Publisher: Springer
Number Of Pages: 195
Publication Date: 2006-04-16
Sales Rank: 2051105
ISBN / ASIN: 3540316957
EAN: 9783540316954
Binding: Hardcover
Manufacturer: Springer
Studio: Springer
Average Rating:
Total Reviews:

Contents
Chapter 1. Introduction .................................................................... 1
1.1 What is Fuzzy Statistics?.......................................................... 1
1.2 Why Do We Need Fuzzy Statistics? ........................................ 2
1.3 How to Carry Out Statistical Inference with Fuzzy Data? ....... 3
Chapter 2. Set-valued Data............................................................... 5
2.1 Random Closed Sets................................................................ 5
2.2 Coarse Data ............................................................................. 9
Chapter 3. Modeling of Fuzzy Data................................................. 13
3.1 Fuzzy Sets................................................................................ 14
3.2 Fuzzy Logics ........................................................................... 19
3.3 Fuzzy Relations ....................................................................... 27
3.4 􀁄-level Sets of Fuzzy Sets...................................................... 28
3.5 Fusion of fuzzy Data ............................................................... 31
Chapter 4. Random Fuzzy Sets ........................................................ 35
4.1 Back to Sampling Surveys....................................................... 35
4.2 Fuzzy Numbers........................................................................ 38
4.3 Fuzzy Set-Valued Random Elements ...................................... 39
Chapter 5. Aspect of Statistical Inference ....................................... 45
5.1 Fuzzy Data in Sampling Surveys ............................................ 45
5.2 Coarse Data ............................................................................. 46
5.3 Large Sample Statistics with Coarse Data............................... 50
5.4 Random Set Data on Finite Spaces.......................................... 53
5.5 Random Set Data on Metric, Compact Space ......................... 67
Chapter 6. Convergence of Random Fuzzy Sets............................. 71
6.1 Stochastic Convergence of Random Sets ................................ 71
6.2 The Choquet Integral............................................................... 73
6.3 A Variational Calculus of Set Functions ................................. 79
6.4 Choquet Weak Convergnece ................................................... 87
Chapter 7. Fuzzy Statistical Analysis and Estimation ................... 109
7.1 The Nature of Fuzzy Samples ................................................. 109
7.2 Fuzzy Sample Mean for Fuzzy Data ....................................... 113
7.3 Fuzzy Sample Median for Fuzzy Data .................................... 115
7.4 Fuzzy Sample Mode ................................................................ 117
7.5 Heuristic Properties Related to the Fuzzy Statistics ................ 119
7.6 Miscellaneous Applications ..................................................... 121
7.7 Concluding Remarks................................................................ 127
Chapter 8. Tests of Hypothesis: Means............................................ 129
8.1 Introduction.............................................................................. 129
8.2 Soft Distance with Fuzzy Samples........................................... 132
8.3 Some Properties of Fuzzy Data................................................ 134
8.4 Hypothesis Testing with Fuzzy Sample................................... 137
8.5 Fuzzy 2 􀁆 -test of Homogeneity ............................................... 140
Chapter 9 Fuzzy Time Series Analysis and Forecasting ................ 145
9.1 Introduction.............................................................................. 145
9.2 Fuzzy Time Series.................................................................... 148
9.3 Multivariate Fuzzy Time Series Modeling and Forecasting 153
9.4 Measuring Beliefs in the Forecasting Process ......................... 162
9.5 Empirical Studies ..................................................................... 169
9.6 Concluding Remarks................................................................ 181
References........................................................................................... 183
Index.................................................................................................... 193
X Contents