zhang and Xu 2015; Liu et al. 2017), pattern recognition (Sun et al. 2018; Zhang et al. 2018b) and so on. Zhu et al. (2012) combined the IFS with HFS, proposed the dual hesitant fuzzy set (DHFS). Similar to IFS, DHFS are also composed of membership function and non-membership function. But different from IFS, their membership function and non-membership function are expressed by several numbers rather than a single number. FS, IFS and HFS can be regarded as special cases of DHFS. Therefore, DHFS has attracted the attention of many scholars. Ye (2014), Tyagi (2015) and Wang et al. (2013) proposed different correlation coefficients for DHFS and their applications. Si
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