Generalized Lower and Upper Approximations in Quantales

Generalized Lower and Upper Approximations in Quantales

Soft Lower and Upper Approximations

In this paper, we introduce the notion of soft (apr P , aprP ) (resp, (Apr P , aprP ), (aprP , AprP ), (AprP , AprP )) rough approximations. Mathematics Subject Classification: 08A05, 54A05, 94A15

The lower and upper approximations in a group

In this paper, we generalize some propositions in [C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. Math. Appl. 59(2010)431-436.] and we give some equivalent conditions for rough subgroups. The notion of minimal upper rough subgroups is introduced and a equivalent characterization is given, which implies the rough version of Lagrange′s Theorem. Keywords—Lower appro...

On the Upper and Lower Approximations of the Curve

The papers [28], [32], [2], [15], [1], [5], [6], [4], [31], [16], [29], [17], [27], [13], [3], [25], [26], [10], [11], [8], [30], [14], [20], [18], [12], [23], [22], [24], [7], [9], [19], and [21] provide the terminology and notation for this paper. In this paper n denotes a natural number. Let C be a simple closed curve. The functor UpperAppr(C) yields a sequence of subsets of the carrier of E...

Approximations of upper and lower probabilities by measurable selections

A random set can be regarded as the result of the imprecise observation of a random variable. Following this interpretation, we study to which extent the upper and lower probabilities induced by the random set keep all the information about the values of the probability distribution of the random variable. We link this problem to the existence of selectors of a multi-valued mapping and with the...