As of August 2024, International Journal "Notes on Intuitionistic Fuzzy Sets" is being indexed in Scopus.
Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: March 2025.

Issue:A "family" of similarity measures for intuitionistic fuzzy set theory and mass assignment theory: Difference between revisions

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
mNo edit summary
category
Line 1: Line 1:
[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
[[Category:Publications on similarity measures|{{PAGENAME}}]]
[[Category:Publications in Notes on IFS|{{PAGENAME}}]]
[[Category:Publications in Notes on IFS|{{PAGENAME}}]]
[[Category:Publications in 2006 year|{{PAGENAME}}]]
[[Category:Publications in 2006 year|{{PAGENAME}}]]

Revision as of 14:28, 7 July 2017

shortcut
http://ifigenia.org/wiki/issue:nifs/12/1/1-23
Title of paper: A "family" of similarity measures for intuitionistic fuzzy set theory and mass assignment theory
Author(s):
Eulalia Szmidt
Systems Research Institute - Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
szmidt@ibspan.waw.pl
Jim Baldwin
Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, England
Jim.Baldwin@bristol.ac.uk
Published in: "Notes on IFS", Volume 12 (2006) Number 1, pages 1—23
Download:  PDF (199  Kb, File info)
Abstract: We remind some similarities/parallels between two of the theories dealing with widely understood (not only as randomness) uncertainty — mass assignment theory and intuitionistic fuzzy set theory. Mass assignment theory is well known tool for dealing with both probabilistic and fuzzy uncertainties whereas intuitionistic fuzzy set theory is an extension of fuzzy set theory which makes it possible to describe imprecise information. Next, we recall the measures of similarity which we have proposed for both theories. The proposed measures take into account not only a pure distance between compared elements but answer the questions if the considered elements/objects are more similar or more dissimilar (the measures take into account and compare two types of distances). It is shown that even if a distance between compared objects is small, it can happen that the objects are completely dissimilar. The disadvantage of the measures is the range of their values — not consistent with the tradition as far as the similarity measures are concerned. In this paper we propose the whole array of the new similarity measures preserving the advantages of the previously proposed similarity measures and the same time following the commonly assumed number values.
AMS Classification: 03E72
References:
  1. Atanassov K. (1983), Intuitionistic Fuzzy Sets. VII ITKR Session. Sofia (Deposed in Centr. Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian).
  2. Atanassov K. (1986), Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 20, 87—96.
  3. Atanassov K. (1989), More on intuitionistic fuzzy sets, Fuzzy Sets and Systems 33, 37—46.
  4. Atanassov K. (1994), New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61, 137—142.
  5. Atanassov K. (1999), Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag.
  6. Baldwin. J.F. (1991), Combining Evidences for Evidential Reasoning. International Journal of Intelligent Systems, 6, 569—616.
  7. Baldwin J.F. (1992a), A Calculus for mass Assignments in Evidential Reasoning. In Advances in the Dempster-Shafer Theory of Evidence. (ed. M. Fedrizzi, J. Kacprzyk, R.R. Yager), John Wiley, 513— 531.
  8. Baldwin J.F. (1992b), The Management of Fuzzy and Probabilistic Uncertainties for Knowledge Based Systems. In Encyclopaedia of AI (ed. S.A. Shapiro), John Wiley (2nd ed.) 528—537.
  9. Baldwin J.F. (1994), Mass assignments and fuzzy sets for fuzzy databases. In. Advances in the Dempster-Shafer theory of evidence. Ed. R. Yager at al. John Wiley, 577—594.
  10. Baldwin J.F., Pilsworth B.W. (1990), Semantic Unification with Fuzzy Concepts in Fril. IPMU’90, Paris.
  11. Baldwin J.F., T.P. Martin, B.W. Pilsworth (1995) FRIL — Fuzzy and Evidential Reasoning in Artificial Intelligence. John Wiley.
  12. Baldwin J.F., Lawry J., Martin T.P.(1995a), A Mass Assignment Theory of the Probability of Fuzzy Events. ITRC Report 229, University of Bristol, UK.
  13. Baldwin J.F., Coyne M.R., Martin T.P.(1995b), Intelligent Reasoning Using General Knowledge to Update Specific Information: A Database Approach. Journal of Intelligent Information Systems, 4, 281—304.
  14. Baldwin J.F., T.P. Martin T.P. (1995c), Extracting Knowledge from Incomplete Databases using the Fril Data Browser. EUFIT’95, Aachen, 111—115.
  15. Baldwin J.F., T.P. Martin (1996), FRIL as an Implementation Language for Fuzzy Information Systems. IPMU’96, Granada, 289—294.
  16. Bouchon-Meunier B., Rifgi M., and Bothorel S. (1996). General measures of comparison of objects. Fuzzy Sets and Systems, Vol. 84, No. 2, 143—153.
  17. Chen S., Yeh M. and Hsiao P. (1995). A comparison of similarity measures of fuzzy values. Fuzzy Sets and Systems, Vol. 72, No. 1, 79—89.
  18. Cross V. and Sudkamp T. (2002) Similarity and Compatibility in Fuzzy Set Theory. Assessment and Applications. (Series: Studies in Fuzziness and Soft Computing). Physica-Verlag.
  19. Dempster A.P. (1968) A generalization of Bayesian inference. J. of the Royal Statistical Society, Series B, 30, 205—247.
  20. Dengfeng L. and Chuntian C. (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, Vol. 23, 221—225.
  21. Dubois D. and Prade H. (1982) A unifying view of comparison indices in a fuzzy settheoretical framework. In R. Yager,editor, Fuzzy Set and Possibility Theory Recent Developments. Pergamon Press, New York, pp. 3—13.
  22. Kahneman D. (2002) Maps of bounded rationality: a perspective on intuitive judgment and choice. Nobel Prize Lecture, December 8, 2002.
  23. Pal N.R. and Pal S.K. (1991) Entropy: a new definition and its applications. IEEE Trans. on Systems, Man, and Cybernetics, Vol. 21, No. 5, 1260—1270.
  24. Pappis C., and Karacapilidis N. (1993). A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems, Vol. 56, 171—174.
  25. Shafer G. (1976) A Mathematical Theory of Evidence. Princeton Univ. Press.
  26. Sugeno M. (1974) Theory of Fuzzy Integrals and its Applications. Tokyo Institute of Technology, Japan.
  27. Sutherland S. (1994) Irrationality. The Enemy Within. Penguin Books.
  28. Szmidt E. (2000) Applications of Intuitionistic Fuzzy Sets in Decision Making. (D.Sc. dissertation) Techn. Univ., Sofia, 2000.
  29. Szmidt E. and Baldwin J. (2003) New Similarity Measure for Intuitionistic Fuzzy Set Theory and Mass Assignment Theory. Notes on IFSs, Vol. 9, No. 3, 60—76.
  30. Szmidt E. and Baldwin J. (2004) Entropy for Intuitionistic Fuzzy Set Theory and Mass Assignment Theory. Notes on IFSs, Vol. 10, No. 3, 15—28.
  31. Szmidt E. and Baldwin J. (2006) Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms. 2006 IEEE World Congress on Computational Intelligence, 237—243.
  32. Szmidt E. and Kacprzyk J. (1996a) Intuitionistic fuzzy sets in group decision making. Notes on IFS, Vol. 2, 15—32.
  33. Szmidt E. and Kacprzyk J. (1996c) Remarks on some applications of intuitionistic fuzzy sets in decision making. Notes on IFS, Vol.2, No.3, 22—31.
  34. E. Szmidt and J. Kacprzyk (1998a) An intuitionistic fuzzy set corresponding to a fuzzy set. Int.Journal of Uncertainty Fuzziness and Knowledge Based Systems, Vol. 6, No. 5, 427—435.
  35. Szmidt E. and Kacprzyk J. (1998a) Group DecisionMaking under Intuitionistic Fuzzy Preference Relations. Proc. IPMU’98, 172—178.
  36. Szmidt E. and Kacprzyk J. (1999). Probability of Intuitionistic Fuzzy Events and their Applications in Decision Making. Proc. of EUSFLAT-ESTYLF Conf. 1999. Palma de Mallorca, 457—460.
  37. Szmidt E. and Kacprzyk J. (1999b) - A Concept of a Probability of an Intuitionistic Fuzzy Event. Proc. of FUZZ-IEEE’99 - 8th IEEE International Conference on Fuzzy Systems, August 22-25, 1999 Seoul, Korea, III 1346—1349.
  38. Szmidt E. and Kacprzyk J. (2000) Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 114, No. 3, 505—518.
  39. E.Szmidt and J. Kacprzyk (2000b) On Measures of Consensus Under Intuitionistic Fuzzy relations. Proc. IPMU’2000, Madrid, July 3-7, 641—647.
  40. E. Szmidt and J. Kacprzyk (2001) — Szmidt E., Kacprzyk J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, vol. 118, No. 3, 2001, 467—477.
  41. E.Szmidt and J. Kacprzyk (2002a) — Analysis of Agreement in a Group of Experts via Distances Between Intuitionistic Fuzzy Preferences. Proc. IPMU’2002, Annecy, France, 1-5 July, 1859—1865.
  42. E.Szmidt and J. Kacprzyk (2002b) An Intuitionistic Fuzzy Set Based Approach to Intelligent Data Analysis (an application to medical diagnosis). In A. Abraham, L. Jain, J. Kacprzyk (Eds.): Recent Advances in Intelligent Paradigms and Applications. Springer-Verlag, 57—70.
  43. E.Szmidt and J. Kacprzyk (2002c) Evaluation of Agreement in a Group of Experts via Distances Between Intuitionistic Fuzzy Sets. Proc. IS’2002 — Int. IEEE Symposium: Intelligent Systems, Varna, Bulgaria, IEEE Catalog Number 02EX499, 166—170.
  44. Szmidt E. and Kacprzyk J. (2004) Similarity of intuitionistic fuzzy sets and the Jaccard coefficient. Proc. 10th Int. Conf. IPMU 2004, Perugia, Italy, 1405—1412.
  45. Szmidt E. and Kacprzyk J. (2005) A New Concept of a Similarity Measure for Intuitionistic Fuzzy Sets and its Use in Group Decision Making. In V. Torra, Y. Narukawa, S. Miyamoto (Eds.): Modelling Decisions for Artificial Intelligence. LNAI 3558, Springer 2005, 272—282.
  46. Tversky A. (1977) Features of similarity. Psychol. Rev. Vol. 84, 327—352.
  47. Wang X., De Baets B., and Kerre E. (1995). A comparative study of similarity measures. Fuzzy Sets and Systems, Vol.73, No. 2, 259—268.
  48. Yager R.R. (1979) - On the measure of fuziness and negation. Part I: Membership in the unit interval. Internat. J. of Gen. Systems, Vol. 5, 189—200.
  49. Yager R.R. (1982) Measuring tranguillity and anxiety in decision making: An application of fuzzy sets. Inter. J. of Gen. Systems, 8, 139—146.
  50. Yager R.R. (1990) Ordinal measures of specifity. Inter. J. of Gen. Systems, 17, 57—72.
  51. Yager R.R. (1991) Similarity based measures of specifity. Inter. J. of Gen. Systems, 19, 91—106.
  52. Zadeh L.A. (1965) Fuzzy sets. Information and Control, 8, 338—353.
  53. Zadeh L.A. (1978) Fuzzy Sets as the Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1, 3—28.
  54. Zwick R., Carlstein E., Budescu D. (1987). Measures of similarity among fuzzy concepts: A comparative analysis. Int. J. of Approx. Reasoning, Vol. 1, 221—242.
Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.

Retrieved from "https://ifigenia.org/index.php?title=Issue:A_%22family%22_of_similarity_measures_for_intuitionistic_fuzzy_set_theory_and_mass_assignment_theory&oldid=9275"