A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula

INTERVAL-VALUED INTUITIONISTIC FUZZY SETS AND SIMILARITY MEASURE

In this paper, the problem of measuring the degree of inclusion and similarity measure for two   interval-valued intuitionistic  fuzzy sets is considered. We propose inclusion and similarity measure by using  order on interval-valued intuitionistic fuzzy sets connected with lexicographical order. Moreover, some properties of inclusion and similarity measure and some correlation, between them an...

Purication of Measure-Valued Maps

Given a measurable mapping f from a nonatomic Loeb probability space (T; T ; P ) to the space of Borel probability measures on a compact metric space A, we show the existence of a measurable mapping g from (T; T ; P ) to A itself such that f and g yield the same values for the integrals associated with a countable class of functions on T A. A corollary generalizes the classical result of Dvoret...

Hyperreal-Valued Probability Measures Approximating a Real-Valued Measure

A New Fuzzy-Valued Additive Measure

In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.

L-fuzzy valued measure and integral

We continue to develop a construction of an L-fuzzy valued measure by extending a measure defined on a σalgebra of crisp sets to an L-fuzzy valued measure defined on a TM-tribe in the case when operations with L-sets and L-fuzzy numbers are defined by using the minimum triangular norm TM . We introduce an L-fuzzy valued integral over an L-set with respect to an L-fuzzy valued measure, consider ...