On Henstock integral of fuzzy-number-valued functions (I)

Fuzzy Ostrowski type inequalities

“…We use a particular case of the Fuzzy Henstock integral (δ(x) = δ 2 ) introduced in [10], Definition 2.1.…”

“…where [u] r + [v] r means the usual addition of two intervals (as subsets of R) and λ [u] r means the usual product between a scalar and a subset of R (see, e.g., [10]). D) is a complete metric space, see [10], with the properties…”

The Cauchy problems for discontinuous fuzzy systems under generalized differentiability

“…In [18], Khastan et al provided sufficient conditions for the global existence of a unique (ii)-solution to an initial value problem for fuzzy functional differential equations using generalized derivative and were of broader applicability than those using Hukuhara derivative. In this paper, we extend and complement those of various authors such as [1,21,22], where the existence of generalized solution to the discontinuous fuzzy functional problem is considered by using properties of strong fuzzy Henstock integrals [32,33] under strong GH-differentiability.…”

On the existence of generalized weak solutions to discontinuous fuzzy differential equations

“…In the theory of integrals, there are some integrals based on the Banach space-valued functions such as Pettis and Bochner integrals [13,14,26,29]. The integrals of fuzzy-number-valued functions, as a natural generalization of set-valued functions, have been discussed by Puri and Ralescu [27], Kaleva [22], and other authors [36,37,40]. Recently, Wu and Gong [15,18,19] have combined the fuzzy set theory and nonabsolute integration theory, and discussed the fuzzy Henstock integrals of fuzzy-number-valued functions which extended Kaleva [22] integration.…”