Recently, a new type of set, called random permutation set (RPS), is proposed by considering all the permutations elements in certain set. For measuring uncertainty RPS, entropy RPS presented. However, maximum principle has not been discussed. To address this issue, paper presents RPS. The analytical solution and its PMF condition are proven Besides, numerical examples used to illustrate entrop...

The members of Martin-Löf random closed sets under a distribution studied by Barmpalias et al. are exactly the infinite paths through Martin-Löf random Galton-Watson trees with survival parameter 2 3 . To be such a member, a sufficient condition is to have effective Hausdorff dimension strictly greater than γ = log2 3 2 , and a necessary condition is to have effective Hausdorff dimension greate...

we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...