Ergodic theorems for random compact sets and fuzzy variables in Banach spaces
References (23)
Integrals of set-valued functions
J. Math. Anal. Appl.
(1965)Radon-Nikodým theorem and conditional expectation of fuzzy-valued measures and variables
Fuzzy Sets and Systems
(1990)Remarks on the set-valued integrals of Debreu and Aumann
J. Math. Anal. Appl.
(1978)Radon-Nikodým theorems for set-valued measures
J. Multivariate Anal.
(1978)The strong law of large numbers for fuzzy random variables
Inform. Sci.
(1982)- et al.
Differentials of fuzzy functions
J. Math. Anal. Appl.
(1983) - et al.
General Competitive Analysis
(1971) Fuzzy random variables and their limit properties
Ph.D. Thesis
(1989)- et al.
A vector valued random ergodic theorem
Convergence of Probability Measures
(1968)
Integration of correspondences
Cited by (15)
Convex hull of a fuzzy set and triangular norms
2021, Fuzzy Sets and SystemsCitation Excerpt :For an excellent introduction to the theory of fuzzy sets based on α-cuts see [6]. Shapley-Folkman theorem was used in the proof of ergodic theorem for fuzzy random variables [3] and in the proof of convergence of Bernstein approximation of a fuzzy random variable to its convex hull [17]. As an application of the results regarding T-convex hull of a fuzzy set we show an example from game theoretic setting, where t-norm fuzzy sets is used to handle uncertainty in a repeated two player game.
A note on Ulam stability of some fuzzy number-valued functional equations
2019, Fuzzy Sets and SystemsCitation Excerpt :In this section, we recall some necessary notions and fundamental results which are used in this paper. The reader is referred to [2] for more information and details. In this section, we shall establish the Ulam stability of the Eq. (1)–(2), in which f means a fuzzy number-valued mapping.
Bounded variation, absolute continuity and absolute integrability for fuzzy-number-valued functions
2002, Fuzzy Sets and SystemsAn embedding theorem for fuzzy numbers on Banach spaces and its applications
2002, Fuzzy Sets and SystemsLimit Theorems for Sums of Random Fuzzy Sets
2001, Journal of Mathematical Analysis and ApplicationsOn the convergence and representation of random fuzzy number integrals
1999, Fuzzy Sets and Systems