Rough data envelopment analysis (RDEA) evaluates the performance of the decision making units (DMUs) under rough uncertainty assumption. In this paper, new discussion regarding RDEA is extended. The RSBM model is proposed by integrating SBM model and rough set theory. The process of reaching solution is presented and this model is applied to efficiency evaluation of the DMUs with uncertain ...

Uncertain set theory is a generalization of uncertainty theory that has become a new branch of mathematics for modeling human belief degrees. Uncertain set is a fundamental concept to describe unsharp concepts in uncertain set theory. The moments are important characteristics of an uncertain set. This paper studies the moments and central moments of uncertain set and gives some formulas to calc...

Metaset is a new concept of set with partial membership relation. It is directed towards computer implementations and applications. The degrees of membership for metasets are expressed as binary sequences and they may be evaluated as real numbers too. The forcing mechanism discussed in this paper is used to assign certainty values to sentences involving metasets. It turns out, that for a senten...

R d with a Lévy density given by c|x| 1{|x|<1} for some constant c. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality for nonnegative harmonic nonnegative functions of these processes. We also establish a boundary Harnack principle for nonnegative functions which are harmonic with respect to these processes in bounded co...

ion Refinement via Inductive Learning Alexey Loginov, Thomas Reps, and Mooly Sagiv 1 Comp. Sci. Dept., University of Wisconsin; {alexey,reps}@cs.wisc.edu 2 School of Comp. Sci., Tel-Aviv University; [email protected] Abstract. This paper concerns how to automatically create abstractions for program analysis. We show that inductive learning, the goal of which is to identify general rules fro...

We propose a simple order-theoretic generalization of set-theoretic inductive de nitions. This generalization covers inductive, co-inductive and bi-inductive de nitions and is preserved by abstraction. This allows the structural operational semantics to describe simultaneously the nite/terminating and in nite/diverging behaviors of programs. This is illustrated on the structural bi nitary small...

In this article we show that a number of apparently different properties coincide on tite set of holomorpitic functions on a strict inductive limit (aH inductive limits are asgumed to be countable and proper) of Banach spaces and that they are ¿II satisfied only ‘u tite trivial case of a strict inductive limit of finite dimensional spaces. Thus tite linear properties of a strict inductive Iimit...

We propose a simple order-theoretic generalization of set-theoretic inductive de nitions. This generalization covers inductive, co-inductive and bi-inductive de nitions and is preserved by abstraction. This allows the structural operational semantics to describe simultaneously the nite/terminating and in nite/diverging behaviors of programs. This is illustrated on the structural bi nitary small...

In clause (i) of Lemma 2.1 of [1] it is claimed that in BST we can show the existence of ω as the least inductive set. BST contains the axiom of Infinity saying that “there is an inductive set”. However one cannot see how to prove the existence of a least inductive set without either ∈-induction or at least Π1-Separation, both of which are not included in BST. The simplest way to correct this f...