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A Novel Decision-Making Method Based on Rough Fuzzy Information

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Abstract

Fuzzy sets and rough sets are two different mathematical models to cope with vagueness, but they are correlated. Dubois and Prade combined these two sets to make new hybrid models including fuzzy rough sets and rough fuzzy sets. In this research study, we introduce several basic notions, concerning rough fuzzy digraph, and investigate some related properties. We present applications of rough fuzzy digraphs in decision-making problems. In particular, we develop efficient algorithms to solve decision-making problems.

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References

  1. Aggarwal, M.: Representation of uncertainty with information and probabilistic information granules. Int. J. Fuzzy Syst. (2016). doi:10.1007/s40815-016-0242-5

    Google Scholar 

  2. Akram, M., Ashraf, A., Sarwar, M.: Novel applications of intuitionistic fuzzy digraphs in decision support systems. Sci. World J. 2014 Article ID 904606 (2015)

  3. Akram, M., Alshehri, N., Davvaz, B., Ashraf, A.: Bipolar fuzzy digraphs in decision support systems. J. Mult. Valued Log. Soft Comput. 27, 531–551 (2016)

    Google Scholar 

  4. Banerjee, M., Pal, S.K.: Roughness of a fuzzy set. Inf. Sci. 93, 235–246 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Biswas, R.: On rough sets and fuzzy rough sets. Bull. Pol. Acad. Sci. Math. 42, 345–349 (1994)

    MathSciNet  MATH  Google Scholar 

  6. Biswas, R.: On rough fuzzy sets. Bull. Pol. Acad. Sci. Math. 42, 352–355 (1994)

    MathSciNet  MATH  Google Scholar 

  7. Bhattacharya, P.: Some remarks on fuzzy graphs. Pattern Recognit. Lett. 6, 297–302 (1987)

    Article  MATH  Google Scholar 

  8. Bhutani, R.K.: On automorphism of fuzzy graphs. Pattern Recognit. Lett. 9, 159–162 (1989)

    Article  MATH  Google Scholar 

  9. Chakrabarty, K., Biswas, R., Nanda, S.: Fuzziness in rough sets. Fuzzy Sets Syst. 110, 247–251 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Corsini, P., Leoreanu-Fotea, V.: Fuzzy sets and join spaces associated with rough sets. Rendiconti del Circolo Matematico di Palermo 51(3), 527–536 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–209 (1990)

    Article  MATH  Google Scholar 

  12. Faizi, S., Rashid, T., Salabun, W., Zafar, S., Watróbski, J.: Decision making with uncertainty using hesitant fuzzy sets. Int. J. Fuzzy Syst. (2017). doi:10.1007/s40815-017-0313-2

    Google Scholar 

  13. Feng, F., Akram, M., Davvaz, B., Fotea, V.L.: Attribute analysis of information systems based on elementary soft implications. Knowl. Based Syst. 70, 281–292 (2014)

    Article  Google Scholar 

  14. Feng, F., Li, C., Davvaz, B., Ali, M.I.: Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput. 14(9), 899–911 (2010)

    Article  MATH  Google Scholar 

  15. Feng, F.: Soft rough sets applied to multicriteria group decision making. Ann. Fuzzy Math. Inform. 2(1), 69–80 (2011)

    MathSciNet  MATH  Google Scholar 

  16. Feng, F., Liu, X., Leoreanu-Fotea, B., Jun, Y.B.: Soft sets and soft rough sets. Inf. Sci. 181(6), 1125–1137 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Habib, S., Akram, M., Ashraf, A.: Fuzzy climate decision support systems for tomatoes in high tunnels. Int. J. Fuzzy Syst. 19(3), 751–775 (2017)

    Article  Google Scholar 

  18. Kauffman, A.: Introduction a la Theorie des Sous-emsembles Flous. Masson et Cie, vol. 1. (1973)

  19. Leoreanu-Fotea, V.: The lower and upper approximations in a hypergroup. Inf. Sci. 178(18), 3605–3615 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Leoreanu-Fotea, V.: Fuzzy rough n-ary subhypergroups. Iran. J. Fuzzy Syst. 5(3), 45–56 (2008)

    MathSciNet  MATH  Google Scholar 

  21. Mordeson, J.N., Peng, C.S.: Operations on fuzzy graphs. Inf. Sci. 79, 159–170 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  22. Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs, Second Edition 2001. Physica Verlag, Heidelberg (1998)

    Google Scholar 

  23. Nakamura, A.: Fuzzy rough sets. Note Mult. Valued Log. Jpn. 9(8), 1–8 (1988)

    Google Scholar 

  24. Nanda, S.: Fuzzy rough sets. Fuzzy Sets Syst. 45, 157–160 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  25. Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1982)

    Article  MATH  Google Scholar 

  26. Pawlak, Z.: Rough sets and fuzzy sets. Fuzzy Sets Syst. 17, 99–102 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  27. Pawlak, Z.: Rough sets, rough relations and rough functions. Fundam. Inform. 27(2), 103–108 (1996)

    MathSciNet  MATH  Google Scholar 

  28. Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and Their Applications, pp. 77–95. Academic Press, New York (1975)

    Google Scholar 

  29. Sun, B.Z., Ma, W., Liu, Q.: An approach to decision making based on intuitionistic fuzzy rough sets over two universes. J. Oper. Res. Soc. 64(7), 1079–1089 (2013)

    Article  Google Scholar 

  30. Sun, B.Z., Ma, W.: Soft fuzzy rough sets and its application in decision making. Artif. Intell. Rev. 41, 67–80 (2014)

    Article  Google Scholar 

  31. Wu, S.Y.: The compositions of fuzzy digraphs. J. Res. Educ. Sci. 31, 603–628 (1986)

    Google Scholar 

  32. Yao, Y.Y., Zhao, Y.: Attribute reduction in decision-theoretic rough set models. Inf. Sci. 178, 3356–3373 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  33. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MATH  Google Scholar 

  34. Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3(2), 177–200 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  35. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  36. Zhang, H., Shu, L., Liao, S.: Intuitionistic fuzzy soft rough set and its application in decision making. Abstract and Applied Analysis, vol. 2014. (2014)

  37. Zhang, H., Shu, L.: Generalized interval-valued fuzzy rough set and its application in decision making. Int. J. Fuzzy Syst. 17(2), 279–291 (2015)

    Article  MathSciNet  Google Scholar 

  38. Zhang, X., Dai, J., Yu, Y.: On the union and intersection operations of rough sets based on various approximation spaces. Inf. Sci. 292, 214–229 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are very thankful to the editor and referees for their valuable comments and suggestions for improving the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

    Fariha Zafar & Muhammad Akram

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  1. Fariha Zafar
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  2. Muhammad Akram
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Correspondence to Muhammad Akram.

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Zafar, F., Akram, M. A Novel Decision-Making Method Based on Rough Fuzzy Information. Int. J. Fuzzy Syst. 20, 1000–1014 (2018). https://doi.org/10.1007/s40815-017-0368-0

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