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Another view on knowledge measures in atanassov intuitionistic fuzzy sets

  • Fuzzy systems and their mathematics
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Abstract

Information quantification in numerical form for any given data is very useful in decision-making problems. In Atanassov intuitionistic fuzzy sets (A-IFSs), such quantification becomes more important due to uncertainties such as intuitionism and fuzziness. Distribution of these uncertainties is a key to determine knowledge associated with Atanassov intuitionistic values (A-IFVs). In this paper, first distribution of the above-mentioned uncertainties and their relationship are discussed. Then, knowledge measures are defined as a function of entropy and uncertainty index, with certain desired properties. Existence of such knowledge measures has been established. Further, it is shown that how proposed knowledge measures are useful in multi-criteria group decision-making (MCGDM) problems.

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References

  • Ali MI, Feng F, Mahmood T, Mehmood I, Faizan H (2019) A graphical method for ranking Atanassov’s intuitionistic fuzzy values using the uncertainty index and entropy. Int J Intell Syst 34:2692–2712

    Article  Google Scholar 

  • Atanassov K (1986) Intuitionistic fuzzy Sets. Fuzzy Sets Syst 20:87–96

    Article  Google Scholar 

  • Atanassov K (1999) Intuitionistic fuzzy sets theory and applications. Phys Verlag

  • Atanassov K, Szmidt E, Kacprzyk J (2010) On some ways of determining membership and non-membership functions characterizing fuzzy sets. Notes IFS 16:26–30

    MATH  Google Scholar 

  • Bustince H, Fernandez J, Kolesárová A, Mesiar R (2013) Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst 220:69–77

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Chen T (2011) A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings. Inf Sci 181:3652–3676

    Article  Google Scholar 

  • De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst 117:209–213

    Article  Google Scholar 

  • De Luca A, Termini S (1972) A definition of non-probabilistic entropy in the setting of fuzzy sets theory. Inf Control 20:301–312

    Article  Google Scholar 

  • Farhadinia B (2013) A theoretical development on the entropy of interval valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure. Knowl-Based Syst 39:79–84

    Article  Google Scholar 

  • Guo K (2014) Amount of information and attitudinal-based method for ranking Atanassov’s intuitionistic fuzzy values. IEEE Trans Fuzzy Syst 1(22):177–188

    Article  Google Scholar 

  • Guo K (2016) Knowledge measure for Atanassov’s intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 24:1072–1078

    Article  Google Scholar 

  • Guo K, Xu H (2018) Knowledge measure for intuitionistic fuzzy sets with attitude towards non-specificity. Int J Mach Learn Cybern (1):13

  • Hung WL, Yang MS (2006) Fuzzy entropy on intuitionistic fuzzy sets. Int J Intell Syst 4(22):443–551

    Article  Google Scholar 

  • Kharal A (2009) Homeopathic drug selection using intuitionistic fuzzy sets. Homeopathy 98:35–39

    Article  Google Scholar 

  • Lalotra S, Singh S (2020) Knowledge measure of hesitant fuzzy set and its application in multi-attribute decision-making. Comput Appl Math 39:86

    Article  MathSciNet  Google Scholar 

  • Liu B (2007) A survey of entropy of fuzzy variables. J Uncertain Syst 1:4–13

    Google Scholar 

  • Lin L, Yuan X, Xia Z (2007) Multi-criteria fuzzy decision-making methods based on intuitionistic fuzzy sets. J Comput Syst Sci 73:84–88

    Article  Google Scholar 

  • Liu H, Wang G (2007) Multi-criteria decision making methods based on Intuitionistic fuzzy sets. Eur J Oper Res 179:220–233

    Article  Google Scholar 

  • Nguyen H (2016) A new interval-valued knowledge measure for interval-valued intuitionistic fuzzy sets and application in decision making. Expert Syst Appl 56:143–155

    Article  Google Scholar 

  • Nguyen H (2015) A new knowledge-based measure for Intuitionistic Fuzzy Sets and its application in multiple attribute group decision making. Expert Syst Appl 42:8766–8774

    Article  Google Scholar 

  • Ouyang Y, Pedrycz W (2016) A new model for intuitionistic fuzzy multi-attributes decision making. Eur J Oper Res 249:677–682

    Article  MathSciNet  Google Scholar 

  • Pal NR, Bustince H, Pagola M, Mukherjee UK, Goswami DP, Belikov G (2013) Uncertainties with Atanssov’s intuitionistic fuzzy sets: fuzziness and lack of knowledge. Inf Sci 228:61–74

    Article  Google Scholar 

  • Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423

  • Szmidt E, Kacprzyk J (2010) Measuring information and knowledge in the context of Atanassov's intuitionistic fuzzy sets. In: 10th international conference on intelligent systems design and applications, 78–1–4244–8136–1/10 (2010)

  • Szmidt E, Baldwin J (2004) Entropy for intuitionistic fuzzy set theory and mass assignment theory. Notes IFSs, 3(10):15–28

    Google Scholar 

  • Szmidt E, Baldwin J (2003) New similarity measure for intuitionistic fuzzy set theory and mass assignment theory. Notes IFSs, 3(9):60–76

    MathSciNet  MATH  Google Scholar 

  • Szmidt E, Baldwin J (2006) Intuitionistic fuzzy set functions, mass assignment theory, possibility theory and histograms. IEEE World Congress on Comput Intel 237–243

  • Szmidt E, Kacprzyk J (2006) An application of intuitionistic fuzzy set similarity measures to a multi-criteria decision making problem, ICAISC 2006, LNAI 4029, Springer, 314–323

  • Szmidt E, Kacprzyk J (2009) Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives. In: Rakus-Andersson E, Yager R, Ichalkaranje N, Jain LC (eds) Recent advances in decision making, SCI 222., Springer, pp 7–19

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Szmidt E, Kacprzyk J (2004) Similarity of intuitionistic fuzzy sets and the Jaccard coefficient, IPMU, 1405–1412

  • Szmidt E, Kacprzyk J (2014) How to measure the amount of knowledge conveyed by Atanassov’s intuitionistic fuzzy sets. Inf Sci 257:276–285

    Article  MathSciNet  Google Scholar 

  • Wei C, Liang X (2013) New entropy similarity measure of intuitionistic fuzzy sets and their applications in group decision making. Int J Comput Intel Syst 5(6):987–1001

    Google Scholar 

  • Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy environment. Int J General Syst 417—433

  • Yu D (2014) Intuitionistic fuzzy information aggregation under confidence levels. Appl Soft Comput 19:147–160

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Islamabad Model College for Boys, F-10/3, Islamabad, Pakistan

    Muhammad Irfan Ali

  2. Department of Mathematics, Hubei University for Nationalities, Enshi, 445000, Hubei Province, China

    Jianming Zhan

  3. KMUTT Fixed Point Research Laboratory, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Muhammad Jabir Khan

  4. Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan

    Tahir Mahmood & Haider Faizan

Authors
  1. Muhammad Irfan Ali
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  2. Jianming Zhan
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  3. Muhammad Jabir Khan
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  4. Tahir Mahmood
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  5. Haider Faizan
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Correspondence to Tahir Mahmood.

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Ali, M.I., Zhan, J., Khan, M.J. et al. Another view on knowledge measures in atanassov intuitionistic fuzzy sets. Soft Comput 26, 6507–6517 (2022). https://doi.org/10.1007/s00500-022-07127-3

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  • DOI: https://doi.org/10.1007/s00500-022-07127-3

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