Efficiency of Fuzzy Rough Set Decision Algorithms

  1. Chacón-Gómez, Fernando
  2. Cornejo, M. Eugenia
  3. Medina, Jesús
  4. Ramírez-Poussa, Eloísa
Book:
Computational Intelligence and Mathematics for Tackling Complex Problems 5

ISSN: 1860-949X,  1860-9503

ISBN: 9783031469787,  9783031469794

Year of publication: 2024

Pages: 17-24

Type: Book chapter

DOI: 10.1007/978-3-031-46979-4_3 GOOGLE SCHOLAR lock_openOpen access editor

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Abstract

This paper addresses the study of decision algorithms given in Rough Set Theory. Considering the fuzzy framework, we present a generalized notion of efficiency, which is one of the most important notions associated with decision algorithms. This new notion can be used to know the usefulness of a fuzzy rough set decision algorithm, as well as to compare it with other fuzzy decision algorithms.

Bibliographic References

  • Chacón-Gómez, F., Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Fuzzy rough set decision algorithms. Commun. Comput. Inf. Sci. 1601, 63–76 (2022)
  • Cock, M.D., Cornelis, C., Kerre, E.E.: Fuzzy rough sets: the forgotten step. IEEE Trans. Fuzzy Syst. 15(1), 121–130 (2007)
  • Cornelis, C., Medina, J., Verbiest, N.: Multi-adjoint fuzzy rough sets: definition, properties and attribute selection. Int. J. Approx. Reason. 55, 412–426 (2014)
  • De Cock, M., Cornelis, C., Kerre, E.: Elicitation of fuzzy association rules from positive and negative examples. Fuzzy Sets Syst. 149(1), 73–85 (2005)
  • De Luca, A., Termini, S.: A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Inf. Control 20(4), 301–312 (1972)
  • Dubois, D., Prad, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17(2–3), 191–209 (1990)
  • Feng, T., Fan, H.-T., Mi, J.-S.: Uncertainty and reduction of variable precision multigranulation fuzzy rough sets based on three-way decisions. Int. J. Approx. Reason. 85, 36–58 (2017)
  • Li, J., Mei, C., Lv, Y.: Incomplete decision contexts: Approximate concept construction, rule acquisition and knowledge reduction. Int. J. Approx. Reason. 54(1), 149–165 (2013)
  • Medina, J.: Towards multi-adjoint property-oriented concept lattices. Lect. Notes Artif. Intell. 6401, 159–166 (2010)
  • Medina, J.: Multi-adjoint property-oriented and object-oriented concept lattices. Inf. Sci. 190, 95–106 (2012)
  • Medina, J.: Relating attribute reduction in formal, object-oriented and property-oriented concept lattices. Comput. Math. Appl. 64(6), 1992–2002 (2012)
  • Morsi, N.N., Yakout, M.M.: Axiomatics for fuzzy rough sets. Fuzzy Sets Syst. 100, 327–342 (1998)
  • Nakamura, A.: Fuzzy rough sets. Note Mult.-Valued Log. Jpn. 9, 1–8 (1988)
  • Nanda, S., Majumdar, S.: Fuzzy rough sets. Fuzzy Sets Syst. 45, 157–160 (1992)
  • Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Norwell, MA, USA (1992)
  • Pawlak, Z.: Rough sets and decision algorithms. In: Ziarko, W., Yaopages, Y. (eds.) Rough Sets and Current Trends in Computing, pp. 30–45. Springer, Berlin (2001)
  • Stawicki, S., Ślȩzak, D., Janusz, A., Widz, S.: Decision bireducts and decision reducts—a comparison. Int. J. Approx. Reason. 84, 75–109 (2017)
  • Wang, C.Y.: Topological structures of l-fuzzy rough sets and similarity sets of l-fuzzy relations. Int. J. Approx. Reason. 83, 160–175 (2017)
  • Yao, Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180(3), 341–353 (2010)
  • Zedam, L., Bouremel, H., De Baets, B.: Left- and right-compatibility of order relations and fuzzy tolerance relations. Fuzzy Sets Syst. 360, 65–81 (2019)