Abstract. In this paper we show the nonequivalence of combinations of several natural geometric restrictions on trapezoid representations of trapezoid orders. Each of the properties unit parallelogram, unit trapezoid and proper parallelogram, unit trapezoid and parallelogram, unit trapezoid, proper parallelogram, proper trapezoid and parallelogram, proper trapezoid, parallelogram, and trapezoid...

Along with the direction that generalizes interval graphs and permutation graphs to trapezoid graphs, researchers are now trying to generalize the class known as trapezoid graphs. A circle trapezoid is the region in a circle that lies between two non-crossing chords; thus, circle trapezoid graphs are the intersecting graphs of circle trapezoids within a circle. It should be noted that circle tr...

Trapezoid graphs are a class of cocomparability graphs containing interval graphs and permutation graphs as subclasses. They were introduced by Dagan et al. [3]. They propose an 0(n2) algorithm for chromatic number and a less efficient algorithm for maximum clique on trapezoid graphs. Based on a geometric representation of trapezoid graphs by boxes in the plane we design optimal, i.e., O(n log ...

Trapezoid graphs are a class of cocomparability graphs containing interval graphs and permutation graphs as subclasses. They were introduced by Dagan, Golumbic and Pinter DGP]. They propose an O(n 2) algorithm for chromatic number and a less eecient algorithm for maximum clique on trapezoid graphs. Based on a geometric representation of trapezoid graphs by boxes in the plane we design optimal, ...

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.

The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing problems in VLSI design and identifying the optimal chain of non-overlapping fragments in bioinformatics. Using modified binary indexed tree data structure, we de...

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...