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Reduction of an information system

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Abstract

Notion of soft binary relation is studied here. Some properties of lower and upper approximations with the help of soft equivalence relations are given. Actually, approximations of a subset by a soft binary relation give rise to two soft sets. This new setting is very clear and provides approximations related to every parameter/attribute under consideration. For any subset X,  there is an associated fuzzy subset with respect to each parameter. These fuzzy sets are very helpful in decision-making problems. Parametric reduction helps to reduce the size of data. A technique has been presented for this purpose.

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References

  • Ali MI (2011) A note on soft sets, rough sets and fuzzy soft sets. Appl Soft Comput 11:3329–3332

    Article  Google Scholar 

  • Ali MI (2012) Another view on reduction of parameters in soft sets. Appl Soft Comput 12:1814–1821

    Article  Google Scholar 

  • Ali MI, Shabir M (2014) Logic connectives for soft sets and fuzzy soft sets. IEEE Trans Fuzzy Syst 22:1431–1442

    Article  Google Scholar 

  • Ali MI, Feng F, Liu XY, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57:1547–1553

    Article  MathSciNet  Google Scholar 

  • Ali MI, Shabir M, Feng F (2017) Representation of graphs based on neighborhoods and soft sets. Int J Mach Learn Cybern 8:1525–1535

    Article  Google Scholar 

  • Cagman N, Enginoglu S (2010a) Soft matrix theory and its decision-making. Comput Math Appl 59:3308–3314

    Article  MathSciNet  Google Scholar 

  • Cagman N, Enginoglu S (2010b) Soft set theory and uni-int decision-making. Eur J Oper Res 207:848–855

    Article  MathSciNet  Google Scholar 

  • Chen D, Tsang ECC, Yeung DS, Wang X (2005) The parameterization reduction of soft sets and its applications. Comput Math Appl 49:757–763

    Article  MathSciNet  Google Scholar 

  • Davvaz B, Mahdavipour M (2008) Rough approximations in a general approximation space and their fundamental properties. Int J Gen Syst 37:373–386

    Article  MathSciNet  Google Scholar 

  • Fei L, Deng Y (2019) Multi-criteria decision making in Pythagorean fuzzy environment. Intell Appl. https://doi.org/10.1007/s10489-019-01532-2

    Article  Google Scholar 

  • Fei L, Wang H, Chen L, Deng Y (2019) A new vector valued similarity measure for intuitionistic fuzzy sets based on OWA operators. Iran J Fuzzy Syst 16:113–126

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Feng F, Liu XY, Leoreanu-Fotea V, Jun YB (2011) Soft sets and soft rough sets. Inf Sci 181:1125–1137

    Article  MathSciNet  Google Scholar 

  • Jiang Y, Liu H, Tang Y, Chen Q (2011) Semantic decision making using ontology-based soft sets. Math Comput Modell 53:1140–1149

    Article  MathSciNet  Google Scholar 

  • Kondo M (2006) On the structure of generalized rough sets. Inf Sci 176:589–600

    Article  MathSciNet  Google Scholar 

  • Kong Z, Gao L, Wang L, Li S (2008) The normal parameter reduction of soft sets and its algorithm. Comput Math Appl 56:3029–3037

    Article  MathSciNet  Google Scholar 

  • Ma X, Zhan J, Ali MI, Mehmood N (2018) A survey of decision making methods based on two classes of hybrid soft set models. Artif Intell Rev 49:511–529

    Article  Google Scholar 

  • Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44:1077–1083

    Article  MathSciNet  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555–562

    Article  MathSciNet  Google Scholar 

  • Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602

    MathSciNet  MATH  Google Scholar 

  • Molodtsov D (1999) Soft set theory—first results. Comput Math Appl 37:19–31

    Article  MathSciNet  Google Scholar 

  • Molodtsov D (2004) The theory of soft sets. URSS Publishers, Moscow (in Russian)

    Google Scholar 

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

    Article  Google Scholar 

  • Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht

    Book  Google Scholar 

  • Pawlak Z, Skowron A (2007a) Rudiments of rough sets. Inf Sci 177:3–27

  • Pawlak Z, Skowron A (2007b) Rough sets: some extensions. Inf Sci 177:28–40

    Article  MathSciNet  Google Scholar 

  • Rehman N, Ali A, Ali MI, Park C (2018) SDMGRS soft dominance based multi granulation rough sets and their applications in conflict analysis problems. IEEE Access 31399–31416

  • Shah N, Rehman N, Shabir M, Ali MI (2018) Another approach to roughness of soft graphs with applications in decision making. Symmetry 10:145. https://doi.org/10.3390/sym10050145

    Article  Google Scholar 

  • Skowron A, Stepaniuk J (1995) Generalized approximation spaces. In: Lin TY, Wildberger AM (eds) Soft computing. The Society for Computer Simulation, San Diego, pp 18–21

    Google Scholar 

  • Wu WZ, Zhang WX (2002) Neighborhood operator systems and approximations. Inf Sci 144:201–217

    Article  MathSciNet  Google Scholar 

  • Wybraniec-Skardowska U (1989) On a generalization of approximation space. Bull Pol Acad Sci Math 37:51–65

    MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  Google Scholar 

  • Zhu W (2009) Relationship between generalized rough sets based on binary relation and covering. Inf Sci 179:210–225

    Article  MathSciNet  Google Scholar 

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Acknowledgements

Authors are thankful to anonymous reviewers and the editors for their very nice suggestions which enhanced the quality of this paper by a great deal.

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam university, Islamabad, Pakistan

    Muhammad Shabir & Rani Sumaira Kanwal

  2. Islamabad Model College for Boys G-11/1, Islamabad, Pakistan

    Muhammad Irfan Ali

Authors
  1. Muhammad Shabir
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  2. Rani Sumaira Kanwal
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  3. Muhammad Irfan Ali
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Correspondence to Muhammad Shabir.

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Shabir, M., Kanwal, R.S. & Ali, M.I. Reduction of an information system. Soft Comput 24, 10801–10813 (2020). https://doi.org/10.1007/s00500-019-04582-3

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