In this work, a formula for the regularized trace of second order differential operator given in a finite interval which has unbounded operator coefficients is found.

In this paper we introduce for the first time the concept of correlation coefficients of interval valued neutrosophic set (INS for short). Respective numerical examples are presented.

Interval Newton methods are widely used to find reliable enclosures for the roots of the polynomial systems. But the computation process needs the evaluation of an enclosure for the derivative of the polynomial and evaluation of the polynomial at a particular point. Again, the subdivisions (if any are needed) will require repeated evaluation of the function values. We propose an alternative app...

Traditional statistical tools for performing regression cannot handle the large uncertainties present in a fuzzy number dataset. Therefore we will have to rely on techniques developed for interval analysis (Moore 1966; Moore 1979). A useful property of algorithms that handle fuzzy numbers is that they can be rewritten in terms of intervals allowing the powerful mathematical tools of interval an...

This paper proposes an improved score function for the effective ranking order of interval-valued intuitionistic fuzzy sets (IVIFSs) and an interval-valued intuitionistic fuzzy TOPSIS method based on the score function to solve multicriteria decision-making problems in which all the preference information provided by decision-makers is expressed as interval-valued intuitionistic fuzzy decision ...

In this paper, a design method for a robust PI/PID controller for fuzzy parametric uncertain systems is proposed. An uncertain Linear Time Invariant (LTI) system with fuzzy coefficients is referred as fuzzy parametric uncertain system. The fuzzy coefficients are approximated by intervals (crisp sets) using the nearest interval approximation approach to obtain an interval system. Further, a robu...

In this paper, we address the problem of safety verification of interval hybrid systems in which the coefficients are intervals instead of explicit numbers. A hybrid symbolicnumeric method, based on SOS relaxation and interval arithmetic certification, is proposed to generate exact inequality invariants for safety verification of interval hybrid systems. As an application, an approach is provid...

It is known that in general, solving interval linear systems is NP-hard. There exist several proofs of this NP-hardness, and all these proofs use examples with intervals of different width – corresponding to different accuracy in measuring different coefficients. For some classes of interval linear systems with the same accuracy, feasible algorithms are known. We show, however, that in general,...

data envelopment analysis (dea) is a method for measuring the relative efficiencies of a set of decision-making units (dmus) that use multiple inputs to produce multiple outputs. in this paper, we study the measurement of dmu performances in dea in situations where input and/or output values are given as imprecise data. by imprecise data we mean situations where we only know that the actual val...