In this paper, several new algebraic mathematics for positive fuzzy numbers of type (a,a,a,a) are devised and do not need the computation of α-cut of the fuzzy number. Direct mathematical expressions to evaluate exponential, square root, logarithms, inverse exponential etc. of positive fuzzy numbers of type (a,a,a,a) are obtained using the basic analytical principles of algebraic mathematics an...

We study arithmetic properties of a new tree-based canonical number representation, recursively run-length compressed natural numbers, defined by applying recursively a run-length encoding of their binary digits. We design arithmetic and boolean operations with recursively runlength compressed natural numbers that work a block of digits at a time and are limited only by the representation compl...

Let G be the arithmetic Grassmannian over SpecZ with the natural invariant Kähler metric on G(C). We study the combinatorics of the arithmetic Schubert calculus in the Arakelov Chow ring CH(G). We obtain formulas for the arithmetic Littlewood-Richardson numbers and the Faltings height of G under the Plücker embedding, using ‘rim hook operations’ on Young diagrams. An analysis of the duality inv...

This study discusses the implementation of sequences and series in economics. The research method used this is a qualitative method. data collection technique was literature study. A sequence an arrangement numbers formed according to certain order. Sequences consist two parts each, namely arithmetic geometric as well series. In economics concepts lines are for matters relating calculations suc...

In this paper, we present a new fuzzy risk analysis method based on generalized fuzzy numbers. Firstly, we define new arithmetic operations between generalized fuzzy numbers. Then, we propose a new method to measure the degree of similarity between generalized fuzzy numbers. Finally, we apply the new arithmetic operations between generalized fuzzy numbers and proposed similarity measure to deve...

The vague sum (product) of a finite number of real numbers and the vague integral multiples (powers) of real numbers based on a perfect vague addition (multiplication) operation are introduced, and some of their fundamental properties are pointed out. Furthermore, some examples are designed to show how they can be practically implemented. Keyword: Fuzzy arithmetic, Vague arithmetic, Vague arith...

Fuzzy numbers in number theory are a foundation of fuzzy sets and fuzzy mathematics that extend the domain of numbers from those of real numbers to fuzzy numbers. Fuzzy arithmetic is a system of fuzzy operations on fuzzy numbers. A theory of fuzzy arithmetic is presented towards a fuzzy mathematical structure for fuzzy inference and cognitive computation. The mathematical models of fuzzy number...

The main purposes of this paper are to probe for the entropy differences between arithmetically manipulated Triangular Fuzzy Numbers (TFNs) using Shannon’s Function; and to study the relationships between any two TFNs. Simultaneously, we expand on the articles of Wang et al. [6] and Wang et al. [5]. The entropy differences between two TFNs subjected to different arithmetic operations are classi...

Introduction: Mental arithmetic analysis based on Electroencephalogram (EEG) signal for monitoring the state of the user’s brain functioning can be helpful for understanding some psychological disorders such as attention deficit hyperactivity disorder, autism spectrum disorder, or dyscalculia where the difficulty in learning or understanding the arithmetic exists. Most mental arithmetic recogni...

Commercial applications and databases typically store numerical data in decimal format. Currently, however, microprocessors do not provide instructions or hardware support for decimal floating-point arithmetic [ 1 ]. Consequently, decimal numbers are often read into computers, converted to binary numbers, and then processed using binary floating-point arithmetic. Results are then converted back...