Background The impact of axial spondyloarthritis (axSpA) on health-related quality life can be substantial [1] , affecting both physical and mental health [2] . There is a need to assess the effect with disease-specific instruments. A global collaboration developed Assessments SpondyloArthritis international Society Health Index (ASAS HI) Environmental Factors Item Set (EFIS). These instruments...

The Rand index is a measure commonly used to compare crisp partitions. Campello (2007) and Hüllermeier and Rifqi (2009) respectively, proposed two extensions of this index capable to compare fuzzy partitions. These approaches are useful when continuous values of attributes are discretized using fuzzy sets. In previous works we experimented with these extensions and compared their accuracy with ...

The paper presents the method developed to assess rating points of objects with qualitative indexes. The novelty of the method lies in the fact that the authors use linguistic scales that allow to formalize the values of the indexes with the help of fuzzy sets. As a result it is possible to operate correctly with dissimilar indexes on the unified basis and to get stable final results. The obtai...

We introduce FMG (Fraenkel-Mostowski Generalised) set theory, a generalisation of FM set theory which allows binding of infinitely many names instead of just finitely many names. We apply this generalisation to show how three presentations of syntax — de Bruijn indices, FM sets, and name-carrying syntax — have a relation generalising to all sets and not only sets of syntax trees. We also give s...

Palle E.T. Jorgensen and Steen Pedersen Abstra t. We describe a class of measurable subsets Ω in Rd such that L(Ω) has an orthogonal basis of frequencies eλ(x) = e (x ∈ Ω) indexed by λ ∈ Λ ⊂ Rd. We show that such spectral pairs (Ω,Λ) have a self-similarity which may be used to generate associated fractal measures μ (typically with Cantor set support). The Hilbert space L(μ) does not have a tota...

Our submissions to the Crowdsourcing and Web tracks emphasized simplicity in either method, construction or both. Based on preliminary results, we found that if the number of relevance assessments is low, researchers may be better off “self-sourcing” the assessments, i.e. performing the relevance assessments themselves, rather than crowdsourcing the work. For the Crowdsourcing consensus task, w...

Value sets (VSs) used in electronic clinical quality measures are lists of codes from standard terminologies ("extensional" VSs), whose purpose ("intension") is not always explicitly stated. We elicited the intension for the 09/01/2014 release of extensional medication value sets by comparison to drug classes from the October 2014 release of RxClass. Value sets matched drug classes if they shar...

We investigate compositional iteration of fractional order for transseries. For any large positive transseries T of exponentiality 0, there is a family T [s] indexed by real numbers s corresponding to iteration of order s. It is based on Abel’s Equation. We also investigate the question of whether there is a family T [s] all sharing a single support set. A subset of the transseries of exponenti...

The problem of consensus reaching in the group decision making situations is considered. Assuming a heterogeneous and linguistic group decision making context various linguistic consensus measures are presented to guide the consensus process. Considering linguistic preference relations to provide experts' opinions, they are deened in three levels of action: level of the pairs alternatives, leve...

We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the Moran-like deterministic or random recursive constructions considered by various authors. Among other applications, we consider various extensions of Mandelbrot's...