Translation of Classical Dimension Theory into a valued context should allow a comprehensible view of alternatives, by means of an informative representation, being this representation still manageable by decision makers. In fact, there is an absolute need for this kind of representations, since being able to comprehend a valued preference relation is most of the time the very first difficulty ...

We introduce a new familiy of random compact metric spaces Sα for α∈(1,2), which we call stable shredded spheres. They are constructed from excursions α-stable Lévy processes on [0,1] possessing no negative jumps. Informally, viewing the graph excursion in plane, each jump process is “cut open” and replaced by circle, then all points at equal height, not separated jump, identified. show that sp...

A new framework is presented that uses tools from duality theory of linear programming to derive graph-cut based combinatorial algorithms for approximating NP-hard classification problems. The derived algorithms include αexpansion graph cut techniques merely as a special case, have guaranteed optimality properties even in cases where α-expansion techniques fail to do so and can provide very tig...

The exemplar-based data clustering problem can be formulated as minimizing an energy function defined on a Markov random field (MRF). However, most algorithms for optimizing MRF energy function can’t be directly applied to the task of clustering, as the problem has a high-order energy function. In this paper, we first show that the high order energy function for the clustering problem can be si...

The Kac-Moody algebras has been attracting the attention of a lot of Mathematicians because of its various connections and applications to different branches of Mathematics and Mathematical Physics since the introduction of the subject in 1968, developed simultaneously and independently by Kac and Moody. On the other hand, Fuzzy sets first originated in a seminar paper by Lotfi A.Zadeh in 1965....

Statistical control charts are useful tools in monitoring the state of a manufacturing process. Control charts are used to plot process data and compare it to the limits set for the process. Points plotting outside these limits indicate an out-of-control condition. Standard control charting procedures, however, are limited in that they cannot take into account the case when data is of a fuzzy n...

ABSTRACT We measure the evolution of rest-frame UV luminosity function (LF) and stellar mass (SMF) Lyman-α (Ly α) emitters (LAEs) from z ∼ 2 to 6 by exploring ∼4000 LAEs SC4K sample. find a correlation between Ly α (LLy (MUV), with best fit M$_{\rm UV}=-1.6_{-0.3}^{+0.2}\log _{10} (\rm L_{Ly\,\alpha }/erg\, s^{-1})+47_{-11}^{+12}$ shallower relation LLy (M⋆), $\log M_\star /{\rm M}_\odot)=0.9_{...