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...

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...

Nous considérons la réécriture de graphes en tant que sémantique opérationnelle des langages “équationnels”. Nous nous plaçons dans le cadre des signatures avec constructeurs. Nous commençons par caractériser un sous-ensemble de graphes dits graphes admissibles. Un graphe est admissible si aucun de ses cycles ne contient de fonction définie. Ensuite, nous considérons la relation de réécriture s...