Boolean-width is a recently introduced graph width parameter. If a boolean decomposition of width w is given, several NP-complete problems, such as Maximum Weight Independent Set, k-Coloring and Minimum Weight Dominating Set are solvable in O∗(2O(w)) time [5]. In this paper we study graph classes for which we can compute a decomposition of logarithmic boolean-width in polynomial time. Since 2 =...

We present some inequalities of Ostrowski and trapezoid type with complex exponential weight, for complex-valued absolutely continuous functions. These inequalities are related to Pompeiu’s mean value theorem. Special cases of these inequalities are applied to obtain (i) some approximation results for the finite Fourier and Laplace transforms; (ii) refinements of the Ostrowski and trapezoid ine...

We study the multi-attribute group decision making (MAGDM) problems in which the attribute values provided by the decision makers take the form of intuitionistic trapezoid fuzzy linguistic (ITrFL) information considering the uncertainty and inaccuracy of input arguments. Some new aggregation operators called intuitionistic trapezoid fuzzy linguistic weighted average (ITrFLWA), intuitionistic tr...

In this paper we present a new class of operators based on Trapezoid Fuzzy numbers such as Trapezoid Fuzzy Prioritized Weighted Mean (TFPWM) operator, Trapezoid Fuzzy Prioritized Weighted Geometric Average (TFPWG), Trapezoid Fuzzy Prioritized Weighted Harmonic Average(TFPWH) operators to solve multiple attribute group decision making (MAGDM) problems. Unlike other (MAGDM) techniques here the at...

In this paper, we utilize a variant of the Grüss inequality to obtain some new perturbed trapezoid inequalities. We improve the error bound of the trapezoid rule in numerical integration in some recent known results. Also we give a new Iyengar’s type inequality involving a second order bounded derivative for the perturbed trapezoid inequality.

A new method is proposed to solve the multiple attribute decision making (MADM) problems with the trapezoid fuzzy linguistic variables ( Vs TFL ) based on the trapezoid fuzzy linguistic hybrid harmonic averaging (TFLHHA ) operator. To begin with, this paper reviews the concept and operational rules of the Vs TFL , the calculation method of the possibility degree with Vs TFL , and the comparison...

The authors report two cases of isolated, undisplaced, fractures of the trapezoid bone. Because of its well-protected position in the wrist, traumatic lesions of the trapezoid bone are rare. Dislocation of the trapezoid has been reported in 30 patients; fractures are seen even less frequently and usually go with dorsal displacement. To our knowledge and based on a Medline literature review, onl...

In this paper we study collective additive tree spanners for families of graphs that either contain or are contained in AT-free graphs. We say that a graph G = (V,E) admits a system of μ collective additive tree r-spanners if there is a system T (G) of at most μ spanning trees of G such that for any two vertices x, y of G a spanning tree T ∈ T (G) exists such that dT (x, y) ≤ dG(x, y) + r. Amon...

Trapezoid fractures are relatively rare upper limb fractures. The case report of a trapezoid stress fracture in the dominant hand of a 22 year old international standard shot-putter is presented.