Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle
محل انتشار: مجله سیستم های فازی، دوره: 19، شماره: 1
سال انتشار: 1401
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 215
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شناسه ملی سند علمی:
JR_IJFS-19-1_009
تاریخ نمایه سازی: 28 آذر 1400
چکیده مقاله:
A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant fuzzy analysis and takes some applications that were discussed in recent literature. In this paper, we develop the hesitant fuzzy arithmetic, which is based on the extension principle for hesitant fuzzy sets. Employing this principle, standard arithmetic operations on fuzzy numbers are extended to HFNs and we show that the outcome of these operations on two HFNs are an HFN.Also we use the extension principle in HFSs for the ranking of HFNs, which may be an interesting topic.In this paper, we show that the HFNs can be ordered in a natural way. To introduce a meaningful ordering of HFNs, we use a new lattice operation on HFNs based upon extension principle and defining the Hamming distance on them.Finally, the applications of them are explained on optimization and decision-making problems.
کلیدواژه ها:
Hesitant fuzzy number ، extension principle on hesitant fuzzy sets ، arithmetic operations on hesitant fuzzy number ، ordering of hesitant fuzzy numbers
نویسندگان
M. Ranjbar
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
S. M. Miri
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
S. Effati
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran