An information-based approach to handle various types of uncertainty in fuzzy bodies of evidence


Autoři: Atiye Sarabi-Jamab aff001;  Babak N. Araabi aff002
Působiště autorů: School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran aff001;  Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran aff002
Vyšlo v časopise: PLoS ONE 15(1)
Kategorie: Research Article
doi: 10.1371/journal.pone.0227495

Souhrn

Fuzzy evidence theory, or fuzzy Dempster-Shafer Theory captures all three types of uncertainty, i.e. fuzziness, non-specificity, and conflict, which are usually contained in a piece of information within one framework. Therefore, it is known as one of the most promising approaches for practical applications. Quantifying the difference between two fuzzy bodies of evidence becomes important when this framework is used in applications. This work is motivated by the fact that while dissimilarity measures have been surveyed in the fields of evidence theory and fuzzy set theory, no comprehensive survey is yet available for fuzzy evidence theory. We proposed a modification to a set of the most discriminative dissimilarity measures (smDDM)-as the minimum set of dissimilarity with the maximal power of discrimination in evidence theory- to handle all types of uncertainty in fuzzy evidence theory. The generalized smDDM (FsmDDM) together with the one previously introduced as fuzzy measures make up a set of measures that is comprehensive enough to collectively address all aspects of information conveyed by the fuzzy bodies of evidence. Experimental results are presented to validate the method and to show the efficiency of the proposed method.

Klíčová slova:

Algorithms – Decision making – Decision theory – Entropy – Information theory – Monte Carlo method – Reasoning – Surveys


Zdroje

1. Dempster A.P., Upper and lower probabilities induced by a multivariate mapping.pdf, Ann. Math. Stat. 38 (1967) 325–339.

2. Shafer G., A Mathematical Theory of Evidence, 1976.

3. Denœux T., Decision-making with belief functions: A review, Int. J. Approx. Reason. 109 (2019) 87–110.

4. Tessem B., Approximations for efficient computation in the theory of evidence, Artif. Intell. 61 (1993) 315–329.

5. Sarabi-Jamab A., Araabi B.N., Information-Based Evaluation of Approximation Methods in Dempster-Shafer Theory, Int. J. Uncertainty, Fuzziness Knowledge-Based Syst. 24 (2016) 503–535.

6. Petit-Renaud S., Denœux T., Nonparametric regression analysis of uncertain and imprecise data using belief functions, Int. J. Approx. Reason. 35 (2004) 1–28.

7. Sarabi-Jamab A., Araabi B.N., PiLiMoT: A modified combination of LoLiMoT and PLN learning algorithms for local linear neurofuzzy modeling, J. Control Sci. Eng. 2011 (2011).

8. Guo H., Shi W., Deng Y., Evaluating Sensor Reliability in Classification Problems Based on Evidence Theory, 36 (2006) 970–981.

9. Sarabi-Jamab A., Araabi B.N., How to decide when the sources of evidence are unreliable: A multi-criteria discounting approach in the Dempster–Shafer theory, Inf. Sci. (Ny). 448–449 (2018) 233–248.

10. Deng Y., Sadiq R., Jiang W., Tesfamariam S., Risk analysis in a linguistic environment: A fuzzy evidential reasoning-based approach, Expert Syst. Appl. 38 (2011) 15438–15446.

11. Martin A., Osswald C., Ea E.I., Ix Q.C.G.J., Conflict measure for the discounting operation on belief functions, (n.d.) 1003–1010.

12. Liu Z., Liu Y., Dezert J., Cuzzolin F., Evidence Combination Based on Credal Belief Redistribution for Pattern Classification, IEEE Trans. Fuzzy Syst. (2019) 1–15.

13. Liu Z., Pan Q., Dezert J., Martin A., Combination of classifiers with optimal weight based on evidential reasoning, IEEE Trans. Fuzzy Syst. 6706 (2017) 1–15.

14. Denœux T., Masson M., EVCLUS: Evidential Clustering of Proximity Data, 34 (2004) 95–109.

15. Hwang C., Yang M., Generalization of Belief and Plausibility Functions to Fuzzy Sets Based on the Sugeno Integral, Intell. Syst. 22 (2007) 1215–1228.

16. Ishizuka M., FU K.S., Inference Procedmes under Uncertainty for the Problem-Reduction Method*, Inf. Sci. (Ny). 28 (1982) 179–206.

17. Lucas C., Araabi B.N., Member S., Generalization of the Dempster–Shafer Theory: A Fuzzy-Valued Measure, 7 (1999) 255–270.

18. Ogawa H., Fu K.S., An Inexact Inference For Damage Assessment Of Existing Structurest, Int. J. Man. Mach. Stud. 22 (1985) 295–306.

19. Smets P., The Degree of Belief in a Fuzzy Event, Inf. Sci. (Ny). 25 (1981) 1–19.

20. Yager R.R., Generalized Probabilities of Fuzzy Events from Fuzzy Belief Structures, Inf. Sci. (Ny). 28 (1982) 45–62.

21. Deng X., Jiang W., Evaluating Green Supply Chain Management Practices Under Fuzzy Environment: A Novel Method Based on D Number Theory, Int. J. Fuzzy Syst. (2019).

22. Sarabi-Jamab A., Araabi B.N., Augustin T., Information-based dissimilarity assessment in Dempster-Shafer theory, Knowledge-Based Syst. 54 (2013).

23. Bloch I., On fuzzy distances and their use in image processing under imprecision, Pattern Recognit. 32 (1999) 1873–1895.

24. Campos L.M., Lamata M.T., Moral S., Distances between fuzzy measures through associated probabilities: some applications, Fuzzy Sets Syst. 35 (1990) 57–68.

25. Zadeh L.A., A Simple View of the Dempster-Shafer Theory of Evidence and its Implication for the Rule of Combination, AI Mag. 7 (1986) 85–90.

26. Xiao F., Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy, Inf. Fusion. 46 (2019) 23–32.

27. Zadeh L.A., FUZZY SETS AND INFORMATION GRANULARITY, Fuzzey Sets, Fuzzy Logic, Fuzzy Syst. (1996) 433–448.

28. Zadeh L.A., Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets Syst. 90 (1997) 111–127.

29. DE Luca A., Termini S., A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory, Inf. Control. 20 (1972) 301–312.

30. Yen J., Generalizing the Dempster- S hafer of Fuzzy Sets, IEEE Trans. Cybern. Man, Cybern. 20 (1990) 559–570.

31. Yang M.S., Chen T.C., Wu K.L., Generalized belief function, plausibility function, and Dempster’s combinational rule to fuzzy sets, Int. J. Intell. Syst. 18 (2003) 925–937.

32. Liu W., Analyzing the degree of conflict among belief functions, Artif. Intell. 170 (2006) 909–924.

33. Jousselme A.L., Maupin P., Distances in evidence theory: Comprehensive survey and generalizations, Int. J. Approx. Reason. 53 (2012) 118–145.

34. Pal N.R., Bezdek J.C., Uncertainty Measures for Evidential Reasoning II: A New Measure of Total Uncertainty, (1993) 1–16.

35. Wen C., Wang Y., Xu X., Fuzzy Information Fusion Algorithm of Fault Diagnosis Based on Similarity Measure of Evidence\rAdvances in Neural Networks—ISNN 2008, 5264 (2008) 506–515.

36. Yager R.R., ENTROPY AND SPECIFICITY IN A MATHEMATICAL THEORY OF EVIDENCE, Int. J. Gen. Syst. 9 (1983) 249–260.

37. George T., Pal N.R., QUANTIFICATION OF CONFLICT IN DEMPSTER-SHAFER FRAMEWORK: A NEW APPROACH, Int. J. Gen. Syst. 24 (1996) 407–423.

38. Hoehle U., A General Theory of Fuzzy Plausibility measures, J. Math. Anal. Appl. 127 (1987) 346–364.

39. Burkov A., Michaud G., Valin P., An Empirical Study of Uncertainty Measures in the Fuzzy Evidence Theory, Decis. Support Syst. (2011) 453–460.

40. Zhu H., Basir O., A novel fuzzy evidential reasoning paradigm for data fusion with applications in image processing, Soft Comput. 10 (2006) 1169–1180.

41. Gupta P., Sheoran A., Harmonic Measures of Fuzzy Entropy and their Normalization, Int. J. Stat. Math. 10 (2014) 47–51.

42. Ebanks B.R., On Measure of fuzziness and their Representations, J. Math. Anal. Appl. 94 (1983) 24–37.

43. Kapur J.N., Measures of Fuzzy Information, Mathematical Science Trust Society, (1997).

44. Kaufmann A., Introduction to the Theory of Fuzzy Subsets, (1975).

45. Parkash O., Sharma P.K., Mahajan R., New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle, Inf. Sci. (Ny). 178 (2008) 2389–2395.

46. Yager R.R., Filev D.P., Including Probabilistic Uncertainty in Fuzzy Logic Controller Modeling Using Dempster-Shafer Theory, IEEE Trans. Syst. Man Cybern. 25 (1995) 1221–1230.


Článek vyšel v časopise

PLOS One


2020 Číslo 1