We reformulate Mesiar’s hypothesis [Possibility measures, integration and fuzzy possibility measures, Fuzzy Sets and Systems 92 (1997) 191196], which as such was shown to be untrue by Murofushi [Two-valued possibility measures induced by σ-finite σ-additive measures, Fuzzy Sets and Systems 126 (2002) 265268]. We prove that a two-valued σ-maxitive measure can be induced by a σ-additive measure u...

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

In 2011, Mallozzi et al. [Fuzzy Sets and Systems 165(2011) 98105] introduced a core-like concept (called F-core) and a balanced-like condition for games in which the worth of any coalition is given by means of a fuzzy interval. They proved that a balanced-like condition is necessary but not sufficient enough to guarantee the F-core to be non-empty. In this paper, we study deeply on this problem...

A partition of the positive integers into sets A and B avoids a set S ⊂ N if no two distinct elements in the same part have a sum in S. If the partition is unique, S is uniquely avoidable. For any irrational α > 1, Chow and Long constructed a partition which avoids the numerators of all convergents to α, and conjectured that the set Sα which this partition avoided was uniquely avoidable. We pro...

We address the problem of uniquely reconstructing F-type icosahedral quasicrystals from few images produced by quantitative high resolution transmission electron microscopy and explain recent results in the discrete tomography of these sets.

In this paper we prove several new stability results for the reconstruction of binary images from two projections. We consider an original image that is uniquely determined by its projections and possible reconstructions from slightly different projections. We show that for a given difference in the projections, the reconstruction can only be disjoint from the original image if the size of the ...

For photoproduction reactions with final states consisting of two pseudoscalar mesons and a spin-1/2 baryon, eight complex amplitudes need to be determined uniquely. A modified version Moravcsik's theorem is employed for these reactions, resulting in slightly overcomplete sets polarization observables that are able determine the Further steps were taken reduce found minimal complete sets. As re...

In this paper, we shall give examples to answer that an open problem posed by De Baets et al. in “Triangular norms on product lattices (Fuzzy Sets and Systems 104(1999), 61-75)”.