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Research on K-medoids Algorithm with Probabilistic-based Expressions and Its Applications

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Abstract

Nowadays, the decision environment is becoming more and more complicated due to the development of society and science, and people receiving different types of information every day and gradually form their unique cognitions and knowledge backgrounds. In this situation, people tend to provide their preferences or evaluations through multiple information expression formats, such as the probabilistic hesitant fuzzy sets, the probabilistic linguistic term sets and the probabilistic interval preference ordering sets. In this paper, we deeply investigate the relationships among these three probabilistic-based expressions and introduce two transformation functions for them in order to make the information formats unified. Besides, for the probabilistic hesitant fuzzy sets, three novel distance measures are proposed, i.e., the minimal distance, the central distance, and the improved distance, which are useful tools to measure the difference between the probabilistic hesitant fuzzy elements. In order to fuse the different formats of information and get valuable results from it, the K-medoids algorithm for the probabilistic-based expressions is developed. The algorithm is applied to classify the merchants on the website of Dianping.com, so that the results can be provided to customers to help them make decisions.

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References

  1. Tan RQ, Zhang WD, Yang LH, Chen SQ (2019) Multi-attribute decision-making method based on prospect theory in heterogeneous information environment and its application in typhoon disaster assessment. Int J Comput Intell Syst 12:881–896

    Article  Google Scholar 

  2. Xu ZS (2007) Multiple-attribute group decision making with different formats of preference information on attributes. IEEE Trans Syst Man Cybernet B 37(6):1500–1511

    Article  Google Scholar 

  3. Yue C (2019) A normalized projection-based group decision-making method with heterogeneous decision information and application to software development effort assessment. Appl Intell 49:3587–3605

    Article  Google Scholar 

  4. Xu ZS, Cai XQ, Liu SS (2011) Nonlinear programming model integrating different preference structures. IEEE Trans Syst Man Cybernet A 41:169–177

    Article  Google Scholar 

  5. Chiclana F, Herrera F, Herrera-Viedma E (1998) Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets Syst 97:33–48

    Article  MathSciNet  Google Scholar 

  6. Chen X, Zhang H, Dong Y (2015) The fusion process with heterogeneous preference structures in group decision making: A survey. Inform Fusion 24:72–83

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8:199–249

    Article  MathSciNet  Google Scholar 

  9. Brans JP, Mareschal B (2016) PROMETHEE methods. Multiple Criteria Decision Analysis State of the Art Surveys 78:163–186

  10. Chiclana F, Herrera F, Herrera-Viedma E, Poyatos MC (1996) A classification method of alternatives for multiple preference ordering criteria based on fuzzy majority. J Math 4:801–814

    MathSciNet  MATH  Google Scholar 

  11. Xu ZS (2007) Approaches to multiple attribute decision making with intuitionistic fuzzy preference information. Syst Eng Theory Pract 27(11):62–71

    Article  Google Scholar 

  12. Delgado M, Herrera F, Herrera-Viedma E (1998) Combining numerical and linguistic information in group decision making. Inf Sci 107:177–194

    Article  MathSciNet  Google Scholar 

  13. Zhu B (2014) Decision making methods and applications. Southeast University

    Google Scholar 

  14. Pang Q, Wang H, Xu ZS (2016) Probabilistic linguistic term sets in multi-attribute group decision making. Inf Sci 269:128–143

    Article  Google Scholar 

  15. He Y, Xu ZS, Jiang WL (2017) Probabilistic interval preference ordering sets in multi-criteria group decision making. Int J Uncert Fuzz Knowledge-Based Syst 25:189–212

    Article  Google Scholar 

  16. Wu ZB, Jin BM, Xu JP (2018) Local feedback strategy for consensus building with probability-hesitant fuzzy preference relations. Appl Soft Comput 67:691–705

    Article  Google Scholar 

  17. Ding J, Xu ZS, Zhao N (2017) An interactive approach to probabilistic hesitant fuzzy multi-attribute group decision making with incomplete weight information. J Intell Fuzzy Syst 32:2523–2536

    Article  Google Scholar 

  18. Xie WY, Xu ZS, Ren ZL, Wang H (2018) Probabilistic linguistic analytic hierarchy process and its application on the performance assessment of Xiongan new area. Int J Inf Technol Decis Mak 10:1–32

    Google Scholar 

  19. Chang J Y, Liao H C, Mi XM, Al-Barakati A (2021) A probabilistic linguistic TODIM method considering cumulative probability-based Hellinger distance and its application in waste mobile phone recycling. Appl Intell. https://doi.org/10.1007/s10489-021-02185-w

  20. Zhang YX, Xu ZS, Wang H, Liao HC (2016) Consistency-based risk assessment with probabilistic linguistic preference relation. Appl Soft Comput 49:817–833

    Article  Google Scholar 

  21. Zhang Z, Guo C, Martínez L (2017) Managing multigranular linguistic distribution assessments in large-scale multiattribute group decision making. IEEE Trans Syst Man Cybernet Syst 47:3063–3076

    Article  Google Scholar 

  22. Wu ZB, Xu JP (2016) Possibility distribution-based approach for MAGDM with hesitant fuzzy linguistic information. IEEE Trans Cybernet 46:694–705

    Article  Google Scholar 

  23. Zhang G, Dong Y, Xu Y (2014) Consistency and consensus measures for linguistic preference relations based on distribution assessments. Inform Fusion 17:46–55

    Article  Google Scholar 

  24. Huang F, Zhu Q, Zhou J, Tao J, Zhou X C, Jin D, Tan X C Wang L Z (2017) Research on the parallelization of the DBSCAN clustering algorithm for spatial data mining based on the spark platform. Remote Sens 9:1301

  25. Peng H, Li B, Ling H, Hu W, Xiong WH, Maybank SJ (2017) Salient object detection via structured matrix decomposition. IEEE Trans Pattern Analy Mach Intell 39:818–832

    Article  Google Scholar 

  26. Zhang D, Hsu CH, Chen M, Chen Q, Xiong N, Lloret J (2017) Cold-start recommendation using bi-clustering and fusion for large-scale social recommender systems. IEEE Trans Emerg Top Comput 2:239–250

    Article  Google Scholar 

  27. Nima G S, LourenzuttI R, Fayek, AR (2020) A fuzzy clustering algorithm for developing predictive models in construction applications. Appl Soft Comput 96:106679

  28. Xu Y, Yang CJ, Peng SL, Nojima Y (2020) A hybrid two-stage financial stock forecasting algorithm based on clustering and ensemble learning. Appl Intell 50:3852–3867

    Article  Google Scholar 

  29. Kollem S, Reddy KR, Rao DS (2020) An optimized SVM based possibilistic fuzzy c-means clustering algorithm for tumor segmentation. Multimed Tools Appl 80:409–437

    Article  Google Scholar 

  30. Arora P, Deepali D, Varshney S (2016) Analysis of K-Means and K-Medoids algorithm for big data. Procedia Comput Sci 78:507–512

    Article  Google Scholar 

  31. Park HS, Jun CH (2009) A simple and fast algorithm for K-medoids clustering. Expert Syst Appl 36:3336–3341

    Article  Google Scholar 

  32. Krishnapuram R, Joshi A, Nasraoui O, Yi L (2001) Low-complexity fuzzy relational clustering algorithms for Web mining. IEEE Trans Fuzzy Syst 9:595–607

    Article  Google Scholar 

  33. Yu D, Liu G, Guo M, Liu X (2017) An improved K-medoids algorithm based on step increasing and optimizing medoids. Expert Syst Appl 92:464–473

    Article  Google Scholar 

  34. Diamond P (1994) Kloeden P. Metric Spaces of Fuzzy Sets, Theory and Applications. World Scientific

    Google Scholar 

  35. Krawczyk JB (1998) Multistage fuzzy control. Control Eng Pract 2:299

    Google Scholar 

  36. Kacprzyk J (1996) Multistage fuzzy control: a prescriptive approach. Wiley

  37. Tseng VS, Kao CP (2007) A novel similarity-based fuzzy clustering algorithm by integrating PCM and Mountain Method. IEEE Trans Fuzzy Syst 15:1188–1196

    Article  Google Scholar 

  38. Zhang M, Zhang W, Sicotte H, Yang P (2016) A new validity measure for a correlation-based fuzzy C-means clustering algorithm. Int Conf IEEE:3865–3868

  39. Yang MS, Nataliani Y (2017) A feature-reduction fuzzy clustering algorithm based on feature-weighted entropy. IEEE Trans Fuzzy Syst 26:817–835

    Article  Google Scholar 

  40. Gou XJ, Xu ZS, Liao HC (2016) Multiple criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information. Soft Comput 21:1–15

    MATH  Google Scholar 

  41. Ahmed MN, Yamany SM, Mohamed N, Farag AA, Moriarty T (2002) A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data. IEEE Trans Med Imaging 21:193–199

    Article  Google Scholar 

  42. Shalaby M, Mohammed A, Kassem S (2021) Supervised fuzzy C-means techniques to solve the capacitated vehicle routing problem. Int Arab J Inform Technol. https://doi.org/10.34028/iajit/18/3A/9

  43. Wang XZ, Wang YD, Wang LJ (2004) Improving fuzzy c-means clustering based on feature-weight learning. Pattern Recogn Lett 25:1123–1132

    Article  Google Scholar 

  44. Bezdek J. C. (1981) Pattern Recognition With Fuzzy Objective Function Algorithms

  45. Gao J, Xu ZS, Liao HC (2017) A dynamic reference point method for emergency response under hesitant probabilistic fuzzy environment. Int J Fuzzy Syst 19:1261–1278

    Article  Google Scholar 

  46. Xie XL, Beni G (1991) A validity measure for fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 13:841–847

    Article  Google Scholar 

  47. Rousseeuw PJ (1999) Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J Comput Appl Math 20:53–65

    Article  Google Scholar 

  48. Zhou SB, Zhenyuan XU, Tang XQ (2010) Method for determining optimal number of clusters in K-means clustering algorithm. Comput Eng Appl 30:1995–1998

    Google Scholar 

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Authors and Affiliations

  1. Sichuan University West China Second University Hospital, Chengdu, 610041, Sichuan, China

    Yue He

  2. Business School, Sichuan University, Chengdu, 610064, China

    Zeshui Xu & Nana Liu

Authors
  1. Yue He
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  2. Zeshui Xu
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  3. Nana Liu
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Correspondence to Zeshui Xu.

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He, Y., Xu, Z. & Liu, N. Research on K-medoids Algorithm with Probabilistic-based Expressions and Its Applications. Appl Intell 52, 12016–12033 (2022). https://doi.org/10.1007/s10489-021-02937-8

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