A general framework for multi-granulation rough decision-making method under q -rung dual hesitant fuzzy environment
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A general framework for multi‑granulation rough decision‑making method under q‑rung dual hesitant fuzzy environment Yabin Shao1 · Xiaoding Qi1 · Zengtai Gong2
© Springer Nature B.V. 2020
Abstract In the realistic decision-making (DM) process, the DM results were provided by multiple DM experts, which are more accurate than those based on one DM expert. Therefore, the multi-granulation rough set (MGRS) model is more accurate in DM problems. It is imperative to apply the idea of multi-granulation to the complex fuzzy uncertain information. By combining q-rung dual hesitant fuzzy sets (q-DHFSs) with multi-granulation rough sets (MGRSs) over two universes, we propose a q-rung dual hesitant fuzzy multi-granulation rough set (q-RDHFMGRS) over two universes, and prove some of their basic properties. Then, based on this model, we propose a new multi-attribute DM algorithm. Finally, we validate the practicability and validity of the algorithm through an example of medical diagnosis. Keywords q-rung dual hesitant fuzzy set · Multi-granulation rough set · Decision rule · Medical diagnosis
1 Introduction In medical diagnosis, doctors need to make a diagnosis based on the symptoms the patient presents. However, people’s preference expression is uncertain, and the information about the various symptoms used for diagnosis is not always clear. In order to solve the above incomplete, vague problems, Zadeh (1965) put forward the fuzzy set theory, which is a This work was supported by the National Natural Science Foundation of China (Grant Nos. 61763044, 61876201 and 11901265) * Yabin Shao [email protected] Zengtai Gong zt‑[email protected] 1
School of Science, Chongqing University of Posts and Telecommunications, Nanan, Chongqing 400065, People’s Republic of China
2
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, People’s Republic of China
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mathematical tool for dealing with the uncertain information. Fuzzy sets describe the concept of fuzziness by a membership function. The membership degree of elements is an exact value between [0, 1]. Nevertheless, in dealing with many incomplete information, there will be some limitations in the DM process due to the multiple fuzziness of information sources. To avoid this shortcoming, some extended models of FSs are proposed, such as L−fuzzy sets (Goguen 1967), fuzzy soft sets (Maji et al. 2001), T − 2 fuzzy sets (Zadeh 1975), etc. Apparently, the above models only consider the membership degree of elements, and do not discuss the nonmembership degree. Atanassov (1986) proposed another extended model of classical fuzzy sets, intuitionistic fuzzy set (IFS), which considered not only the membership degree of elements, but also the nonmembership degree and hesitancy degree of elements. To a great extent, it extends the application scope of classical fuzzy sets. However, IFS can not deal with the case that the sum of membership degree and nonmembership degree of elements is greater than 1. To solve this problem,
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