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Performance and Feasibility Model Generation Using Learning-Based Approach
Published in Soumya Pandit, Chittaranjan Mandal, Amit Patra, Nano-Scale CMOS Analog Circuits, 2018
Soumya Pandit, Chittaranjan Mandal, Amit Patra
The problem of constructing the application bounded space Da may be considered to be finding solutions of fa(X̅) ≤ 0 over an interval of X̅ An approach to solve this is through interval analysis technique. The interval analysis technique is based on the concepts of interval arithmetic [74]. In interval arithmetic, real numbers are replaced by intervals which are combinations of a lower bound and an upper bound on the allowable value range of a variable. All basic arithmetic operations like addition, multiplication, etc., are replaced by interval versions. Whenever there is more than one variable in the problem, the solution is enclosed within a multidimensional interval rectangle. The commonly used methods for solving equations/inequalities using interval analysis technique are the Krawczyk method, and the Hansen and Sengupta method [74]. The application bounded space Da for a component block is constructed by combining the interval rectangles corresponding to all the specification parameters. The application bounded space is therefore constructed in a top-down fashion. This space is represented by a hyperbox as is shown in Fig. 4.25.
Floating-Point Hardware
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
The possibility of selecting rounding to positive infinity or negative infinity (round-up and round-down) allows the use of a technique known as interval arithmetic. Interval arithmetic is based on executing a series of calculations twice: once rounding up and once rounding down. This allows the determination of the upper and lower bounds of the error. Using interval arithmetic, it is possible, in many cases, to certify that the correct result is a value not larger than the result obtained while rounding up, and no smaller than the result obtained while rounding down. This places the exact result within a certain boundary.
Reliability Dependent Imperfect Production Inventory Optimal Control Fractional Order Model for Uncertain Environment Under Granular Differentiability
Published in Fuzzy Information and Engineering, 2022
Based on fuzzy standard interval arithmetic; addition, subtraction, and multiplication of two fuzzy numbers and are characterised as follows, respectively: [+] = [, ],[-] = [, ],[] = [min{, , , },max{, , , }].
The Fuzzy Arithmetic Operations of Transmission Average on Pseudo-Hexagonal Fuzzy Numbers and Its Application in Fuzzy System Reliability Analysis
Published in Fuzzy Information and Engineering, 2021
[13] (Fuzzy arithmetic operations based on interval arithmetic(- cut)) A popular way to carry out fuzzy arithmetic operations is by way of interval arithmetic. This is possible because any - cut of a fuzzy number is always an interval. Therefore, any fuzzy number may be represented as a series of intervals. Let us consider two interval numbers [a,b] and [c,d] where and . Then the following arithmetic operations proceed as shown below: addition: [a, b ] + [ c, d ] = [ a + c, b + d ],subtraction: [ a, b ]−[ c, d ] = [ a–d, b–c ],multiplication: [ a, b ] . [ c, d ] = [ m i n { a c, a d, b c, b d }, m a x { a c, a d, b c, b d } ],division: [ a, b ]/[ c, d ] = [ a, b ] . [ 1/d, 1/c ].
A novel method of combined interval analysis and homotopy continuation in indoor building reconstruction
Published in Engineering Optimization, 2019
Ali Jamali, Francesc Antón Castro, Darka Mioc
In this section, an interval-valued homotopy model of the measurement of horizontal angles by the magnetometer component of the rangefinder is presented. This model blends interval analysis and homotopy continuation. Interval analysis is a well-known method for computing the bounds of a function, having been given bounds on the variables of that function (Ramon Moore and Cloud 2009). The basic mathematical object in interval analysis is the interval instead of the variable. The operators need to be redefined to operate on intervals instead of real variables. This leads to interval arithmetic. In the same way, most usual mathematical functions are redefined by an interval equivalent. Interval analysis allows one to certify computations on intervals by providing bounds on the results. The uncertainty of each measure can be represented using an interval defined either by a lower bound and a higher bound or by a midpoint value and a radius.