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Information Journal Paper

Title

Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle

Pages

  97-114

Abstract

 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 de ning the Hamming distance on them. Finally, the applications of them are explained on optimization and decision-making problems.

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    • Cite

    APA: Copy

    RANJBAR, M., Miri, S. M., & Effati, S.. (2022). Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle. IRANIAN JOURNAL OF FUZZY SYSTEMS, 19(1 ), 97-114. SID. https://sid.ir/paper/412595/en

    Vancouver: Copy

    RANJBAR M., Miri S. M., Effati S.. Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2022;19(1 ):97-114. Available from: https://sid.ir/paper/412595/en

    IEEE: Copy

    M. RANJBAR, S. M. Miri, and S. Effati, “Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 19, no. 1 , pp. 97–114, 2022, [Online]. Available: https://sid.ir/paper/412595/en

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