A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread

Information Sciences

Volumn 179, Issue 23, 2009, Pages 3964-3972

  Trutschnig, Wolfgang ^a   González Rodríguez, Gil ^b   Colubi, Ana ^c   Gil, María Ángeles ^c  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b EUROPEAN CENTRE FOR SOFT COMPUTING   (Spain)

^c UNIVERSITY OF OVIEDO   (Spain)

Author keywords

Convex compact sets; Distance; Fuzzy sets; Generalized mid and spread; Imprecise data analysis; Support functions

Indexed keywords

CONVEX COMPACT SETS; DISTANCE; GENERALIZED MID AND SPREAD; IMPRECISE DATA ANALYSIS; SUPPORT FUNCTIONS;

METRIC SYSTEM; POWDERS;

FUZZY SETS;

EID: 70349097188     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2009.06.023     Document Type: Article

References (23)

1. Alonso M.C., Brezmes T., Lubiano M.A., and Bertoluzza C. A generalized real-valued measure of the inequality associated with a fuzzy random variable. International Journal of Approximate Reasoning 26 (2001) 47-66
2. Bertoluzza C., Corral N., and Salas A. On a new class of distances between fuzzy numbers. Mathware Soft Computing 2 (1995) 71-84
3. Baudrit C., Guyonnet D., and Dubois D. Joint propagation of variability and imprecision in assessing the risk of groundwater contamination. Journal of Contaminant Hydrology 93 (2007) 72-84
4. A. Colubi, Statistical inference about the means of fuzzy random variables: applications to the analysis of fuzzy- and real-valued data, Fuzzy Sets and Systems, doi:10.1016/j.fss.2007.12.019.
5. Colubi A., Domínguez-Menchero J.S., López-Díaz M., and Ralescu D.A. On the formalization of fuzzy random variables. Information Sciences 133 (2001) 3-6
6. Diamond P., and Kloeden P. Metric Spaces of Fuzzy Sets: Theory and Applications (1994), World Scientific, Singapore
7. J. Elstrodt, Mass- und Integrationstheorie, Springer, Berlin, Heidelberg, New York, 2009.
8. Fei W. Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients. Information Sciences 177 20 (2007) 4329-4337
9. García D., Lubiano M.A., and Alonso M.C. Estimating the expected value of fuzzy random variables in the stratified random sampling from finite populations. Information Sciences 138 (2001) 165-184
10. Gil M.A. Fuzzy random variables. Information Sciences 133 (2001) 1-2
11. Gil M.A., Lubiano M.A., Montenegro M., and López-García M.T. Least squares fitting of an affine function and strength of association for interval-valued data. Metrika 56 (2002) 97-111
12. Gil M., Montenegro M., González-Rodríguez G., Colubi A., and Casals M. Bootstrap approach to the multi-sample test of means with imprecise data. Computational Statistics & Data Analysis 51 1 (2006) 148-162
13. González-Rodríguez G., Colubi A., and Trutschnig W. Simulation of fuzzy random variables. Information Sciences 179 (2009) 642-653
14. González-Rodríguez G., Montenegro M., Colubi A., and Gil M.A. Bootstrap techniques and fuzzy random variables: synergy in hypothesis testing with fuzzy data. Fuzzy Sets and Systems 157 (2006) 2608-2613
15. Klement E.P., Puri M.L., and Ralescu D.A. Limit theorems for fuzzy random variables. Proceedings of the Royal Society of London Series A 407 (1986) 171-182
16. Krätschmer V. Some complete metrics on spaces of fuzzy subsets. Fuzzy Sets and Systems 130 (2002) 357-365
17. Montenegro M., Casals M.R., Lubiano M.A., and Gil M.A. Two-sample hypothesis tests of means of a fuzzy random variable. Information Sciences 133 (2001) 89-100
18. Möller B., Graf W., and Beer M. Safety assessment of structures in view of fuzzy randomness. Computers and Structures 81 (2003) 1567-1582
19. Schneider R. Convex Bodies: The Brunn-Minkowski Theory (1993), Cambridge University Press
20. p metrics for compact, convex sets. Journal of Approximation Theory 45 (1985) 280-287
21. Zadeh L. The concept of a linguistic variable and its application to approximate reasoning, I. Information Sciences 8 (1975) 199-249
22. Zadeh L. Toward a generalized theory of uncertainty - an outline. Information Sciences 172 (2005) 1-40
23. Zadeh L. Is there a need for fuzzy logic?. Information Science 178 (2008) 2751-2779