The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...

We show the existence result of viable solutions to the differential inclusion ẋ(t) ∈ G(x(t)) + F (t, x(t)) x(t) ∈ S on [0, T ], where F : [0, T ] × H → H (T > 0) is a continuous set-valued mapping, G : H → H is a Hausdorff upper semi-continuous set-valued mapping such that G(x) ⊂ ∂g(x), where g : H → R is a regular and locally Lipschitz function and S is a ball, compact subset in a separable H...

In multi-valued model checking, a temporal logic formula is interpreted relative to a structure not as a truth value but as a lattice element. In this paper we present new algorithms for multi-valued model checking. We first show how to reduce multi-valued model checking with any distributive DeMorgan lattice to standard, two-valued model checking. We then present a direct, automata-theoretic a...

Unlike monotone single-valued functions, multi-valued mappings may have none, one or (possibly infinitely) many minimal fixed-points. The contribution of this work is twofold. At first we overview and investigate about the existence and computation of minimal fixed-points of multi-valued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these res...

This paper describes our multi-valued symbolic modelchecker χChek. χChek is a generalization of an existing symbolic model-checking algorithm for a multi-valued extension of the temporal logic CTL. Multi-valued modelchecking supports reasoning with values other than just TRUE and FALSE. Multi-valued logics are useful in software engineering because they support explicit modeling of uncertainty,...

In a previous work the authors proved under a complex assumption on the set-valued mapping, the existence of Lipschitz solutions for second order convex sweeping processes in p-uniformly smooth and q-uniformly convex Banach spaces. In the present work we prove the same result, under a condition on the distance function to the images of the set-valued mapping. Our assumption is much simpler than...

Multi-valued model-checking is an extension of classical model-checking to reasoning about systems with uncertain information, which are common during early design stages. The additional values of the logic are used to capture the degree of uncertainty. In this paper, we show that the multi-valued -calculus model-checking problem is reducible to several classical model-checking problems. The re...

Multiple-output switching functions can be simulated by multiple-valued decision diagrams (MDDs) at a signi cant reduction in computation time. We analyze the following approaches to the representation problem: shared multiple-valued decision diagrams (SMDDs), multi-terminal multiple-valued decision diagrams (MTMDDs), and shared multi-terminal multiple-valued decision diagrams (SMTMDDs). For ex...