The formulation of strong and weak laws of large numbers for fuzzy random variables based on variance is given. The concept of the variance of fuzzy random variables, introduced by K1 orner (Fuzzy Sets and Systems 92 (1997) 83) and by Feng (Fuzzy Sets and Systems 120 (2001) 487) demonstrates its e2ciency. c © 2002 Elsevier Science B.V. All rights reserved.

In this note, we show by counterexamples that some results of Qiu and colleagues [On the restudy of fuzzy complex analysis: Part I. The sequence and series of fuzzy complex numbers and their convergences, Fuzzy Sets and Systems 115 (2000) 445–450; On the restudy of fuzzy complex analysis: Part II. The continuity and differentiation of fuzzy complex functions, Fuzzy Sets and Systems 120 (2001) 5...

The aim of this paper is to point out and correct some errors of two theorems for IFSs in Atanassov (Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 2000) and bring forward a new theorem for IFSs. In the end, some elementary, but non-standard equalities between IFSs were formulated.

Using mid-infrared and radio criteria, we select a sample of candidate z ∼ 2 obscured quasars. Optical spectroscopy confirms about half of these as type-2 quasars, and modelling the population suggests 50-80% of the quasars are obscured. We find some flat radio spectrum type-2 quasars, and tentative evidence for obscuration unrelated to the torus. Using a similar sample, we also find evidence f...

A maximum stable set in a graph G is a stable set of maximum size. S is a local maximum stable set of G, and we write S ∈0(G), if S is a maximum stable set of the subgraph spanned by S ∪ N (S), where N (S) is the neighborhood of S. A matching M is uniquely restricted if its saturated vertices induce a subgraph which has a unique perfect matching, namely M itself. Nemhauser and Trotter Jr. (Math...