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Erschienen in: International Journal of Machine Learning and Cybernetics 6/2019

20.06.2018 | Original Article

Novel decision-making algorithms based on intuitionistic fuzzy rough environment

verfasst von: Jianming Zhan, Hafsa Masood Malik, Muhammad Akram

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 6/2019

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Abstract

Intuitionistic fuzzy sets and rough sets are two different mathematical models to deal the problem of how to understand and manipulate imperfect knowledge. An intuitionistic fuzzy rough framework is made by combining these two models, which is a more flexible and expressive for modeling and processing incomplete information in information systems. In this research study, we introduce intuitionistic fuzzy rough graphs, and describe certain types of intuitionistic fuzzy rough graphs with several examples. We present applications of intuitionistic fuzzy rough graphs in decision-making problems. We develop efficient algorithms to solve decision-making problems and compute time complexity of each algorithm.

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Literatur
1.
Zurück zum Zitat Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353MATH Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353MATH
2.
3.
Zurück zum Zitat Atanassov KT (1986) Intuitionististic fuzzy sets. Fuzzy Sets Syst 20(1):87–96MathSciNet Atanassov KT (1986) Intuitionististic fuzzy sets. Fuzzy Sets Syst 20(1):87–96MathSciNet
4.
Zurück zum Zitat Atanassov KT (1999) Intuitionistic fuzzy sets: theory and applications. Springer Physica-Verlag, BerlinMATH Atanassov KT (1999) Intuitionistic fuzzy sets: theory and applications. Springer Physica-Verlag, BerlinMATH
5.
Zurück zum Zitat Atanassov KT, Pasi G, Yager R, Atanassova V (2003) Intuitionistic fuzzy graph interpretations of multi-person multi-criteria decision making. Proceedings of the 3rd Conference of the European Society for Fuzzy Logic and Technology, Zittau, Germany, September 10–12, pp 115–119 Atanassov KT, Pasi G, Yager R, Atanassova V (2003) Intuitionistic fuzzy graph interpretations of multi-person multi-criteria decision making. Proceedings of the 3rd Conference of the European Society for Fuzzy Logic and Technology, Zittau, Germany, September 10–12, pp 115–119
6.
Zurück zum Zitat Atanassov KT, Pasi G, Yager R (2007) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 36(14):859–868MathSciNetMATH Atanassov KT, Pasi G, Yager R (2007) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 36(14):859–868MathSciNetMATH
7.
Zurück zum Zitat Pawlak Z (1991) Rough sets-theoretical aspects to reasoning about data. Kluwer Academic Publisher, BostonMATH Pawlak Z (1991) Rough sets-theoretical aspects to reasoning about data. Kluwer Academic Publisher, BostonMATH
8.
Zurück zum Zitat Pawalak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356 Pawalak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356
9.
Zurück zum Zitat Liu GL (2010) Rough set theory based on two universal sets and its applications. Knowl Based Syst 23(2):110–115 Liu GL (2010) Rough set theory based on two universal sets and its applications. Knowl Based Syst 23(2):110–115
10.
Zurück zum Zitat Griffin G, Chen Z (1998) Rough set extension of Tcl for data mining. Knowl Based Syst 11(3–4):249–253 Griffin G, Chen Z (1998) Rough set extension of Tcl for data mining. Knowl Based Syst 11(3–4):249–253
11.
Zurück zum Zitat Pei DW, Xu ZB (2007) Transformation of rough set models. Knowl Based Syst 20(8):745–751 Pei DW, Xu ZB (2007) Transformation of rough set models. Knowl Based Syst 20(8):745–751
13.
Zurück zum Zitat Dai JH, Wei BJ, Zhang XH, Zhang QH (2017) Uncertainty measurement for incomplete interval-valued information systems based on a-weak similarity. Knowl Based Syst 136:159–171 Dai JH, Wei BJ, Zhang XH, Zhang QH (2017) Uncertainty measurement for incomplete interval-valued information systems based on a-weak similarity. Knowl Based Syst 136:159–171
14.
Zurück zum Zitat Li J, Kumar Cherukuri Aswani, Mei Changlin, Wang Xizhao (2017) Comparison of reduction in formal decision contexts. Int J Approx Reason 80:100–122MathSciNetMATH Li J, Kumar Cherukuri Aswani, Mei Changlin, Wang Xizhao (2017) Comparison of reduction in formal decision contexts. Int J Approx Reason 80:100–122MathSciNetMATH
15.
Zurück zum Zitat Li J, Mei C, Lv Y (2013) Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction. Int J Approx Reason 54(1):149–165MathSciNetMATH Li J, Mei C, Lv Y (2013) Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction. Int J Approx Reason 54(1):149–165MathSciNetMATH
16.
Zurück zum Zitat Wang C, Shao M, He Q, Qian Y, Qi Y (2016) Feature subset selection based on fuzzy neighborhood rough sets. Knowl Based Syst 111(1):173–179 Wang C, Shao M, He Q, Qian Y, Qi Y (2016) Feature subset selection based on fuzzy neighborhood rough sets. Knowl Based Syst 111(1):173–179
19.
Zurück zum Zitat Wang C, He Q, Shao M, Xua Y, Hu Q (2017) A unified information measure for general binary relations. Knowl Based Syst 135(1):18–28 Wang C, He Q, Shao M, Xua Y, Hu Q (2017) A unified information measure for general binary relations. Knowl Based Syst 135(1):18–28
20.
Zurück zum Zitat Zhang XH (2017) Fuzzy anti-grouped filters and fuzzy normal filters in pseudo-BCI algebras. J Intell Fuzzy Syst 33:1767–1774MATH Zhang XH (2017) Fuzzy anti-grouped filters and fuzzy normal filters in pseudo-BCI algebras. J Intell Fuzzy Syst 33:1767–1774MATH
21.
Zurück zum Zitat Zhang XH, Park C, Wu SP (2018) Soft set theoretical approach to pseudo-BCI algebras. J Intell Fuzzy Syst 34:559–568 Zhang XH, Park C, Wu SP (2018) Soft set theoretical approach to pseudo-BCI algebras. J Intell Fuzzy Syst 34:559–568
22.
Zurück zum Zitat Dubios D, Prade H (1990) Rough fuzzy and fuzzy rough sets. Int J Gen Syst 17(2–3):191–209MATH Dubios D, Prade H (1990) Rough fuzzy and fuzzy rough sets. Int J Gen Syst 17(2–3):191–209MATH
23.
Zurück zum Zitat Chakrabarty K, Biswas R, Nanda S (2000) Fuzziness in rough sets. Fuzzy Sets Syst 110(2):247–251MathSciNetMATH Chakrabarty K, Biswas R, Nanda S (2000) Fuzziness in rough sets. Fuzzy Sets Syst 110(2):247–251MathSciNetMATH
24.
Zurück zum Zitat Mi JS, Zhang WX (2002) Composition of general fuzzy approximation spaces. Springer, Berlin, pp 497–501MATH Mi JS, Zhang WX (2002) Composition of general fuzzy approximation spaces. Springer, Berlin, pp 497–501MATH
25.
Zurück zum Zitat Cornelis C, De Cock M, Kerre EE (2003) Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge. Expert Syst 20(5):260–271 Cornelis C, De Cock M, Kerre EE (2003) Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge. Expert Syst 20(5):260–271
26.
Zurück zum Zitat Xu W, Liu Y, Sun W Intuitionistic fuzzy rough sets model based on \((\Theta , \Phi )\)-operators. 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2012): 234–238 Xu W, Liu Y, Sun W Intuitionistic fuzzy rough sets model based on \((\Theta , \Phi )\)-operators. 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2012): 234–238
27.
Zurück zum Zitat Zhou L, Wu WZ (2008) On generalerized intuitionistic fuzzy rough approximation operators. Inf Sci 178(11):2448–2465MATH Zhou L, Wu WZ (2008) On generalerized intuitionistic fuzzy rough approximation operators. Inf Sci 178(11):2448–2465MATH
28.
Zurück zum Zitat Huang B, Guo C, Zhuang YL, Li H, Zhou X (2014) Intuitionistic fuzzy multigranulation rough sets. Inf Sci 277:299–320MathSciNetMATH Huang B, Guo C, Zhuang YL, Li H, Zhou X (2014) Intuitionistic fuzzy multigranulation rough sets. Inf Sci 277:299–320MathSciNetMATH
29.
Zurück zum Zitat Wu WZ Intuitionistic fuzzy rough sets determined by intuitionistic fuzzy implicators. 2010 IEEE International Conference on Granular Computing, 536–540 Wu WZ Intuitionistic fuzzy rough sets determined by intuitionistic fuzzy implicators. 2010 IEEE International Conference on Granular Computing, 536–540
30.
Zurück zum Zitat Guo ZL, Yang HL, Wang J (2015) Rough set over dual-universes in intuitionistic fuzzy approximation space and its application. J Intell Fuzzy Syst 28(1):169–178MathSciNetMATH Guo ZL, Yang HL, Wang J (2015) Rough set over dual-universes in intuitionistic fuzzy approximation space and its application. J Intell Fuzzy Syst 28(1):169–178MathSciNetMATH
31.
Zurück zum Zitat Yang HL, Li SG, Guo ZL, Ma CH (2012) Transformation of bipolar fuzzy rough set models. Knowl Based Syst 27:60–68 Yang HL, Li SG, Guo ZL, Ma CH (2012) Transformation of bipolar fuzzy rough set models. Knowl Based Syst 27:60–68
32.
Zurück zum Zitat Yang HL, Li SG, Wang S, Wang J (2012) Bipolar fuzzy rough set model on two different universes and its application. Knowl Based Syst 35:94–101 Yang HL, Li SG, Wang S, Wang J (2012) Bipolar fuzzy rough set model on two different universes and its application. Knowl Based Syst 35:94–101
33.
Zurück zum Zitat Zhu K, Zhan J (2016) Fuzzy parameterized fuzzy soft sets and decision making. Int J Mach Learn Cybern 7(6):1207–1212 Zhu K, Zhan J (2016) Fuzzy parameterized fuzzy soft sets and decision making. Int J Mach Learn Cybern 7(6):1207–1212
34.
Zurück zum Zitat Zhan J, Liu Q, Herawan T (2017) A novel soft rough set: soft rough hemirings and its multicriteria group decision making. Appl Soft Comput 54:393–402 Zhan J, Liu Q, Herawan T (2017) A novel soft rough set: soft rough hemirings and its multicriteria group decision making. Appl Soft Comput 54:393–402
35.
Zurück zum Zitat Shahzamanian MH, Shirmohammadi M, Davvaz B (2010) Roughness in Cayley graphs. Inf Sci 180:3362–3372MathSciNetMATH Shahzamanian MH, Shirmohammadi M, Davvaz B (2010) Roughness in Cayley graphs. Inf Sci 180:3362–3372MathSciNetMATH
36.
Zurück zum Zitat Kauffman A (1973) Introduction a la Theorie des Sous-emsembles Flous. Masson et Cie 12(4):213–227 Kauffman A (1973) Introduction a la Theorie des Sous-emsembles Flous. Masson et Cie 12(4):213–227
37.
Zurück zum Zitat Rosenfeld A (1975) Fuzzy graphs. In: Zadeh LA, Fu KS, Shimura M (eds) Fuzzy sets and their applications. Academic Press, New York Rosenfeld A (1975) Fuzzy graphs. In: Zadeh LA, Fu KS, Shimura M (eds) Fuzzy sets and their applications. Academic Press, New York
38.
Zurück zum Zitat Bhattacharya P (1987) Some remarks on fuzzy graphs. Pattern Recognit Lett 6(5):297–302MATH Bhattacharya P (1987) Some remarks on fuzzy graphs. Pattern Recognit Lett 6(5):297–302MATH
39.
40.
Zurück zum Zitat Mordeson JN, Nair PS (2000) Fuzzy graphs and fuzzy hypergraphs. Springer Physica-Verlag, Heidelberg GmblMATH Mordeson JN, Nair PS (2000) Fuzzy graphs and fuzzy hypergraphs. Springer Physica-Verlag, Heidelberg GmblMATH
41.
Zurück zum Zitat Sunitha MS, Vijayakumar A (2002) Complement of a fuzzy graph. Indian J Pure Appl Math 33(9):1451–1464MathSciNetMATH Sunitha MS, Vijayakumar A (2002) Complement of a fuzzy graph. Indian J Pure Appl Math 33(9):1451–1464MathSciNetMATH
42.
43.
Zurück zum Zitat Mathew S, Sunitha M (2013) Strongest strong cycles and fuzzy graphs. IEEE Trans Fuzzy Syst 21:1096–1104 Mathew S, Sunitha M (2013) Strongest strong cycles and fuzzy graphs. IEEE Trans Fuzzy Syst 21:1096–1104
48.
Zurück zum Zitat Parvathi R, Karunambigai MG, Atanassov KT (2009) Operations on intuitionistic fuzzy graphs. IEEE International Conference on Fuzzy Systems, Jeju Island, Korea 20–24:1396–1401 Parvathi R, Karunambigai MG, Atanassov KT (2009) Operations on intuitionistic fuzzy graphs. IEEE International Conference on Fuzzy Systems, Jeju Island, Korea 20–24:1396–1401
49.
Zurück zum Zitat Akram M, Ashraf A, Sarwar M (2014) Novel applications of intuitionistic fuzzy digraphs in decision support systems. The Scientific World Journal 2014. Article ID 904606 Akram M, Ashraf A, Sarwar M (2014) Novel applications of intuitionistic fuzzy digraphs in decision support systems. The Scientific World Journal 2014. Article ID 904606
50.
Zurück zum Zitat Akram M, Saira N (2016) Fuzzy soft graphs with applications. J Intell Fuzzy Syst 30(6):3619–3632MATH Akram M, Saira N (2016) Fuzzy soft graphs with applications. J Intell Fuzzy Syst 30(6):3619–3632MATH
52.
Zurück zum Zitat Akram M, Alshehri N, Davvaz B, Ashraf A (2016) Bipolar fuzzy digraphs in decision support systems. J. Multiple-Valued Logic Soft Comput 27:531–551MATH Akram M, Alshehri N, Davvaz B, Ashraf A (2016) Bipolar fuzzy digraphs in decision support systems. J. Multiple-Valued Logic Soft Comput 27:531–551MATH
53.
Zurück zum Zitat Molina-Solana M, Birch D, Guo Y (2017) Improving data exploration in graphs with fuzzy logic and large-scale visualisation. Appl Soft Comput 53:227–235 Molina-Solana M, Birch D, Guo Y (2017) Improving data exploration in graphs with fuzzy logic and large-scale visualisation. Appl Soft Comput 53:227–235
Metadaten
Titel
Novel decision-making algorithms based on intuitionistic fuzzy rough environment
verfasst von
Jianming Zhan
Hafsa Masood Malik
Muhammad Akram
Publikationsdatum
20.06.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 6/2019
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-018-0827-4

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