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...

T is my great pleasure to welcome you to the inaugural I issue of the IEEE TRANSACTIONS ON FUZZY SYSTEMS. Many of you are probably quite familiar with the basic ideas underlying fuzzy sets and systems that utilize fuzzy models. However, there will also be readers who are looking at the contents of this issue, wondering what it’s all about. For this latter group, the papers in this first issue m...

The concepts of fuzzy e-open sets and fuzzy e-continuous are introduced and studied in fuzzifying topology and by making use of these concepts, we introduce and study T e 0 -, R e 0-, T e 1 -, R e 1-, T e 2 -, T e 3 -, T e 4 -, strong T e 3 and strong T e 4 separation axioms in fuzzifying topology and give some of their characterizations as well as the relations of these axioms and other separa...

Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several geometric characteristics, namely all the intrinsic volumes (i.e. volume, surface area, Euler characteristic etc.) of the parallel sets of a fractal. Motivate...

In this paper we associate the three concepts of language, thinking, and meaning with Fuzzy Sets and Systems and Fuzzy Logic. We present some developments in 20 th century history of science and of humanities that show deep links between these concepts and we give a proposal for a fuzzy theoretical interpretation of what is meaning.

Recently, Vemuri and Jayaram proposed a novel method of generating fuzzy implications from a given pair of fuzzy implications. Viewing this as a binary operation ~ on the set I of all fuzzy implications they obtained, for the first time, a monoid structure (I,~) on the set I. Some algebraic aspects of (I,~) had already been explored and hitherto unknown representation results for the Yager’s fa...

This paper is a continuation of the first part of our study on type 〈1, 1〉 fuzzy quantifiers determined by fuzzy measures, in which the basic notions and examples were introduced. Here, we study the properties of permutation invariance and isomorphism invariance of fuzzy quantifiers determined by pairs of functionals (S, φ) and their special cases, e.g., fuzzy quantifiers defined by fuzzy measu...

In this paper, we provide a complete answer to the question of characteristic cones for a general discrete autonomous nD system described by partial difference equations with real constant coefficients. A characteristic cone is a special subset (having the structure of a cone) of the domain, here Zn, such that the knowledge of the trajectories on this set uniquely determines them over the whole...

1. Closed ideals. (1.1) Definition. Let 5 be an arbitrary set, and 2 a Boolean ring of subsets of 5. The algebra B(S, 2) consists of all uniform limits of finite linear combinations of characteristic functions of sets in 2. The norm in B(S, 2) is given by the formula ||/|| =SupseS \f(s) | • This definition is slightly more general than that given in [l ] where 2 is required to be a field of set...