ARTÍCULO
TITULO

Execution of arithmetic operations involving the second-order fuzzy numbers

Lev Raskin    
Oksana Sira    

Resumen

The need to improve the adequacy of conventional models of the source data uncertainty in order to undertake research using fuzzy mathematics methods has led to the development of natural improvement in the analytical description of the fuzzy numbers' membership functions. Given this, in particular, in order to describe the membership functions of the three-parametric fuzzy numbers of the (L-R)-type, the modification implies the following. It is accepted that these functions' parameters (a modal value, the left and right fuzzy factors) are not set clearly by their membership functions. The numbers obtained in this way are termed the second-order fuzzy numbers (bi-fuzzy). The issue, in this case, is that there are no rules for operating on such fuzzy numbers. This paper has proposed and substantiated a system of operating rules for a widely used and effective class of fuzzy numbers of the (L-R)-type whose membership functions' parameters are not clearly defined. These rules have been built as a result of the generalization of known rules for operating on regular fuzzy numbers. We have derived analytical ratios to compute the numerical values of the membership functions of the fuzzy results from executing arithmetic operations (addition, subtraction, multiplication, division) over the second-order fuzzy numbers. It is noted that the resulting system of rules is generalized for the case when the numbers-operands' fuzziness order exceeds the second order. The examples of operations execution over the second-order fuzzy numbers of the (L-R)-type have been given.

 Artículos similares

       
 
HanBit Kim, Seokhie Hong and HeeSeok Kim    
A masking method is a widely known countermeasure against side-channel attacks. To apply a masking method to cryptosystems consisting of Boolean and arithmetic operations, such as ARX (Addition, Rotation, XOR) block ciphers, a masking conversion algorith... ver más
Revista: Applied Sciences

 
Gizem Ermis, Bülent Çatay     Pág. 409 - 418
Graphics processor units (GPUs) are many-core processors that perform better than central processing units (CPUs) on data parallel, throughput-oriented applications with intense arithmetic operations. Thus, they can considerably reduce the execution time... ver más

 
John L. Gustafson     Pág. 38 - 53
If we are willing to give up compatibility with IEEE 754 floats and design a number format with goals appropriate for 2016, we can achieve several goals simultaneously: Extremely high energy efficiency and information-per-bit, no penalty for decimal oper... ver más