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Multigranulation vague rough set over two universes and its application to group decision making

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Abstract

This article studies the rough approximation of a vague concept based on multiple granularity over two universes. With the description of the background of risk decision making problems in reality, we first present the optimistic multigranulation rough vague set, pessimistic multigranulation rough vague set and variable precision multigranulation rough vague set on the multigranulation approximation space over two universes. Then, under the multigranulation fuzzy approximate space over two universes, we establish the corresponding three types of multigranulation vague rough set over two universes. Subsequently, the interesting properties and results as well as the relationship between the multigranulation rough vague set models and multigranulation vague rough set model over two universes are investigated in detail. The results show that multigranulation vague rough set models are extensions of the existing generalized rough set models under the framework of two universes. At the same time, we construct a new approach to group decision making under uncertainty by using the theory of multigranulation vague rough set over two universes. The basic principal and the detailed steps of the decision making model given in this paper are presented in detail. Meanwhile, an example of handling a medical diagnosis group decision making problem illustrates this approach. The main contribution of this paper is twofold. One is to provide the theoretical model of multigranulation vague rough set over two universes. Another is to try making a new way to handle group decision making problems under uncertainty based on multigranulation vague rough set theory and methodologies over two universes.

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References

  • Abu-Donia G (2012) Multi knowledge based rough approximations and applications. Knowl Based Syst 26(1):20–29

    Article  Google Scholar 

  • Al-Rababah A, Biswas R (2008) Rough vague sets in an approximation space. Int J Comput Cognit 6(4):60–63

    Google Scholar 

  • Altuzarra A, Moreno-Jiménez J, Salvador M (2010) Consensus building in AHP-group decision making: a Bayesian approach. Oper Res 58(6):1755–1773

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Changdar C, Pal R, Mahapatra G (2017) A genetic ant colony optimization based algorithm for solid multiple travelling salesmen problem in fuzzy rough environment. Soft Comput 21(16):4661–4675

    Article  Google Scholar 

  • Chebrolu S, Sanjeevi S (2017) Attribute reduction on real-valued data in rough set theory using hybrid artificial bee colony: extended FTSBPSD algorithm. Soft Comput 21(24):7543–7569

    Article  Google Scholar 

  • Chen S, Lee L (2012) Autocratic decision making using group recommendations based on the ILLOWA operator and likelihood-based comparison relations. IEEE Trans Syst Man Cybern Part A Syst Hum 42:115–130

    Article  Google Scholar 

  • Chen S, Tan J (1994) Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 67:163–172

    Article  MathSciNet  MATH  Google Scholar 

  • Dong Y, Zhang H, Herrera-Viedma E (2016) Consensus reaching model in the complex and dynamic MAGDM problem. Knowl Based Syst 106:206–219

    Article  Google Scholar 

  • Feng T, Mi J (2016) Variable precision multigranulation decision-theoretic fuzzy rough sets. Knowl Based Syst 91:93–101

    Article  Google Scholar 

  • Gau W, Buehrer D (1993) Vague sets. IEEE Trans Syst Man Cybern Part A Syst Hum 23:610–614

    Article  MATH  Google Scholar 

  • Hamidzadeh J, Zabihimayvan M, Sadeghi R (2018) Detection of Web site visitors based on fuzzy rough sets. Soft Comput 22(7):2175–2188

    Article  Google Scholar 

  • Han S, Sostak A (2018) On the measure of M-rough approximation of L-fuzzy sets. Soft Comput 22(12):3843–3855

    Article  MATH  Google Scholar 

  • Herrera-Viedma E, Martínez L, Mata F, Chiclana F (2005) A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Trans Fuzzy Syst 13:644–659

    Article  Google Scholar 

  • Hong D, Choi C (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114:103–113

    Article  MATH  Google Scholar 

  • Honko P (2016) Attribute reduction: a horizontal data decomposition approach. Soft Comput 20(3):951–966

    Article  MATH  Google Scholar 

  • Hu C, Liu S, Huang X (2017) Dynamic updating approximations in multigranulation rough sets while refining or coarsening attribute values. Knowl Based Syst 130:62–73

    Article  Google Scholar 

  • Huang B, Guo C, Zhang Y, Li H, Zhou X (2014) Intuitionistic fuzzy multigranulation rough sets. Inf Sci 277:299–320

    Article  MathSciNet  MATH  Google Scholar 

  • Kamis N, Chiclana F, Levesley J (2018) Preference similarity network structural equivalence clustering based consensus group decision making model. Appl Soft Comput 67:706–720

    Article  Google Scholar 

  • Liang J, Wang F, Dang C, Qian Y (2012) An efficient rough feature selsction algorithm with a multi-granulation view. Int J Approx Reason 53(7):1080–1093

    Article  Google Scholar 

  • Lin G, Qian Y, Liang J (2012) NMGRS: neighborhood-based multigranulation rough sets. Int J Approx Reason 53(7):1080–1093

    Article  MathSciNet  MATH  Google Scholar 

  • Lin G, Liang J, Qian Y (2015) An information fusion approach by combining multigranulation rough sets and evidence theory. Inf Sci 314:184–199

    Article  MathSciNet  MATH  Google Scholar 

  • Mata F, Martínez L, Herrera-Viedma E (2009) An adaptive consensus support model for group decision-making problems in a multigranular fuzzy linguistic context. IEEE Trans Fuzzy Set Syst 17:279–291

    Article  Google Scholar 

  • Mi J, Zhang W (2004) An axiomatic characterization of a fuzzy generalization of rough sets. Inf Sci 160:235–249

    Article  MathSciNet  MATH  Google Scholar 

  • Morsi N, Yakout M (1998) Axiomatics for fuzzy rough sets. Fuzzy Sets Syst 100(1–3):327–342

    Article  MathSciNet  MATH  Google Scholar 

  • Pawlak Z (1982) Rough sets. Intern J Inf Sci 11(5):341–356

    MATH  Google Scholar 

  • Perfilieva I, Singh A, Tiwari S (2017) On the relationship among F-transform, fuzzy rough set and fuzzy topology. Soft Comput 21(13):3513–3523

    Article  MATH  Google Scholar 

  • Prasad V, Rao T, Babu M (2016) Thyroid disease diagnosis via hybrid architecture composing rough data sets theory and machine learning algorithms. Soft Comput 20(3):1179–1189

    Article  Google Scholar 

  • Qian Y, Liang J, Dang C (2010a) Incomplete multigranulation rough set. IEEE Trans Syst Man Cybern Part A Syst Hum 20:420–431

    Article  Google Scholar 

  • Qian Y, Liang J, Yao Y, Dang C (2010b) MGRS: a multi-granulation rough set. Inf Sci 180:949–970

    Article  MathSciNet  MATH  Google Scholar 

  • Qian Y, Liang X, Lin G (2017) Local multigranulation decision-theoretic rough sets. Int J Approx Reason 82:119–137

    Article  MathSciNet  MATH  Google Scholar 

  • Shafer G (1987) Belief functions and possibility measures. Anal Fuzzy Inf 1:51–84

    MathSciNet  MATH  Google Scholar 

  • She Y, He X (2012) On the structure of the multigranulation rough set model. Knowl Based Syst 36:81–92

    Article  Google Scholar 

  • Straszecka E (2007) Combining uncertainty and imprecision in models of medical diagnosis. Inf Sci 176(20):3026–3059

    Article  MathSciNet  Google Scholar 

  • Sun B, Ma M (2015) Multigranulation rough set theory over two universes. J Intell Fuzzy Syst 28(3):1251–1269

    MathSciNet  MATH  Google Scholar 

  • Sun B, Ma W, Qian Y (2017) Multigranulation fuzzy rough set over two universes and its application to decision making. Knowl Based Syst 123:61–74

    Article  Google Scholar 

  • Sun B, Ma W, Chen X, Li X (2018) Heterogeneous multigranulation fuzzy rough set-based multiple attribute group decision making with heterogeneous preference information. Comput Ind Eng 122:24–38

    Article  Google Scholar 

  • Tan A, Wu W, Li J, Lin G (2016) Evidence-theory-based numerical characterization of multigranulation rough sets in incomplete information systems. Fuzzy Sets Syst 294:18–35

    Article  MathSciNet  MATH  Google Scholar 

  • Wang J, Liu S, Zhang J (2005) Roughness of a vague set. Int J Comput Cognit 3(3):83–87

    Google Scholar 

  • Wang H, Xu Z, Pedrycz W (2017) An overview on the roles of fuzzy set techniques in big data processing: trends, challenges and opportunities. Knowl Based Syst 118(15):15–30

    Article  Google Scholar 

  • Wong S, Wang L, Yao Y (1993) On modeling uncertainty with interval structures. Comput Intell 11:406–426

    Article  MathSciNet  Google Scholar 

  • Wu W, Leung Y (2011) Theory and applications of granular labeled partitions in multi-scale decision tables. Inf Sci 181(18):3878–3897

    Article  MATH  Google Scholar 

  • Wu Z, Xu J (2012) A consistency and consensus based decision support model for group decision making with multiplicative preference relations. Decis Support Syst 52(3):757–767

    Article  Google Scholar 

  • Wu W, Mi J, Zhang W (2003) Generalized fuzzy rough sets. Inf Sci 151:263–282

    Article  MathSciNet  MATH  Google Scholar 

  • Wu J, Dai L, Chiclana F, Fujita H, Herrera-Viedma E (2017) A minimum adjustment cost feedback mechanism based consensus model for group decision making under social network with distributed linguistic trust. Inf Fusion 41:232–242

    Article  Google Scholar 

  • Xu W, Wang Q, Luo S (2014) Multi-granulation fuzzy rough sets. J Intell Fuzzy Syst 26(3):1323–1340

    MathSciNet  MATH  Google Scholar 

  • Xu Y, Li K, Wang H (2014) Incomplete interval fuzzy preference relations and their applications. Comput Ind Eng 67:93–103

    Article  Google Scholar 

  • Xu Y, Cabrerizo F, Herrera-Viedma E (2017) A consensus model for hesitant fuzzy preference relations and itsapplication in water allocation management. Appl Soft Comput 58:265–284

    Article  Google Scholar 

  • Yang X, Song X, Dou H, Yang J (2011) Multi-granulation rough set: from crisp to fuzzy case. Ann Fuzzy Math Informat 1:55–70

    MathSciNet  MATH  Google Scholar 

  • Yang X, Qian Y, Yang J (2012a) Hierarchical structures on multigranulation spaces. J Comput Sci Technol 27:1169–1183

    Article  MathSciNet  MATH  Google Scholar 

  • Yang X, Song X, Chen Z, Yang J (2012b) On multigranulation rough sets in incomplete information system. Int J Mach Learn Cybern 3:223–232

    Article  Google Scholar 

  • Yang J, Wang G, Zhang Q (2018) Knowledge distance measure in multigranulation spaces of fuzzy equivalence relations. Inf Sci 448:18–35

    Article  MathSciNet  Google Scholar 

  • Yao Y, She Y (2016) Rough set models in multigranulation spaces. Inf Sci 327:40–56

    Article  MathSciNet  MATH  Google Scholar 

  • Yao Y, Wong S, Wang L (1995) A non-numeric approach to uncertain reasoning. Int J Gen Syst 23:343–359

    Article  MATH  Google Scholar 

  • Yu J, Zhang B, Chen M (2018) Double-quantitative decision-theoretic approach to multigranulation approximate space. Int J Approx Reason 98:236–258

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh L (1971) Similarity relations and fuzzy ordering. Inf Sci 3:177–200

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh L (1996) Fuzzy logic equals computing with words. IEEE Trans Fuzzy Syst 4(2):103–111

    Article  Google Scholar 

  • Zhang C, Li D, Mu Y, Song D (2017) An interval-valued hesitant fuzzy multigranulation rough set over two universes model for steam turbine fault diagnosis. Appl Math Model 42:693–704

    Article  MathSciNet  Google Scholar 

  • Zhao S, Tsang E, Chen D (2009) The model of fuzzy variable precision rough sets. IEEE Trans Fuzzy Syst 17(2):451–467

    Article  Google Scholar 

  • Zhou L, Wu W (2008) On generalized intuitionistic fuzzy rough approximation operators. Inf Sci 178(11):2448–2465

    MathSciNet  MATH  Google Scholar 

  • Zhou L, Wu W, Zhang W (2009) On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators. Inf Sci 179(7):883–898

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors are very grateful to the Associate Editor Professor Fang-Yie Leu, and the two anonymous referees for their thoughtful comments and valuable suggestions. Some remarks directly benefit from the referees’ comments. The work was partly supported by the National Natural Science Foundation of China (71571090, 61772019), the National Science Foundation of Shaanxi Province of China (2017JM7022), the Key Strategic Project of Fundamental Research Funds for the Central Universities (JBZ170601), the Interdisciplinary Foundation of Humanities and Information (RW180167). The fourth author was supported by MOE (Ministry of Education in China) Project of Humanities and Social Sciences (No. 16YJC790140).

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Authors and Affiliations

  1. School of Economics and Management, Xidian University, Xi’an, 710071, Shaanxi, People’s Republic of China

    Bingzhen Sun & Xiong Zhang

  2. School of Economics and Management, Tongji University, Shanghai, 200092, People’s Republic of China

    Weimin Ma

  3. Business Administration Department, Wenzhou Vocational and Technical College, Wenzhou, 325035, Zhejiang, People’s Republic of China

    Xiangtang Chen

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  1. Bingzhen Sun
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Correspondence to Weimin Ma.

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Communicated by V. Loia.

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Sun, B., Ma, W., Chen, X. et al. Multigranulation vague rough set over two universes and its application to group decision making. Soft Comput 23, 8927–8956 (2019). https://doi.org/10.1007/s00500-018-3494-1

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