continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

Fuzzy multiple criteria decision making (FMCDM) problem is an important issue in the field of decision making. Traditional weighted method is on the basis of disputed arithmetic operation and comparison operation on fuzzy numbers, the accuracy of decision is doubtful. In this paper, a new method is proposed to solve the FMCDM problem based on the generalized fuzzy numbers and power average oper...

Executing formal operation contracts is an important technique for requirements validation and rapid prototyping. Current approaches require additional guidance from the user or exhibit poor performance for underspecified contracts that describe the operation results non-constructively. We present an efficient and fully automatic approach to executing OCL operation contracts which uses a satisf...

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with interval-valued dual hesitant fuzzy linguistic information. Then, motivated by the ideal of traditional arithmetic operation, we have developed some aggregation operators for aggregating interval-valued dual hesitant fuzzy linguistic information: i...

We propose a novel application of sBs in embedded optical fibers as a building block for the implementation of optical neural net based on smart structures. By employing well established technology in fiber embedding in structures, and exploiting the ability of sBs as a highly versatile ambient sensor, and its nonlinear optical property of energy addition and subtraction to perform optical arit...

Residue Number System (RNS) are becoming popular for designing high performance DSP processors because of their ability to offer carry free arithmetic operation. The carry free operations lead to concurrent execution of arithmetic operations on the residues. However in RNS, moduli selection is one of the most important parameter that determines bit efficiency, area, power consumption, speed etc...

A scheme is proposed for representing 2’s-complement binary numbers in which there are two least-significant bits (LSBs). Benefits of the extra LSB include making the number representation range symmetric (i.e. from 22 to 2 for k-bit integers), allowing sign change by simple bitwise logical inversion, facilitating multiprecision arithmetic and enabling the truncation of results in lieu of round...

We suggest the use of piecewise monotonic interpolations to approximate and represent a fuzzy number (or interval) and to derive a procedure to control the absolute error associated to the arithmetic operations (+,−, ·, :) between fuzzy numbers, in order to reduce the distance between the true result of the operation and its approximation. The monotonic functions are then used to define a param...

A hardware unit for interval arithmetic (including division by an interval that contains zero) is described in this paper. After a brief introduction an instruction set for interval arithmetic is defined which is attractive from the mathematical point of view. These instructions consist of the basic arithmetic operations and comparisons for intervals including the relevant lattice operations. T...