Abstract Fractional calculus operators play a very important role in generalizing concepts of used diverse fields science. In this paper, we use Riemann–Liouville fractional integrals to establish generalized identities, which are further applied obtain midpoint and trapezoidal inequalities for convex function with respect strictly monotone function. These reproduce convex, harmonic p -convex, ...

We give some sufficient conditions such that a crisp, interval, triangular, trapezoidal, parametric approximation of a fuzzy number, with or without additional requirements, to have the properties of invariance to translations or scale invariance.

The d-dimensional Catalan numbers form a well-known sequence of numbers which count balanced bracket expressions over an alphabet of size d. In this paper, we introduce and study what we call d-dimensional prime Catalan numbers, a sequence of numbers which count only a very specific subset of indecomposable balanced bracket expressions. We further introduce the notion of a trapezoidal diagram o...

The objective of this paper is to present multi-criteria group decision making in intuitionistic fuzzy environment based on grey relational analysis for weaver selection in Khadi institution. Weaver selection is a group decision making process involving qualitative and quantitative criteria. Intuitionistic trapezoidal fuzzy weighted arithmetic average operator and intuitionistic trapezoidal fuz...

Recently, we derived some new numerical quadrature formulas of trapezoidal rule type for the integrals I (1)[g] = ∫ b a g(x) x−t dx and I (2)[g] = ∫ b a g(x) (x−t)2 dx . These integrals are not defined in the regular sense; I (1)[g] is defined in the sense ofCauchy PrincipalValuewhile I (2)[g] is defined in the sense of Hadamard Finite Part. With h = (b − a)/n, n = 1, 2, . . ., and t = a+kh for...

In this paper, we investigate multiple attribute group decision making (MAGDM) problems where decision makers represent their evaluation of alternatives by trapezoidal fuzzy two-dimensional uncertain linguistic variable. To begin with, we introduce the definition, properties, expectation, operational laws of trapezoidal fuzzy two-dimensional linguistic information. Then, to improve the accuracy...

There is always a need to analyze current signals generated by various DC–DC converters. For example, determine the stress experienced semiconductor devices and evaluate active reactive power consumption in The study demonstrates that shape of signal dictates analytical expressions required average RMS values as well value ripple signal. also shows can be treated composite waveforms comprising ...