Abstract
Rough set theory has been combined with intuitionistic fuzzy sets in dealing with uncertainty decision making. This paper proposes a general decision-making framework based on the intuitionistic fuzzy rough set model over two universes. We first present the intuitionistic fuzzy rough set model over two universes with a constructive approach and discuss the basic properties of this model. We then give a new approach of decision making in uncertainty environment by using the intuitionistic fuzzy rough sets over two universes. Further, the principal steps of the decision method established in this paper are presented in detail. Finally, an example of handling medical diagnosis problem illustrates this approach.
Similar content being viewed by others
References
Atanassov K (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20 (1): 87–96.
Atanassov K (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag: Heidelberg.
Banerjeem M and Pal SK (1996). Roughness of a fuzzy set. Information Sciences 93 (3–4): 235–246.
Bustince H and Burillo P (1996). Structures on intuitionistic fuzzy relations. Fuzzy Sets and Systems 78 (3): 293–303.
Cattaneo G and Ciucci D (2006). Basic intuitionistic principles in fuzzy set theories and its extensions (a terminological debate on Atanassov IFS). Fuzzy Sets and Systems 157 (24): 3198–3219.
Chakrabarty K, Gedeon T and Koczy L (1998). Intuitionistic fuzzy rough set. In: Proceedings of Fourth Joint Conference on Information Sciences (JCIS). Research Triangle Park (North Carolina, USA), Durham, NC, pp 211–214.
Coker D (1998). Fuzzy rough sets are intuitionistic L-fuzzy sets. Fuzzy Sets and Systems 96 (3): 381–383.
Cornelis C, Cock MD and Kerre EE (2003). Intuitionistic fuzzy rough sets: At the crossroads of imperfect knowledge. Expert Systems 20 (5): 260–270.
De SK, Biswas A and Roy R. (2001). An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems 117 (2): 209–213.
Feng L, Wang GY and Li XX (2010). Knowledge acquisition in vague objective information systems based on rough sets. Expert Systems 27 (2): 129–141.
Gerstenkorn T and Manko J (1995). Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems 74 (2): 237–244.
Gong ZT and Sun BZ (2008). Probability rough sets model between different universes and its applications. IEEE on International Conference on Machine Learning and Cybernetics 561–565.
Han J and Kamber M (2006). Data Mining: Concepts and Techniques. Elsevier, Kaufmann: Morgan, San Mateo, CA.
Jena SP and Ghosh SK (2002). Intuitionistic fuzzy rough sets. Notes on Intuitionistic Fuzzy Sets 8: 1–18.
Liu GL (2010). Rough set theory based on two universal sets and its applications. Knowledge-Based Systems 23 (2): 110–115.
Ma WM and Sun BZ (2012a). Probabilistic rough set over two universes and rough entropy. International Journal of Approximate Reasoning 53 (4): 608–619.
Ma WM and Sun BZ (2012b). On relationship between probabilistic rough set and Bayesian risk decision over two universes. International Journal of General Systems 41 (3): 225–245.
Nanda S and Majumda S (1992). Fuzzy rough sets. Fuzzy Sets and Systems 45 (2): 157–160.
Pei DW (2005). A generalized model of fuzzy rough sets. International Journal of General Systems 34 (5): 603–613.
Pei DW and Xu ZB (2007). Transformation of rough set models. Knowledge-Based Systems 20 (7): 745–751.
Pawlak Z (1982). Rough sets. International Journal of Computer and Information Sciences 11 (5): 341–356.
Radzikowska AM (2006). Rough approximation operations based on IF sets. In: Rutkowski L, Tadeusiewicz R and Zadeh LA (eds.) ICAISC 2006, Lecture Notes in Computer Science. Vol. 4029, Springer: Berlin, pp 528–537.
Radzikowska AM and Kerre EE (2002). A comparative study of fuzzy rough sets. Fuzzy Sets and Systems 126 (2): 137–155.
Rizvi S, Naqvi HJ and Nadeem D (2002). Rough intuitionistic fuzzy set. In: Proceedings of the Sixth Joint Conference on Information Sciences (JCIS). Research Triangle Park: Durham, NC, pp 101–104.
Samanta SK and Mondal TK (2001). Intuitionistic fuzzy rough sets and rough intuitionistic fuzzy sets. Journal of Fuzzy Mathematics 9 (3): 561–582.
Straszecka E (2007). Combining uncertainty and imprecision in models of medical diagnosis. Information Sciences 176 (20): 3026–3059.
Sun BZ and Ma WM (2011a). Fuzzy rough set model on two different universes and its application. Applied Mathematical Modelling 35 (4): 1798–1809.
Sun BZ and Ma WM (2011b). Conflict analysis decision based on rough sets theory over two universes. Journal of Operational Research (Submitted).
Sun BZ and Ma WM . (2011) Soft fuzzy rough sets and its application in decision making. Artificial Intelligence Review. advance online publication 22 December, DOI 10.1007/s10462-011-9298-7.
Sun BZ and Ma WM (2012). Erratum to Fuzzy rough set model on two different universes and its application. Applied Mathematical Modelling 36: 4539–4541.
Sun BZ, Ma WM and Liu Q (2011). Theory for intuitionistic fuzzy rough sets over two universes. IEEE on International Conference on Machine and Cybernetics: Guilin, 10–13 July, pp. 307–312.
Szmidt E and Kacprzyk J (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118 (3): 467–477.
Wong SKM, Wang LS and Yao YY (1993a). Interval structures: A framework for representing uncertain information. In: Dubois, D., Wellman, M.P., D'Ambrosio, B., and Smets, P. (eds.), Proceeding of 8th Conference on Uncertainty Artificial Intelligence, Stanford University, CA, 7–19 July; Morgan Kaufmann Publishers, pp 336–343.
Wong SKM, Wang LS and Yao YY (1993b). On modeling uncertainty with interval structures. Computer Intelligence 11 (2): 406–426.
Wu WZ and Zhang WX (2003). Generalized fuzzy rough sets. Information Science 151: 263–282.
Wu WZ and Zhou L (2011). On intuitionistic fuzzy topologies based on intuitionistic fuzzy reflexive and transitive relation. Soft Computing 15 (6): 1183–1194.
Xu ZS (2008). Intuitionistic Fuzzy Information Aggregating Theory and Application. Science Press: Beijing, pp 68–77.
Yao YY (1996). Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning 15 (4): 291–317.
Yao YY, Wong SKM and Wang LS (1995). A non-numeric approach to uncertain reasoning. International Journal of General Systems 23 (4): 343–359.
Yan RX, Zheng JG, Liu JL and Zhai YM (2010). Research on the model of rough set over dual-universes. Knowledge-Based Systems 23 (8): 817–822.
Zadeh LA (1965). Fuzzy sets. Information and Control 8 (3): 338–353.
Zhou L and Wu WZ (2008). On generalized intuitionistic fuzzy rough approximation operators. Information Sciences 178 (11): 2448–2465.
Zhou L, Wu WZ and Zhang WX (2009a). On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators. Information Sciences 179 (7): 883–898.
Zhou L, Wu WZ and Zhang WX (2009b). On intuitionistic fuzzy rough sets and their topological structures. International Journal of General Systems 38 (6): 589–616.
Acknowledgements
The work was partly supported by the National Science Foundation of China (71161016, 71071113), a Foundation for the Author of National Excellent Doctoral Dissertation of PR China (200782), the Shuguang Plan of Shanghai Education Development Foundation and Shanghai Education Committee (08SG21), Shanghai Pujiang Program, and Shanghai Philosophical and Social Science Program (2010BZH003), the Fundamental Research Funds for the Central Universities.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sun, B., Ma, W. & Liu, Q. An approach to decision making based on intuitionistic fuzzy rough sets over two universes. J Oper Res Soc 64, 1079–1089 (2013). https://doi.org/10.1057/jors.2012.75
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1057/jors.2012.75