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A novel distance measure on q-rung picture fuzzy sets and its application to decision making and classification problems

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Abstract

In recent years, different higher order fuzzy sets have been introduced to better handle the uncertainty in many practical decision making and data mining problems. The recent proposal of higher order fuzzy set is q-rung picture fuzzy set (q-RPFS) modeled by three parameters positive, negative, and neutral membership function. One of the important topics in q-RPFS is distance measures which play a crucial role in many multi criteria decision making methods and data mining applications. In this paper, we introduce a novel distance measure for q-RPFS which is the combination of q-rung orthopair fuzzy set (q-ROFS) and picture fuzzy set (PFS). The proposed distance measure is used in q-rung picture fuzzy (q-RPF) ELECTRE integrated with TOPSIS as a new approach for group decision making in q-RPF environment. To demonstrate the effectiveness of our proposed method, a comparison is made with the q-RPF approach based on aggregation operators using a numerical example for decision making problem. Furthermore, the proposed distance measure is utilized in a q-RPF k nearest neighborhood (kNN) algorithm for classification. The proposed classification algorithm is applied to twenty UCI machine learning classification data sets. A comparison with other algorithms is performed and the results show that the proposed classification algorithm has the highest average classification accuracy.

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References

  • Ai Z, Xu Z, Yager RR, Ye J (2020) q-Rung Orthopair Fuzzy Archimedean t-Norms and t-Conorms and their application. IEEE T Fuzzy Syst. https://doi.org/10.1109/tfuzz.2020.2965887

    Article  Google Scholar 

  • Alcalá-Fdez J, Fernández A, Luengo J, Derrac J, García S, Sánchez L, Herrera F (2011) Keel data-mining software tool: data set repository, integration of algorithms and experimental analysis framework. J Mult-Valued Log Soft Comput 17:255–287

    Google Scholar 

  • Alcalá-Fdez J et al (2009) KEEL: a software tool to assess evolutionary algorithms for data mining problems. Soft Comput 13:307–318

    Article  Google Scholar 

  • Arif M, Akram MU (2010) Pruned fuzzy K-nearest neighbor classifier for beat classification. J Biomed Sci Eng 3:380

    Article  Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96. https://doi.org/10.1016/S0165-0114(86)80034-3

    Article  MATH  Google Scholar 

  • Atanassov KT (ed) (1999) Intuitionistic Fuzzy Sets. In: Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag HD, Heidelberg, pp 1–137. https://doi.org/10.1007/978-3-7908-1870-3_1

  • Boran FE, Akay D (2014) A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf Sci 255:45–57. https://doi.org/10.1016/j.ins.2013.08.013

    Article  MathSciNet  MATH  Google Scholar 

  • Cover T, Hart P (1967) Nearest neighbor pattern classification. IEEE Trans Inf Theory 13:21–27

    Article  Google Scholar 

  • Cuong BC, Kreinovich V (2013) Picture fuzzy sets-a new concept for computational intelligence problems. In: 2013 Third world congress on information and communication technologies (WICT 2013). IEEE, pp 1–6

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

    Article  Google Scholar 

  • Denouex T (1995) A k-nearest neighbor classification rule based on dempster-shafer theory. IEEE Trans Syst Man Cybern 25:804–813

    Article  Google Scholar 

  • Du WS (2018) Minkowski-type distance measures for generalized orthopair fuzzy sets. Int J Intell Syst 33:802–817

    Article  Google Scholar 

  • Dutta P (2017) Medical diagnosis via distance measures on picture fuzzy sets. AMSE J-AMSE IIETA Publ-2017-Ser: Adv A 54:657–672

  • Dutta P (2018) Medical diagnosis based on distance measures between picture fuzzy sets. Int J Fuzzy Syst Appl (IJFSA) 7:15–36

    Google Scholar 

  • Grzegorzewski P (2004) Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 148:319–328

    Article  MathSciNet  Google Scholar 

  • Guha D, Chakraborty D (2010) A theoretical development of distance measure for intuitionistic fuzzy numbers. Int J Math Math Sci 2010:949143. https://doi.org/10.1155/2010/949143

    Article  MathSciNet  MATH  Google Scholar 

  • He J, Wang X, Zhang R, Li L (2019) Some q-rung picture fuzzy Dombi Hamy mean operators with their application to project assessment. Mathematics 7:468

    Article  Google Scholar 

  • Intarapaiboon P (2016) A hierarchy-based similarity measure for intuitionistic fuzzy sets. Soft Comput 20:1909–1919

    Article  Google Scholar 

  • Keller JM, Gray MR, Givens JA (1985) A fuzzy K-nearest neighbor algorithm. IEEE Trans Syst Man Cybern 15:580–585. https://doi.org/10.1109/tsmc.1985.6313426

    Article  Google Scholar 

  • Kuncheva L (1995) An intuitionistic fuzzy k-nearest neighbors rule. Notes Intuit Fuzzy Sets 1:56–60

    MathSciNet  Google Scholar 

  • Li L, Zhang R, Wang J, Shang X, Bai K (2018) A novel approach to multi-attribute group decision-making with q-rung picture linguistic information. Symmetry 10:172

    Article  Google Scholar 

  • Li Y, Cheng B (2009) An improved k-nearest neighbor algorithm and its application to high resolution remote sensing image classification. In: 2009 17th international conference on geoinformatics. IEEE, pp 1–4

  • Liang Z, Shi P (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recogn Lett 24:2687–2693

    Article  Google Scholar 

  • Liu P, Wang P (2018) Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33:259–280

    Article  Google Scholar 

  • Lin M, Huang C, Xu Z (2020a) MULTIMOORA based MCDM model for site selection of car sharing station under picture fuzzy environment. Sustain Urban Areas 53:101873

    Google Scholar 

  • Lin M, Li X, Chen L (2020b) Linguistic q-rung orthopair fuzzy sets and their interactional partitioned Heronian mean aggregation operators. Int J Intell Syst 35(2):217–249

    Article  Google Scholar 

  • Luo M, Zhao R (2018) A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis. Artif Intell Med 89:34–39

    Article  Google Scholar 

  • Narukawa Y, Torra V (2006) Non-monotonic fuzzy measures and intuitionistic fuzzy sets. In: International conference on modeling decisions for artificial intelligence. Springer, pp 150-160

  • Peng X, Dai J (2017) Algorithm for picture fuzzy multiple attribute decision-making based on new distance measure. Int J Uncertain Quantif 7:177–187. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2017020096

    Article  MathSciNet  Google Scholar 

  • Peng X, Liu L (2019) Information measures for q-rung orthopair fuzzy sets. Int J Intell Syst 34:1795–1834

    Article  Google Scholar 

  • Pinar A, Boran FE (2020) A q-rung orthopair fuzzy multi-criteria group decision making method for supplier selection based on a novel distance measure. Int J Mach Learn Cybern 11:1749–1780. https://doi.org/10.1007/s13042-020-01070-1

    Article  Google Scholar 

  • Rhee F-H, Hwang C (2003) An interval type-2 fuzzy K-nearest neighbor. In: The 12th IEEE International Conference On Fuzzy Systems, 2003. FUZZ'03. IEEE, pp 802–807

  • Shu X, Ai Z, Xu Z, Ye J (2019) Integrations of q-rung orthopair fuzzy continuous information. IEEE Trans Fuzzy Syst 27(10):1974–1985

    Article  Google Scholar 

  • Son LH (2016) Generalized picture distance measure and applications to picture fuzzy clustering. Appl Soft Comput 46:284–295

    Article  Google Scholar 

  • Son LH (2017) Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures. Fuzzy Optim Decis Mak 16:359–378

    Article  MathSciNet  Google Scholar 

  • Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114:505–518. https://doi.org/10.1016/S0165-0114(98)00244-9

    Article  MathSciNet  MATH  Google Scholar 

  • Van Dinh N, Thao NX (2018) Some measures of picture fuzzy sets and their application in multi-attribute decision making. Int J Math Sci Comput (IJMSC) 4:23–41

    Google Scholar 

  • Verma R, Sharma BD (2012) On generalized intuitionistic fuzzy divergence (relative information) and their properties. J Uncertain Syst 6:308–320

    Google Scholar 

  • Wang P, Wang J, Wei G, Wei C (2019) Similarity measures of q-rung orthopair fuzzy sets based on cosine function and their applications. Mathematics 7:340

    Article  Google Scholar 

  • Wang W, Xin X (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recogn Lett 26:2063–2069

    Article  Google Scholar 

  • Wei G (2017) Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making. Informatica 28:547–564

    Article  Google Scholar 

  • Wei G (2018) Some similarity measures for picture fuzzy sets and their applications. Iran J Fuzzy Syst 15:77–89

    MathSciNet  MATH  Google Scholar 

  • Wilson DL (1972) Asymptotic properties of nearest neighbor rules using edited data. IEEE Trans Syst Man Cybern 2:408–421. https://doi.org/10.1109/tsmc.1972.4309137

    Article  MathSciNet  MATH  Google Scholar 

  • Wu M-C, Chen T-Y (2011) The ELECTRE multicriteria analysis approach based on Atanassov’s intuitionistic fuzzy sets. Expert Syst Appl 38(10):12318–12327

    Article  Google Scholar 

  • Xia M, Xu Z (2010) Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. J Syst Sci Syst Eng 19:430–452

    Article  Google Scholar 

  • Xu Z, Chen J (2008) An overview of distance and similarity measures of intuitionistic fuzzy sets. Int J Uncertain Fuzziness Knowl-Based Syst 16:529–555

    Article  MathSciNet  Google Scholar 

  • Xu Z, Yager RR (2009) Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Making 8:123–139

    Article  MathSciNet  Google Scholar 

  • Yager RR (2017) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25:1222–1230. https://doi.org/10.1109/Tfuzz.2016.2604005

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Information control 8:338–353. https://doi.org/10.1016/S0019-9958(65)90241-X

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Turkish Land Forces Logistics Command, 06135, Ankara, Turkey

    Adem Pinar

  2. Department of Energy Systems Engineering, Faculty of Technology, Gazi University, 06500, Ankara, Turkey

    Fatih Emre Boran

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  1. Adem Pinar
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  2. Fatih Emre Boran
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Correspondence to Fatih Emre Boran.

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Pinar, A., Boran, F.E. A novel distance measure on q-rung picture fuzzy sets and its application to decision making and classification problems. Artif Intell Rev 55, 1317–1350 (2022). https://doi.org/10.1007/s10462-021-09990-2

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