Skip to main content
Log in

Complex vague contexts analysis using Cartesian product and granulation

  • Original Paper
  • Published:
Granular Computing Aims and scope Submit manuscript

Abstract

The precise measurement of uncertainty and its fluctuation in the vague attributes is considered as one of the most crucial task by the data analytics researchers. To accomplish this tasks, the calculus of complex vague concept lattice is introduced recently for adequate analysis of vagueness and its graphical visualization. In this process, a problem is addressed while dealing with similar vague attributes exists in the given complex fuzzy contexts. To conquer this problem, a method is proposed for acquisition and transformation of complex vague contexts using the properties of Cartesian product and granular computing with an illustrative example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. https://en.wikipedia.org/wiki/Air_quality_index.

  2. https://en.wikipedia.org/wiki/Retraction.

  3. https://retractionwatch.com/.

References

  • Alcalde C, Burusco A, Fuentes-Gonzalez R (2012) Composition of \(L\)-fuzzy contexts. In: Proceedings of 10th International Conference on Formal Concept Analysis 2012, pp 1–14

  • Ali M, Smarandache F (2017) Complex neutrosophic set. Neural Comput Appl 28(7):1817–1834

    Google Scholar 

  • Burusco A, Fuentes-Gonzalez R (1994) The study of the L-fuzzy concept lattice. Matheware Soft Comput 1(3):209–218

    MathSciNet  MATH  Google Scholar 

  • Burusco A, Fuentes-Gonzales R (2001) The study on interval-valued contexts. Fuzzy Sets Syst 121(3):439–452

    MathSciNet  MATH  Google Scholar 

  • Bustince H, Burillo P (1996) Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst 79(3):403–405

    MathSciNet  MATH  Google Scholar 

  • Chen SM (1995) Measures of similarity between vague sets. Fuzzy Sets Syst 74:217–223

    MathSciNet  MATH  Google Scholar 

  • Chen SM, Lee SH, Lee CH (2010) A new method for generating fuzzy rules from numerical data for handling classification problems. Appl Artif Intell 15(7):645–664

    Google Scholar 

  • Chen SM (2011) Fuzzy forecasting based on high-order fuzzy logical relationships and automatic clustering techniques. Expert Syst Appl 38(12):15425–15437

    Google Scholar 

  • Chen SM, Chang CH (2015) A novel similarity measure between Atanassov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf Sci 291:96–114

    Google Scholar 

  • Chen SM, Chang CH (2016) Fuzzy multiattribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators. Inf Sci 352(C):133–149

    MATH  Google Scholar 

  • Chen SM, Cheng SH, Chiou CH (2016a) Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Inf Fusion 27:215–227

    Google Scholar 

  • Chen SM, Cheng SH, Lan TS (2016b) Multicriteria decision making based on the TOPSIS method and similarity measures between intuitionistic fuzzy values. Inf Sci 367:279–295

    Google Scholar 

  • Chen SM, Cheng SH, Lan TS (2016c) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343:15–40

    MathSciNet  MATH  Google Scholar 

  • Dick S (2005) Toward complex fuzzy logic. IEEE Trans Fuzzy Syst 13(3):405–414

    MathSciNet  Google Scholar 

  • Dubois D, Prade H (2015) Formal concept analysis from the standpoint of possibility theory. In: Proceedings of ICFCA 2015, LNAI 9113, pp 21–38

    MATH  Google Scholar 

  • Dubois D, Prade H (2016) Bridging gaps between several forms of granular computing. Granul Comput 1(2):115–126

    Google Scholar 

  • Gajdos P, Snasel V (2014) A new FCA algorithm enabling analyzing of complex and dynamic data sets. Soft Comput 18(4):683–694

    Google Scholar 

  • Ganter B, Wille R (1999) Formal concept analysis: mathematical foundation. Springer, Berlin

    MATH  Google Scholar 

  • Gau WL, Buehrer DJ (1993) Vague sets. IEEE Trans Syst Man Cybern 23(2):610–614

    MATH  Google Scholar 

  • Lindig C (2000) Fast concept analysis. In: Ganter B, Mineau GW (eds) ICCS 2000. LNCS, vol 1867. Springer, Heidelberg, pp 152–161

    Google Scholar 

  • Liu P, Chen SM (2017) Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Trans Cybern 47(9):2514–2530

    Google Scholar 

  • Pandey LK, Ojha KK, Singh PK, Singh CS, Dwivedi S, Bergey EA (2016) Diatoms image database of India (DIDI): a research tool. Environ Technol Innovat 5:148–160

    Google Scholar 

  • Singh PK, Gani Abdullah (2015) Fuzzy concept lattice reduction using Shannon entropy and Huffman coding. J Appl Non-Classic logic 25(2):101–119

    MathSciNet  MATH  Google Scholar 

  • Singh PK, Kumar Ch Aswani (2016) Analysis of composed fuzzy contexts using projection. Int J Data Anal Tech Strateg 8(3):206–219

    Google Scholar 

  • Singh PK (2016) Processing linked formal fuzzy contexts using non–commutative composition. Inst Integr Omics Appl Biotechnol (IIOAB) J 7(5):21–32

    Google Scholar 

  • Singh PK (2017a) Three-way fuzzy concept lattice representation using neutrosophic set. Int J Mach Learn Cybern 8(1):69–79

    Google Scholar 

  • Singh PK (2017b) Complex vague set based concept lattice. Chaos, Solitons Fract 96:145–153

    MATH  Google Scholar 

  • Singh PK, Kumar Ch Aswani (2017c) Concept lattice reduction using different subset of attributes as information granules. Granular Comput 2(3):159–173

    Google Scholar 

  • Singh PK (2018a) Complex neutrosophic concept lattice and its applications to Air quality analysis. Chaos, Solitons & Fract 109:206–213

    Google Scholar 

  • Singh PK (2018b) Similar vague concepts selection using their Euclidean distance at different granulation. Cognit Comput 10(2):228–241

    Google Scholar 

  • Singh PK (2018c) Concept learning using vague concept lattice. Neural Process Lett 48(1):31–52

    Google Scholar 

  • Singh PK (2018d) Complex fuzzy concept lattice. Neural Processing Letters. https://doi.org/10.1007/s11063-018-9884-7

    Google Scholar 

  • Singh PK (2018e) Concept lattice visualization of data with m-polar fuzzy attribute. Granul Comput 3(2):123–137

    Google Scholar 

  • Ramakrishna N (2009) Vague graphs. Int J Comput Cognit 7:51–58

    Google Scholar 

  • Ramot D, Friedman M, Langholz G, Kandel A (2003) Complex fuzzy logic. IEEE Trans Fuzzy Syst 11(4):450–461

    Google Scholar 

  • Ramot D, Milo R, Friedman M, Kandel A (2005) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10(2):171–186

    Google Scholar 

  • Selvachandrana G, Maji PK, Abed IE, Salleh AR (2016a) Relations between complex vague soft sets. Appl Soft Comput 47:438–448

    Google Scholar 

  • Selvachandran G, Maji PK, Abed IE, Salleh AR (2016b) Complex vague soft sets and its distance measures. J Intell Fuzzy Syst 31:55–68

    MATH  Google Scholar 

  • Selvachandran G, Singh PK (2017) Interval-valued complex fuzzy soft set and its application. Int J Uncertain Quantif 8(2):101–117

    MathSciNet  Google Scholar 

  • Skowron A, Jankowski A, Dutta S (2016) Interactive granular computing. Granul Comput 1(2):95–113

    MathSciNet  MATH  Google Scholar 

  • Ward M, Dilworth RP (1939) Residuated lattices. Trans Am Math Soc 45:335–354

    MathSciNet  MATH  Google Scholar 

  • Wang HY, Chen SM (2008) Evaluating students answerscripts using fuzzy numbers associated with degrees of confidence. IEEE Trans Fuzzy Fuzzy Syst 16(2):403–415

    Google Scholar 

  • Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival I (eds) Ordered sets, NATO advanced study institutes series 83, pp 445–470

    Google Scholar 

  • Yao Y (2016) A triarchic theory of granular computing. Granul Comput 1(2):145–157

    Google Scholar 

  • Zadeh (1965) Fuzzy sets. Inf Control 8(3):338–353

    MATH  Google Scholar 

  • Yazdanbakhsh O, Dick S (2018) A systematic review of complex fuzzy sets and logic. Fuzzy Sets Syst 338(2018):1–20

    MathSciNet  MATH  Google Scholar 

  • Zhang G, Dillon TS, Cai KY, Ma J, Lu J (2009) Operation properties and \(\delta\)-equalities of complex fuzzy sets. Int J Approx Reason 50(2009):1227–1249

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Authors sincerely thank the anonymous reviewers as well as editorial team for their valuable time and comments to improve the quality of this manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Prem Kumar Singh.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, P.K. Complex vague contexts analysis using Cartesian product and granulation. Granul. Comput. 5, 37–53 (2020). https://doi.org/10.1007/s41066-018-0136-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41066-018-0136-z

Keywords

Navigation