Motivated by the recent results on topology determined by the Sugeno and Choquet integrals we study the topology on the space of measurable functions for a non-additive measure, which is determined by the integral IS based on a semicopula S. We define a family of mappings ρS on the set of measurable functions parameterized by a semicopula S and study their properties. We show that for a semicop...

Let h(a1 , •.. , an) denote the harmonic mean n(a1 1 + ... +a; 1) -1 of positive num­ bers a1 , ••. , all' and extend this definition (by continuity) to the non-negative case by setting h(a l' ... , an) = 0 if ai = 0 for some i ~ n. Recall that a measure J1. is non-atomic if every measurable set A of strictly positive measure has a measur­ able subset B ~ A satisfying J1.(A) > J1.(B) > O. A mea...

In order to measure fuzzy event, credibility measure is proposed as a non-additive set function. In this paper, this concept is extended to fuzzy sets. First, a mean measure is defined by Lebesgue integral and some properties are investigated such as the monotonicity theorem, self-duality theorem and subadditivity theorem. Furthermore, by using Sugeno integral, an equilibrium measure is propose...

We present proofs, based on the Shapley-Folkman theorem, of the convexity of the range of a strongly continuous, finitely additive measure, as well as that of an atomless, countably additive measure. We also present proofs, based on diagonalization and separation arguments respectively, of the closure of the range of a purely atomic or purely nonatomic countably additive measure. A combination ...

44 Effects of polyploidy in allohexaploid wheat (Triticum aestivum L.) have primarily been ascribed 45 to increases in coding sequence variation and potential to acquire new gene functions through 46 mutation of redundant loci. However, regulatory variation that arises through new promoter and 47 transcription factor combinations or epigenetic events may also contribute to the effects of 48 pol...