| Title:
|
Estimating the fuzzy inequality associated with a fuzzy random variable in random samplings from finite populations (English) |
| Author:
|
López-García, Hortensia |
| Author:
|
Gil, María Angeles |
| Author:
|
Corral, Norberto |
| Author:
|
López, María Teresa |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
[149]-161 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In a recent paper we have introduced the fuzzy hyperbolic inequality index, to quantify the inequality associated with a fuzzy random variable in a finite population. In previous papers, we have also proven that the classical hyperbolic inequality index associated with real-valued random variables in finite populations can be unbiasedly estimated in random samplings. The aim of this paper is to analyze the problem of estimating the population fuzzy hyperbolic index associated with a fuzzy random variable in random samplings from finite populations. This analysis will lead us to conclude that an unbiased (up to additive equivalences) estimator of the population fuzzy hyperbolic inequality index can be constructed on the basis of the sample index and the expected value of the values fuzzy hyperbolic inequality in the sample. (English) |
| Keyword:
|
fuzzy random variable |
| Keyword:
|
estimation |
| Keyword:
|
fuzzy hyperbolic inequality |
| MSC:
|
04A72 |
| MSC:
|
62A86 |
| MSC:
|
62D05 |
| MSC:
|
62D99 |
| idZBL:
|
Zbl 1274.62096 |
| idMR:
|
MR1621507 |
| . |
| Date available:
|
2009-09-24T19:14:40Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135194 |
| . |
| Reference:
|
[1] Bourguignon F.: Decomposable income inequality measures.Econometrica 47 (1979), 901–920 Zbl 0424.90013, MR 0537636, 10.2307/1914138 |
| Reference:
|
[2] Caso C., Gil M. A.: Estimating income inequality in the stratified sampling from complete data.Part I: The unbiased estimation and applications. Kybernetika 25 (1989), 298–311 Zbl 0682.62087, MR 1015034 |
| Reference:
|
[3] Caso C., Gil M. A.: Estimating income inequality in the stratified sampling from complete data.Part II: The asymptotic behaviour and the choice of sample size. Kybernetika 25 (1989), 312–319 Zbl 0682.62087, MR 1015035 |
| Reference:
|
[4] Corral N., Gil M. A., López-García H.: The fuzzy hyperbolic inequality index of fuzzy random variables in finite populations.Mathware $\&$ Soft Computing 3 (1996), 329–339 Zbl 0859.60004, MR 1489755 |
| Reference:
|
[5] Cox E.: The Fuzzy Systems Handbook.Academic Press, Cambridge 1994 Zbl 0847.68111 |
| Reference:
|
[6] Gastwirth J. L., Nayak T. K., Krieger A. M.: Large sample theory for the bounds on the Gini and related indices of inequality estimated from grouped data.J. Business Econom. Statist. 4 (1986), 269–273 |
| Reference:
|
[7] Gil M. A., Gil P.: On some information measures of degree ${\beta = 2}$; Estimation in simple–stage cluster sampling.Statist. Probab. Lett. 8 (1989), 157–162 Zbl 0677.62008, MR 1017883, 10.1016/0167-7152(89)90009-6 |
| Reference:
|
[8] Gil M. A., Corral N., Casals M. R.: The likelihood ratio test for goodness of fit with fuzzy experimental observations.IEEE Trans. Systems Man Cybernet. 19 (1989), 771–779 10.1109/21.35340 |
| Reference:
|
[9] Gil M. A., López–Díaz M.: Fundamentals and Bayesian analyses of decision problems with fuzzy–valued utilities.Internat. J. Approx. Reason. 15 (1996), 203–224 Zbl 0949.91504, MR 1415767, 10.1016/S0888-613X(96)00073-4 |
| Reference:
|
[10] Gil M. A., Martínez I.: On the asymptotic optimum allocation in estimating inequality from complete data.Kybernetika 28 (1992), 325–332 Zbl 0771.62083, MR 1183623 |
| Reference:
|
[11] Gil M. A., Pérez R., Gil P.: A family of measures of uncertainty involving utilities: definitions, properties, applications and statistical inferences.Metrika 36 (1989), 129–147 MR 1024002, 10.1007/BF02614085 |
| Reference:
|
[12] Jang J.-S. R., Gulley N.: Fuzzy Logic Toolbox for Use with MATLAB.The Math Works Inc., Natick–Massachussets 1995 |
| Reference:
|
[13] Kaufmann A., Gupta M. M.: Introduction to Fuzzy Arithmetic.Van Nostrand Reinhold Co., New York 1985 Zbl 0754.26012, MR 0796665 |
| Reference:
|
[14] Mareš M.: Addition of rational fuzzy quantities: Disjunction–conjunction approach.Kybernetika 25 (1989), 104–116 MR 0995953 |
| Reference:
|
[15] Mareš M.: Algebraic equivalences over fuzzy quantities.Kybernetika 25 (1992), 121–132 MR 1227746 |
| Reference:
|
[16] Mareš M.: Computation over Fuzzy Quantities.CRC Press, Boca Raton 1994 Zbl 0859.94035, MR 1327525 |
| Reference:
|
[17] Puri M. L., Ralescu D. A.: Fuzzy random variables.J. Math. Anal. Appl. 114 (1986), 409–422 Zbl 0605.60038, MR 0833596, 10.1016/0022-247X(86)90093-4 |
| Reference:
|
[18] Zadeh L. A.: The concept of a linguistic variable and its application to approximate reasoning.Inform. Sci. Part 1, 8 (1975), 199–249; Part 2, 8 (1975), 301–353; Part 3, 9 (1975), 43–80 Zbl 0404.68075, MR 0386371, 10.1016/0020-0255(75)90017-1 |
| . |
