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A novel dissimilarity measure on picture fuzzy sets and its application in multi-criteria decision making

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Abstract

With the increase in complexity of real problems, more and more, the decision makers are involved remarkably in the decision-making processes. It is required more efficient technique or tool to give reliable outcomes. This paper proposes a new dissimilarity measure on picture fuzzy sets. A multi-criteria decision-making problem is utilized to apply this new measure to select the optimal alternative. Finally, an example uses the proposed measure to evaluate and select the optimal market segment.

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References

  • Ananda J, Herath G (2009) A critical review of multi-criteria decision- making methods with special reference to forest management and planning. Ecol Econ 68:2535–2548

    Google Scholar 

  • Aruldoss M, Lakshmi TM, Venkatesan VP (2013) A survey on multi criteria decision making and its application. Am J Inf Syst 1(1):31–43

    Google Scholar 

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

    MATH  Google Scholar 

  • Chan KY, Kwong CK, Hu BQ (2012) Market segmentation and ideal point identification for new product design using fuzzy data compression and fuzzy clustering methods. Appl Soft Comput 12(4):1371–1378

    Google Scholar 

  • Cuong BC (2014) Picture fuzzy sets. J Comput Sci Cybern 30(4):409–420

    Google Scholar 

  • Cuong BC, Van Hai P (2015) Some fuzzy logic operators for picture fuzzy sets. In: 2015 seventh international conference on knowledge and systems engineering (KSE), pp 132–137. IEEE

  • Duong TTT, Phong LT, Hoi LQ, Thao NX (2020) A novel model based on similarity measure and quality function deployment on interval neutrosophic sets for evaluation and selection market segments. J Intell Fuzzy Syst 38:5203–5214

    Google Scholar 

  • Ejegwa PA, Akubo AJ, Joshua OM (2014) Intuitionistic fuzzy set and its application in career determination via normalized Euclidean distance method. Eur Sci J ESJ 10(15):6

    Google Scholar 

  • Faghihi F (2007) Generalization of the dissimilarity measure of fuzzy sets. In: International mathematical forum, Vol 2, No 68, pp 3395–3400

  • Ganie AH, Singh S, Bhatia PK (2020) Some new correlation coefficients of picture fuzzy sets with applications. Neural Comput Appl 1:1–17

    Google Scholar 

  • Griffith RL, Pol LG (1994) Segmenting industrial markets. Ind Mark Manag 23(1):39–46

    Google Scholar 

  • Hanafizadeh P, Mirzazadeh M (2011) Visualizing market segmentation using self-organizing maps and Fuzzy Delphi method—ADSL market of a telecommunication company. Expert Syst Appl 38(1):198–205

    Google Scholar 

  • Hatzimichailidis AG, Papakostas GA, Kaburlasos VG (2012) A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems. Int J Intell Syst 27(4):396–409

    Google Scholar 

  • Joshi R, Kumar S, Gupta D, Kaur H (2018) A Jensen-α-norm dissimilarity measure for intuitionistic fuzzy sets and its applications in multiple attribute decision making. Int J Fuzzy Syst 20(4):1188–1202

    MathSciNet  Google Scholar 

  • Kahraman C, Onar SC, Oztaysi B (2015) Fuzzy multicriteria decision-making: a literature review. Int J Comput Intell Syst 8(4):637–666

    MATH  Google Scholar 

  • Kotler P (1980) Marketing management—analysis, planning, and control, 4th edn. Prentice-Hall, London

    Google Scholar 

  • Kotler P, Armstrong G (2003) Principles of marketing, 10th edn. Prentice-Hall, Upper Saddle River

    Google Scholar 

  • Li DF (2004) Some measures of dissimilarity in intuitionistic fuzzy structures. J Comput Syst Sci 68(1):115–122

    MathSciNet  MATH  Google Scholar 

  • Li Y, Qin K, He X (2014) Dissimilarity functions and divergence measures between fuzzy sets. Inf Sci 288:15–26

    MathSciNet  MATH  Google Scholar 

  • Lindblad J, Sladoje N (2014) Linear time distances between fuzzy sets with applications to pattern matching and classification. IEEE Trans Image Process 23(1):126–136

    MathSciNet  MATH  Google Scholar 

  • Maheshwari S, Srivastava A (2016) Study on divergence measures for intuitionistic fuzzy sets and its application in medical diagnosis. J Appl Anal Comput 6(3):772–789

    MathSciNet  MATH  Google Scholar 

  • Mahmood S (2016) Dissimilarity fuzzy soft points and their applications. Fuzzy Inf Eng 8(3):281–294

    MathSciNet  Google Scholar 

  • McDonald M, Dunbar I (2004) Market segmentation how to do it how to do profit from it. Elsevier, New York

    Google Scholar 

  • Meng F, Wang C, Chen X, Zhang Q (2015) Correlation coefficients of interval-valued hesitant fuzzy sets and their application based on the Shapley function. Int J Intell Syst 31(1):17–43

    Google Scholar 

  • Montes I, Pal NR, Janiš V, Montes S (2015) Divergence measures for intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 23(2):444–456

    Google Scholar 

  • Muthukumar P, Krishnan GSS (2016) A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis. Appl Soft Comput 41:148–156

    Google Scholar 

  • Nguyen H (2016) A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition. Expert Syst Appl 45:97–107

    Google Scholar 

  • Nguyen HD, Le SH, Pham TH (2016) Some improvements of fuzzy clustering algorithms using picture fuzzy sets and applications for geographic data clustering. VNU J Sci Comput Sci Commun Eng 32(3):32–38

    Google Scholar 

  • Phuong PTM, Thong PH (2018) Theoretical analysis of picture fuzzy clustering: convergence and property. J Comput Sci Cybern 1(1):17–32

    Google Scholar 

  • Singh P (2015) Correlation coefficients for picture fuzzy sets. J Intell Fuzzy Syst 28(2):591–604

    MathSciNet  MATH  Google Scholar 

  • Smith WR (1956) Product differentiation and market segmentation as alternative marketing strategies. J Market 21(1):3–8

    Google Scholar 

  • Son LH (2015) A novel Kernel fuzzy clustering algorithm for geo-demographic analysis. Inf Sci 317:202–223

    Google Scholar 

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

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Son LH, Viet PV, Hai PV (2017) Picture inference system: a new fuzzy inference system on picture fuzzy set. Appl Intell. https://doi.org/10.1007/s10489-016-0856-1

    Article  Google Scholar 

  • Thao NX (2019) Similarity measures of picture fuzzy sets based on entropy and their application in MCDM. Pattern Anal Appl. https://doi.org/10.1007/s10044-019-00861-9

    Article  Google Scholar 

  • Thao NX, Dinh NV (2015) Rough picture fuzzy set and picture fuzzy topologies. J Comput Sci Cybern 31(3):245–253

    Google Scholar 

  • Thao NX, Duong TTT (2019) Selecting target market by similar measures in interval intuitionistic fuzzy set. Technol Econ Dev Econ 25:934–950

    Google Scholar 

  • Thao NX, Ali M, Nhung LT, Gianey HK, Smarandache F (2019) A new multi-criteria-decision making algorithm for medical diagnosis and classification problems using divergence measure of picture fuzzy sets. J Intell Fuzzy Syst 37(6):7785–7796

    Google Scholar 

  • Tian ZP, Wang JQ, Zhang HY (2018) Hybrid single-valued neutrosophic MCGDM with QFD for market segment evaluation and selection. J Intell Fuzzy Syst 34:177–187

    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 4(3):23–41

    Google Scholar 

  • Van Dinh N, Thao NX, Chau NM (2015) On the picture fuzzy database: theories and application. J. Sci 13(6):1028–1035

    Google Scholar 

  • Van Dinh N, Thao NX, Chau MN (2017) Distance and dissimilarity measure of picture fuzzy sets. In: FAIR’10, pp 104–109

  • Wei G (2016) Picture fuzzy cross-entropy for multiple attribute decision making problems. J Bus Econ Manag 17(4):491–502

    Google Scholar 

  • Wei G (2017a) Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making. Informatica 28(3):547–564

    MATH  Google Scholar 

  • Wei G (2017b) Picture fuzzy aggregation operators and their application to multiple attribute decision making. J Intell Fuzzy Syst 33:713–724

    MATH  Google Scholar 

  • Wei G (2018) Some similarity measures for picture fuzzy sets and their applications. Iranian J Fuzzy Syst 15(1):77–89

    MathSciNet  MATH  Google Scholar 

  • Wei GW, Gao H (2018) The generalized Dice similarity measures for picture fuzzy sets and their applications. Informatica 29(1):1–18

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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Authors and Affiliations

  1. Banking Academy, Ha Noi, Vietnam

    Truong Thi Thuy Duong

  2. Institute of Research and Development, Duy Tan University, Danang, 550000, Vietnam

    Nguyen Xuan Thao

  3. The Faculty of Information Technology, Duy Tan University, Danang, 550000, Vietnam

    Nguyen Xuan Thao

Authors
  1. Truong Thi Thuy Duong
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  2. Nguyen Xuan Thao
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Contributions

Duong and Thao discussed and constructed the measures, found their applications and wrote the paper together.

Corresponding author

Correspondence to Truong Thi Thuy Duong.

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The authors declare that there is no conflict of interest regarding the publication of this paper.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by A. Di Nola.

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Appendix

Appendix

See Tables 8 and 9.

Table 8 The evaluations of experts for four segments (Thao and Duong 2019)
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Table 9 The evaluations of experts for important degree of criteria (Thao and Duong 2019)
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Duong, T.T.T., Thao, N.X. A novel dissimilarity measure on picture fuzzy sets and its application in multi-criteria decision making. Soft Comput 25, 15–25 (2021). https://doi.org/10.1007/s00500-020-05405-6

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