Note on “Fuzzy multi-granulation decision-theoretic rough sets based on fuzzy preference relation”

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In this note, we point out that the transfer function for computing the fuzzy preference degree in Mandal and Ranadive (Soft Comput, 2018. for the construction of upward/downward fuzzy relations is not additive consistent. Appropriate counterexample is given. Further, their modified versions are presented.

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  1. Herrera-Viedma E, Herrera F, Chiclana F, Luque M (2004) Some issues on consistency of fuzzy preference relations. Eur J Oper Res 154:98–109

  2. Hu QH, Yu DR, Gue MZ (2010) Fuzzy preference based rough sets. Inf Sci 180:2003–2022

  3. Mandal P, Ranadive AS (2018) Fuzzy multi-granulation decision-theoretic rough sets based on fuzzy preference relation. Soft Comput.

  4. Pan W, She K, Wei P (2017) Multi-granulation fuzzy preference relation rough set for ordinal decision system. Fuzzy Sets Syst 312:87–108

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Correspondence to Kostaq Hila.

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Communicated by V. Loia.

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Ali, A., Rehman, N. & Hila, K. Note on “Fuzzy multi-granulation decision-theoretic rough sets based on fuzzy preference relation”. Soft Comput (2020) doi:10.1007/s00500-020-04677-2

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  • Fuzzy preference relation
  • Upward fuzzy preference relation
  • Ordinal decision system