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Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets

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Abstract

This paper examines the generalized intuitionistic fuzzy soft set (GIFSS) model which is an intuitively straightforward extension of the intuitionistic fuzzy soft set (IFSS) model. This concept which arises from IFSSs, is generalized by including a moderator’s opinion regarding the validity of the information at hand, thus making it highly suitable for use in decision-making problems that involve uncertain, vague and/or unreliable data. In this paper, we introduce the tools that measure the distance, similarity and the degree of fuzziness of GIFSSs. The axiomatic definitions of the distance measure is introduced and subsequently used to define the similarity measure and intuitionistic entropy induced by this distance measure. Some of the algebraic properties of these measures are also verified. The well-known Hamming, normalized Hamming, Euclidean and normalized Euclidean distances are generalized to make them compatible with the concept of GIFSSs. Subsequently, some relations among these information measures are proposed and verified. These results indicate how these measures are related and how they can be deduced from one another. Finally, we demonstrate the application of the information measure between GIFSSs by applying it to a case study related to the moderation of school-based assessment components of students in externally accredited academic programs.

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References

  1. Molodtsov D (1999) Soft set theory - First results. Computers and Mathematics with Applications 37(4–5):19–31

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  3. Maji PK, Biswas R, Roy AR (2001) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692

    MathSciNet  MATH  Google Scholar 

  4. Maji PK, Biswas R, Roy AR (2004) On intuitionistic fuzzy soft sets. J Fuzzy Math 12(3):669–684

    MathSciNet  MATH  Google Scholar 

  5. Maji PK (2009) More on intuitionistic fuzzy soft sets. Rough Sets, Fuzzy Sets, Data Mining and Granular Computing 2009:231–240

    Article  Google Scholar 

  6. Babitha KV, John SJ (2011) Generalized intuitionistic fuzzy soft sets and its applications. General Mathematics Notes 7(2):1–14

    Google Scholar 

  7. Agarwal M, Biswas KK, Hanmandlu M (2013) Generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl Soft Comput 13(8):3552–3566

    Article  Google Scholar 

  8. Park JH, Hwang J, Kim J, Park B, Son J, Lee S (2016) Similarity measure between generalized intuitionistic fuzzy sets and its application to pattern recognition. J Comput Anal Appl 20(5):984–994

    MathSciNet  MATH  Google Scholar 

  9. Zadeh LA (1968) Probability measure of fuzzy events. J Math Anal Appl 23(2):421–427

    Article  MathSciNet  MATH  Google Scholar 

  10. De Luca A, Termini S (1972) A definition of a nonprobabilistic entropy in the setting of fuzzy set theory. Inf Control 20(4):301–312

    Article  MathSciNet  MATH  Google Scholar 

  11. Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78(3):305–316

    Article  MathSciNet  MATH  Google Scholar 

  12. Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118(3):467–477

    Article  MathSciNet  MATH  Google Scholar 

  13. Chen TY, Li CH (2010) Determining objective weights with intuitionistic fuzzy entropy measures: a comparative analysis. Inf Sci 180(21):4207–4222

    Article  Google Scholar 

  14. Szmidt E, Kacprzyk J (2004) A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. Artificial Intelligence and Soft Computing – ICAISC. Springer, Berlin, pp 388–393

    MATH  Google Scholar 

  15. Szmidt E, Kacprzyk J (2005) A new concept of a similarity measure for intuitionistic fuzzy sets and its use in group decision making. Modelling Decisions for Artificial Intelligence. Springer, Berlin, pp 272–282

    MATH  Google Scholar 

  16. Dengfeng L, Chuntian C (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recogn Lett 23(1):221–225

    Article  MATH  Google Scholar 

  17. Mitchell HB (2003) On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recogn Lett 24(16):3101–3104

    Article  Google Scholar 

  18. Majumdar P, Samanta SK (2008) Similarity measure of soft sets. New Mathematics and Natural Computation 4(1): 1–12

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu Z, Qin K, Pei Z (2014) Similarity measure and entropy of fuzzy soft sets. Sci World J 2014:1–10

    Google Scholar 

  20. Jiang Y, Tang Y, Liu H, Chen Z (2013) Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets. Inf Sci 240:95–114

    Article  MathSciNet  MATH  Google Scholar 

  21. Khalid A, Abbas M (2015) Distance measures and operations in intuitionistic and interval-valued intuitionistic fuzzy soft set theory. International Journal of Fuzzy Systems 17:490–497. doi:10.1007/s40815-015-0048-x

    Article  MathSciNet  Google Scholar 

  22. Thillaigovindan N, Anita Shanthi S, Vadivel Naidu J (2016) A better score function for multiple criteria decision making in fuzzy environment with criteria choice under risk. Expert Syst Appl. doi:10.1016/j.eswa.2016.04.023

    Google Scholar 

  23. Wang C, Qu A (2013) Entropy, similarity measure and distance measure of vague soft sets and their relations. Inf Sci 244:92–106

    Article  MathSciNet  MATH  Google Scholar 

  24. Xu Z, Xia M (2011) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181:2128–2138

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  27. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MathSciNet  MATH  Google Scholar 

  28. Zadeh LA (1965). Fuzzy Sets Inf Control 8:338–353

    Article  Google Scholar 

  29. Majumdar P, Samanta SK (2010) Generalized fuzzy soft sets. Computers and Mathematics with Applications 59(4):1425–1432

    Article  MathSciNet  MATH  Google Scholar 

  30. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433

    Article  MathSciNet  MATH  Google Scholar 

  31. Xu ZS (2007) Intuitionistic preference relations and their applications in group decision making. Inf Sci 177 (1):2363–2379

    Article  MathSciNet  MATH  Google Scholar 

  32. Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):505–518

    Article  MathSciNet  MATH  Google Scholar 

  33. Ramot D, Milo R, Friedman M, Kandel A (2002) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10 (2):171–186

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to gratefully acknowledge the financial assistance received from the Ministry of Education, Malaysia and UCSI University, Malaysia under Grant no. FRGS/1/2014/ST06/UCSI/03/1.

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Authors and Affiliations

  1. Department of Actuarial Science and Applied Statistics, Faculty of Business & Information Science, UCSI University, Jalan Menara Gading, 56000, Cheras, Kuala Lumpur, Malaysia

    Ganeshsree Selvachandran

  2. Department of Mathematics, B.C. College, Asansol, West Bengal, India

    P. K. Maji

  3. School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, DE, Malaysia

    Raghad Qasim Faisal & Abdul Razak Salleh

Authors
  1. Ganeshsree Selvachandran
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  2. P. K. Maji
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  3. Raghad Qasim Faisal
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  4. Abdul Razak Salleh
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Correspondence to Ganeshsree Selvachandran.

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This manuscript is the authors’ original work and has not been published nor has it been submitted simultaneously elsewhere. All authors have checked the manuscript and have agreed to this submission.

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Selvachandran, G., Maji, P.K., Faisal, R.Q. et al. Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets. Appl Intell 47, 132–147 (2017). https://doi.org/10.1007/s10489-016-0884-x

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