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<p>It is well known that, fuzzy set theory in particular fuzzy numbers plays an important role to model uncertainties present in the system parameters when one has less, vague or incomplete information about them. However, fuzzy numbers can not be ordered like real numbers. Therefore, various efforts have been made to develop ranking function to order fuzzy numbers. These existing functions varies depending on the type of the fuzzy numbers, as there are different kind of fuzzy numbers exists. Accordingly, this paper proposes a new ranking function for the generalized <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L{-}R\)</EquationSource> </InlineEquation> fuzzy number using the method of Yager (Inf Sci 24:143–161, 1981) and Maleki et al (Fuzzy Sets Syst 109:21–33, 2000). Left (<i>L</i>) and Right (<i>R</i>) shapes of the fuzzy numbers are considered as the parts of generalized nonlinear functions here. The advantages of this method is that for different values of <i>N</i> ranking of different types of fuzzy numbers can be computed. Various example problems have been considered to verify the proposed ranking function. Also, in special cases comparisons have been made with the existing results to validate the proposed method.</p>

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Development of a ranking function for a generalized \(L{-}R\) fuzzy number

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Diptiranjan Behera,
  • Mahesha Narayana

摘要

It is well known that, fuzzy set theory in particular fuzzy numbers plays an important role to model uncertainties present in the system parameters when one has less, vague or incomplete information about them. However, fuzzy numbers can not be ordered like real numbers. Therefore, various efforts have been made to develop ranking function to order fuzzy numbers. These existing functions varies depending on the type of the fuzzy numbers, as there are different kind of fuzzy numbers exists. Accordingly, this paper proposes a new ranking function for the generalized \(L{-}R\) fuzzy number using the method of Yager (Inf Sci 24:143–161, 1981) and Maleki et al (Fuzzy Sets Syst 109:21–33, 2000). Left (L) and Right (R) shapes of the fuzzy numbers are considered as the parts of generalized nonlinear functions here. The advantages of this method is that for different values of N ranking of different types of fuzzy numbers can be computed. Various example problems have been considered to verify the proposed ranking function. Also, in special cases comparisons have been made with the existing results to validate the proposed method.