Soft Methods in Probability, Statistics and Data Analysis

by Grzegorzewski, Przemyslaw; Hryniewicz, Olgierd; Gil, Maria A.; Gil, Maria A.

• ISBN13: 9783790815269
• ISBN10: 3790815268
• Format: Paperback
• Copyright: 2002-11-01
• Publisher: Physica Verlag

Summary

Classical probability theory and mathematical statistics appear sometimes too rigid for real life problems, especially while dealing with vague data or imprecise requirements. These problems have motivated many researchers to "soften" the classical theory. Some "softening" approaches utilize concepts and techniques developed in theories such as fuzzy sets theory, rough sets, possibility theory, theory of belief functions and imprecise probabilities, etc. Since interesting mathematical models and methods have been proposed in the frameworks of various theories, this text brings together experts representing different approaches used in soft probability, statistics and data analysis.

Table of Contents

Introductory Papers
Quantitative Possibility Theory and its Probabilistic Connections	3	(24)
D. Dubois
H. Prade
Toward a Perception-Based Theory of Probabilistic Reasoning with Imprecise Probabilities	27	(38)
L. A. Zadeh
Soft Methods in Probability - Fundamentals
Independence and Conditioning in a Connectivistic Fuzzy Logic Framework	65	(11)
J. Aguilar-Martin
About Ideals on the Set of Fuzzy Measures	76	(8)
A. G. Bronevich
A. N. Karkishchenko
Operators for Convolution of Fuzzy Measures	84	(8)
A. G. Bronevich
A. E. Lepskiy
Probabilities of Fuzzy Events Based on Scalar Cardinalities	92	(6)
J. Casasnovas
F. Rosello
On the Variation of the f-Inequality of a Random Variable	98	(7)
I. Cascos-Fernandez
M. Lopez-Diaz
M. A. Gil-Alvarez
Probability of Intuitionistic Fuzzy Events	105	(11)
P. Grzegorzewski
E. Mrowka
A New Calculus for Linguistic Prototypes in Data Analysis	116	(10)
J. Lawry
Upper Probabilities and Selectors of Random Sets	126	(8)
E. Miranda
I. Couso
P. Gil
On Multivalued Logic and Probability Theory	134	(6)
B. Riecan
Reversing the Order of Integration in Iterated Expectations of Compact Convex Random Sets	140	(6)
L. J. Rodriguez-Muniz
M. Lopez-Diaz
M. A. Gil
Lower Previsions for Unbounded Random Variables	146	(10)
M. C. M. Troffaes
G. de Cooman
A Hierarchical Uncertainty Model under Incomplete Information	156	(8)
L. V. Utkin
Imprecise Calculation with the Qualitative Information about Probability Distributions	164	(6)
L. U. Utkin
Approximation of Belief Functions by Minimizing Euclidean Distances	170	(8)
T. Weiler
U. Bodenhofer
Variants of Defining the Cardinalities of Fuzzy Sets	178	(11)
M. Wygralak
Soft Methods in Statistics - Fuzzy Stochastic Models
Probabilistic Reasoning in Fuzzy Rule-Based Systems	189	(8)
J. van den Berg
U. Kaymak
W. M. van den Bergh
Acceptance Sampling Plans by Variables for Vague Data	197	(10)
P. Grzegorzewski
Possibilistic Approach to Bayes Statistical Decisions	207	(12)
O. Hryniewicz
Fuzzy Comparison of Frequency Distributions	219	(9)
M. Last
A. Kandel
Test of One-Sided Hypotheses on the Expected Value of a Fuzzy Random Variable	228	(8)
M. Montenegro
A. Colubi
M. R. Casals
M. A. Gil-Alvarez
Blackwell Sufficiency and Fuzzy Experiments	236	(8)
A. Wunsche
Optimal Stopping in Fuzzy Stochastic Processes and its Application to Option Pricing in Financial Engineering	244	(11)
Y. Yoshida
Soft Methods in Data Analysis - Fuzzy, Rough and Other Approaches
Fuzzy Conjoint Analysis	255	(11)
M. Bhattacharyya
Grade Analysis of Repeated Multivariate Measurements	266	(8)
A. Ciok
A Contribution to Stochastic Modeling of Volcanic Petroleum Reservoir	274	(7)
S. Darwis
Improving the Quality of Association Rule Mining by Means of Rough Sets	281	(8)
D. Delic
H. J. Lenz
M. Neiling
Towards Fuzzy c-means Based Microaggregation	289	(6)
J. Domingo-Ferrer
V. Torra
Statistical Profiles of Words for Ontology Enrichment	295	(7)
A. Faatz
C. Seeberg
R. Steinmetz
Quest on New Applications for Dempster-Schafer Theory: Risk Analysis in Project Profitability Calculus	302	(8)
M. A. Klopotek
S. T. Wierzchon
Decision Making Based on Informational Variables	310	(11)
J. L. Kulikowski
An Algorithm for Identifying Fuzzy Measures with Ordinal Information	321	(8)
P. Miranda
M. Grabisch
Exploring an Alternative Method for Handling Inconsistency in the Fusion of Expert and Learnt Information	329	(9)
J. Rossiter
Approximate Reasoning Schemes: Classifiers for Computing with Words	338	(8)
A. Skowron
M. S. Szczuka
Using Consensus Methods to User Classification in Interactive Systems	346	(9)
J. Sobecki
N. T. Nguyen
Aggregation Methods to Evaluate Multiple Protected Versions of the Same Confidential Data Set	355	(8)
A. Valls
V. Torra
J. Domingo-Ferrer
On Multivariate Fuzzy Time Series Analysis and Forecasting	363
B. Wu
Y. Y. Hsu