Intervals are related to the representation of uncertainty. In this sense, we introduce an integral of Gould type for an interval-valued multifunction relative to an interval-valued set multifunction, with respect to Guo and Zhang order relation. Classicaland specific properties of this new type of integral are established and several examples and applications from multicriteria decision making...

Let F be a continuous multifunction on IR with compact convex values. For any vector w, let F(x) ⊆ F (x) be the subset of points which maximize the inner product with w. Call W the set of all continuous functions w : [0, T ] 7→ IR with the following property: all solutions to the Cauchy problem ẋ(t) ∈ F(x(t)), x(0) = 0, are also solutions to ẋ(t) ∈ extF (x(t)). We prove that W is residual in C(...

where F is a Hausdorff continuous multifunction with closed, bounded values. In this paper we prove the local existence of a solution of (1.1 ), assuming that the convex closure of F(x,,) has finite codimension. More precisely, we assume the existence of a closed affine subspace E, G E with finite codimension, such that the interior of E. n E6 F(x,) relative to E,, is nonempty. Two special case...

The paper deals with affine selections of affine (both convex and concave) multifunctions acting between finite-dimensional real normed spaces. It is proved that each affine multifunction with compact values possesses an exhaustive family of affine selections and, consequently, can be represented by its affine selections. Moreover, a convex multifunction with compact values possesses an exhaust...

One configuration for realizing voltage-mode multifunction filters and another configuration for realizing current-mode multifunction filters using current feedback amplifiers (CFAs) are presented. The proposed voltage-mode circuit exhibit simultaneously lowpass and bandpass filters. The proposed current-mode circuit exhibit simultaneously lowpass, bandpass and highpass filters. The proposed ci...

A major concern in the application of multifunction digital relays for the protection of generators is that almost all the electrical protection, including both primary and the backup relay functions, are embodied in one digital package. The failure of that package results in the loss of virtually all generator electrical protection. This paper discusses how multifunction relays can be designed...

We characterize the local single-valuedness and continuity of multifunctions (set-valued mappings) in terms of their submonotonicity and lower semicontinuity. This result completes the well-known condition that lower semicontinuous, monotone multifunctions are single-valued and continuous. We also show that a multifunction is actually a Lipschitz single-valued mapping if and only if it is submo...

n be a continuous multifunction with compact, not necessarily convex values. If F is Lipschitz continuous, it was shown in [4] that there exists a measurable selection f of F such that, for every x 0 , the Cauchy problem ˙ x(t) = f (t, x(t)), x(0) = x 0 has a unique Caratheodory solution, depending continuously on x 0. In this paper, we prove that the above selection f can be chosen so that f (...