scholarly journals Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence

2020 ◽  
Author(s):  
Thierry Denœux
Keyword(s):  
Fuzzy Sets ◽  
General Framework ◽  
Belief Functions ◽  
Random Fuzzy Sets

Random Fuzzy Sets

2009 ◽  
pp. 18-44 ◽  
Author(s):  
Hung T. Nguyen ◽  
Vladik Kreinovich ◽  
Gang Xiang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
General Framework ◽  
Decision Making Under Uncertainty ◽  
Fuzzy Data ◽  
Partially Observed ◽  
Research Problems ◽  
Random Fuzzy Sets ◽  
Bona Fide ◽  
Coarse Data

It is well known that in decision making under uncertainty, while we are guided by a general (and abstract) theory of probability and of statistical inference, each specific type of observed data requires its own analysis. Thus, while textbook techniques treat precisely observed data in multivariate analysis, there are many open research problems when data are censored (e.g., in medical or bio-statistics), missing, or partially observed (e.g., in bioinformatics). Data can be imprecise due to various reasons, for example, due to fuzziness of linguistic data. Imprecise observed data are usually called coarse data. In this chapter, we consider coarse data which are both random and fuzzy. Fuzziness is a form of imprecision often encountered in perception-based information. In order to develop statistical reference procedures based on such data, we need to model random fuzzy data as bona fide random elements, that is, we need to place random fuzzy data completely within the rigorous theory of probability. This chapter presents the most general framework for random fuzzy data, namely the framework of random fuzzy sets. We also describe several applications of this framework.

Power Analysis of the Homoscedasticity Test for Random Fuzzy Sets

2010 ◽  
pp. 537-544 ◽  
Author(s):  
Ana Belén Ramos-Guajardo ◽  
Gil González-Rodríguez ◽  
Manuel Montenegro ◽  
María Teresa López
Keyword(s):  
Fuzzy Sets ◽  
Power Analysis ◽  
Random Fuzzy Sets

-sample tests for equality of variances of random fuzzy sets

2012 ◽  
Vol 56 (4) ◽  
pp. 956-966 ◽  
Author(s):  
Ana Belén Ramos-Guajardo ◽  
María Asunción Lubiano
Keyword(s):  
Fuzzy Sets ◽  
Random Fuzzy Sets

Estimating Measurement Error Based on Evidence Theory

2012 ◽  
Vol 548 ◽  
pp. 839-842
Author(s):  
Ming Zhu Xiao
Keyword(s):  
Measurement Error ◽  
General Framework ◽  
Probability Distributions ◽  
Evidence Theory ◽  
Belief Functions ◽  
Random Set ◽  
Estimation Process

Measurement error is traditionally represented with probability distributions. Although probabilistic representations of measurement error have been successfully employed in many analyses, such representations have been criticized for requiring more refined knowledge with respect to the existing error than that is really present. As a result, this paper proposes a general framework and process for estimating the measurement error based on evidence theory. In this research cumulative belief functions (CBFs) and cumulative plausibility functions (CPFs) are used to estimate measurement error. The estimation includes two steps:(1) modeling the parameters by means of a random set, and discrediting the random set to focal elements in finite numbers; (2)summarizing the propagation error. An example is demonstrated the estimation process.

scholarly journals On Some Nonclassical Algebraic Properties of Interval-Valued Fuzzy Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaoyan Liu ◽  
Feng Feng ◽  
Hui Zhang
Keyword(s):  
Fuzzy Sets ◽  
Soft Computing ◽  
General Framework ◽  
Soft Sets ◽  
Computing Model ◽  
Special Cases ◽  
Algebraic Properties ◽  
Different Types ◽  
Fuzzy Soft Sets ◽  
Interval Valued

Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov’s soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation=L. We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy softJ-equal relations. It is revealed that the soft product operations∧and∨of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy softL-inclusions hold for interval-valued fuzzy soft sets.

scholarly journals Limit Theorems for Sums of Random Fuzzy Sets

2001 ◽  
Vol 259 (2) ◽  
pp. 554-565 ◽  
Author(s):  
Marco Dozzi ◽  
Ely Merzbach ◽  
Volker Schmidt
Keyword(s):  
Fuzzy Sets ◽  
Limit Theorems ◽  
Random Fuzzy Sets

scholarly journals Fuzzy sets and presheaves

2019 ◽  
Vol 1 ◽  
pp. 3
Author(s):  
John F. Jardine
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
General Framework ◽  
Theoretic Approach ◽  
Data Set

This paper presents a presheaf theoretic approach to the construction of fuzzy sets, which builds on Barr's description of fuzzy sets as sheaves of monomorphisms on a locale. Presheaves are used to give explicit descriptions of limit and colimit descriptions in fuzzy sets on an interval. The Boolean localization construction for sheaves on a locale specializes to a theory of stalks for sheaves and presheaves on an interval.The system V∗(X) of Vietoris-Rips complexes for a data set X is both a simplicial fuzzy set and a simplicial sheaf in this general framework. This example is explicitly discussed through a series of examples.

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