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Negations and aggregation operators based on a new hesitant fuzzy partial ordering | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 2، دوره 17، شماره 1، فروردین و اردیبهشت 2020، صفحه 1-12 اصل مقاله (182.31 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2020.5106 | ||
| نویسندگان | ||
| M. Ye* 1؛ J. Jin2؛ Y. Feng2 | ||
| 1Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada | ||
| 2College of Science, Southwest Petroleum University, Chengdu 610500, Sichuan, China | ||
| چکیده | ||
| Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~\cite{GaCa:Pohfs}, in this paper a fuzzy disjunction ${D}$ on the set ${H}$ of finite and nonempty subsets of the unit interval and a t-conorm ${S}$ on the set $\bar{{B}}$ of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negations $N_n$ on ${H}$ and $\mu_n$ on $\bar{{B}}$ are proposed. Particularly, their De Morgan's laws are investigated with respect to binary operations ${C}$ and ${D}$ on ${H}$, as well as ${T}$ and {S} on $\bar{{B}}$ respectively, where ${C}$ is a commutative fuzzy conjunction on $({H},\leq_H)$ and ${T}$ is a t-norm on $(\bar{{B}},\leq_B)$. Finally, the new hesitant fuzzy aggregation operators are presented on ${H}$ and $\bar{{B}}$ and their more general forms are given. Moreover, the validity of the aggregation operations is illustrated by a numerical example on decision making. | ||
| کلیدواژه‌ها | ||
| Hesitant fuzzy sets؛ finite subsets of the unit interval؛ partial ordering؛ t-conorm؛ negation؛ aggregation operation | ||
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