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Granular Computing
Published in: Granular Computing 1/2021

22-05-2019 | Original Paper

Novel distance measures for Pythagorean fuzzy sets with applications to pattern recognition problems

Authors: P. A. Ejegwa, J. A. Awolola

Published in: Granular Computing | Issue 1/2021

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Abstract

Pythagorean fuzzy set (PFS) is a concept that generalizes intuitionistic fuzzy sets. The notion of PFSs is very much applicable in decision science because of its unique nature of indeterminacy. The main feature of PFSs is that it is characterized by membership degree, non-membership degree, and indeterminate degree in such a way that the sum of the square of each of the parameters is one. In this paper, we propose some novel distance measures for PFSs by incorporating the conventional parameters that describe PFSs. We provide a numerical example to illustrate the validity and applicability of the distance measures for PFSs. While analyzing the reliability of the proposed distance measures in comparison with similar distance measures for PFSs in the literature, we discover that the proposed distance measures, especially, \(d_5\) yields the most reasonable measure. Finally, some applications of \(d_5\) to pattern recognition problems are explicated. These novel distance measures for Pythagorean fuzzy sets could be applied in decision making of real-life problems embedded with uncertainty.
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Literature
Atanassov KT (1983) Intuitionistic fuzzy sets. VII ITKR’s Session, SofiaMATH
Atanassov KT (1989) Geometrical interpretation of the elements of the intuitionistic fuzzy objects. Preprint IM-MFAIS-1-89, Sofia
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 291:96–114CrossRef
Chen SM, Chang YC (2011) Weighted fuzzy rule interpolation based on ga-based weight-learning techniques. IEEE Trans Fuzzy Syst 19(4):729–744CrossRef
Chen SM, Cheng SH, Chiou CH (2016a) Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Inf Fusion 27:215–227CrossRef
Chen SM, Cheng SH, Lan TC (2016b) Multicriteria decision making based on the topsis method and similarity measures between intuitionistic fuzzy values. Inf Sci 367–368(1):279–295CrossRef
Chen SM, Huang CM (2003) Generating weighted fuzzy rules from relational database systems for estimating null values using genetic algorithms. IEEE Trans Fuzzy Syst 11(4):495–506CrossRef
Chen SM, Lee SH, Lee CH (2001) A new method for generating fuzzy rules from numerical data for handling classification problems. Appl Artif Intell 15(7):645–664CrossRef
Chen SM, Munif A, Chen GS, Liu HC, Kuo BC (2012) Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. Expert Syst Appl 39(7):6320–6334CrossRef
Chen SM, Tanuwijaya K (2011) Fuzzy forecasting based on high-order fuzzy logical relationships and automatic clustering techniques. Expert Syst Appl 38(12):15425–15437CrossRef
Chen SM, Wang JY (1995) Document retrieval using knowledge-based fuzzy information retrieval techniques. IEEE Trans Syst Man Cybern 25(5):793–803CrossRef
Cheng SH, Chen SM, Jian WS (2016) Fuzzy time series forecasting based on fuzzy logical relationships and similarity measures. Inf Sci 327:272–287MathSciNetMATHCrossRef
De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Set Syst 117(2):209–213MATHCrossRef
Dick S, Yager RR, Yazdanbakhsh O (2016) On Pythagorean and complex fuzzy set operations. IEEE Trans Fuzzy Syst 24(5):1009–1021CrossRef
Du Y, Hou F, Zafar W, Yu Q, Zhai Y (2017) A novel method for multiattribute decision making with interval-valued Pythagorean fuzzy linguistic information. Int J Intell Syst 32(10):1085–1112CrossRef
Ejegwa PA (2015) Intuitionistic fuzzy sets approach in appointment of positions in an organization via max-min-max rule. Glob J Sci Front Res F Math Decis Sci 15(6):1–6
Ejegwa PA, Akubo AJ, Joshua OM (2014) Intuitionistic fuzzzy sets in career determination. J Inf Comput Sci 9(4):285–288
Ejegwa PA, Modom ES (2015) Diagnosis of viral hepatitis using new distance measure of intuitionistic fuzzy sets. Intern J Fuzzy Math Arch 8(1):1–7
Ejegwa PA, Onasanya BO (2019) Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process. Note IFS 25(1):43–58
Gao H, Wei GW (2018) Multiple attribute decision making based on interval-valued Pythagorean fuzzy uncertain linguistic aggregation operators. Int J Knowl Based Intell Eng Syst 22:59–81
Garg H (2017) Generalized Pythagorean fuzzy geometric aggregation operators using einstein t-norm and t-conorm fo multicriteria decision making process. Int J Intell Syst 32(6):597–630CrossRef
Garg H (2018) Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision making process. Int J Intell Syst 33(6):1234–1263CrossRef
Gou XJ, Xu ZS, Ren PJ (2016) The properties of continuous pythagorean fuzzy information. Int J Intell Syst 31(5):401–424CrossRef
Hadi-Venchen A, Mirjaberi M (2014) Fuzzy inferior ratio method for multiple attribue decision making problems. Inf Sci 277:263–272MATHCrossRef
Hatzimichailidis AG, Papakostas AG, Kaburlasos VG (2012) A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems. Int J Intell Syst 27:396–409CrossRef
He X, Du Y, Liu W (2016) Pythagorean fuzzy power average operators. Fuzzy Syst Math 30(6):116–124MATH
Lee LW, Chen SM (2008) Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations. Expert Syst Appl 34(4):2763–2771CrossRef
Li DQ, Zeng WY (2018) Distance measure of Pythagorean fuzzy sets. Int J Intell Syst 33:348–361CrossRef
Liu P, Chen SM (2017) Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Trans Cybern 47(9):2514–2530CrossRef
Liu P, Chen SM (2018) Multiattribute group decision making based on intuitionistic 2-tuple linguistic information. Inf Sci 430–431:599–619MathSciNetMATHCrossRef
Liu P, Chen SM, Liu J (2017) Multiple attribute group decision making based on intuitionistic fuzzy interaction partitioned bonferroni mean operators. Inf Sci 411:98–121MathSciNetMATHCrossRef
Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30:1133–1160CrossRef
Szmidt E (2014) Distances and similarities in intuitionistic fuzzy sets. Springer International Publishing, New YorkMATHCrossRef
Szmidt E, Kacprzyk J (2000) Distances between inuitionistic fuzzy sets. Fuzzy Set Syst 114(3):505–518MATHCrossRef
Szmidt E, Kacprzyk J (2001) Intuitionistic fuzzy sets in some medical applications. Note IFS 7(4):58–64MATH
Szmidt E, Kacprzyk J (2004) Medical diagnostic reasoning using a similarity measure for intuitionistic fuzzy sets. Note IFS 10(4):61–69MATH
Wang HY, Chen SM (2008) Evaluating students’ answerscripts using fuzzy numbers associated with degrees of confidence. IEEE Trans Fuzzy Syst 16(2):403–415CrossRef
Wang W, Xin X (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recognit Lett 26:2063–2069CrossRef
Yager RR (2013a) Pythagorean fuzzy subsets. In: Proc joint IFSAWorld congress NAFIPS annual meeting, pp 57–61
Yager RR (2013b) Pythagorean membership grades in multicriteria decision making. Technical Report MII-3301 Machine Intelligence Institute, Iona College, New Rochelle, NY
Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965CrossRef
Yager RR (2016) Properties and applications of Pythagoean fuzzy sets. Springer, Berlin
Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers and decision making. Int J Intell Syst 28(5):436–452CrossRef
Zhang XL, Xu ZS (2014) Extension of topsis to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29:1061–1078CrossRef
Metadata
Title
Novel distance measures for Pythagorean fuzzy sets with applications to pattern recognition problems
Authors
P. A. Ejegwa
J. A. Awolola
Publication date
22-05-2019
Publisher
Springer International Publishing
Published in
Granular Computing / Issue 1/2021
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI
https://doi.org/10.1007/s41066-019-00176-4

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