We have entered a new era of machine learning (ML), where the most accurate algorithm with superior predictive power may not even be deployable, unless it is admissible under regulatory constraints. This has led to great interest in developing fair, transparent and trustworthy ML methods. The purpose this article introduce information-theoretic framework (admissible learning) algorithmic risk-m...

From the more than two hundred partial orders for fuzzy numbers proposed in literature, only a few are total. In this article, we introduce notion of admissible order equipped with order, i.e., total which refines order. particular, it is given special attention to by Klir and Yuan 1995. Moreover, propose method construct on terms linear defined intervals considering strictly increasing upper d...

based on the convolutional model, a seismic trace is the convolution of seismic source wavelet and reflection coefficient series of the earth. seismic source wavelet estimation is one of the most important stages in processing and interpretation of seismic data. accurate estimation of wavelet increases the efficiency of the deconvolution and temporal resolution of seismic data. on the other han...

A sequence of integers in an interval of length x is called admissible if for each prime there is a residue class modulo the prime which contains no elements of the sequence. The maximum number of elements in an admissible sequence in an interval of length x is denoted by %∗(x). Hensley and Richards showed that %∗(x) > π(x) for large enough x. We increase the known bounds on the set of x satisf...

1 Prologue Ordinals made their entrance in proof theory through Gentzen's second consistency proof for Peano Arithmetic by transsnite induction up to " 0 , the latter being applied only to decidable predicates (cf. Gentzen 1938]). Gentzen's constructive use of ordinals as a method of analyzing formal theories has come to be a paradigm for much of proof theory from then on, particularly as exemp...