Fuzzy arithmetic in economic research

ARITHMETIC-BASED FUZZY CONTROL

Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...

Fuzzy Number Intuitionistic Fuzzy Arithmetic Aggregation Operators

A fuzzy number intuitionistic fuzzy set (FNIFS) is a generalization of intuitionistic fuzzy set. The fundamental characteristic of FNIFS is that the values of its membership function and non-membership function are trigonometric fuzzy numbers rather than exact numbers. In this paper, we define some operational laws of fuzzy number intuitionistic fuzzy numbers, and, based on these operational la...

Fuzzy Arithmetic with Parametric LR Fuzzy Numbers

Future Research in Computer Arithmetic

There are several areas in computer arithmetic which are fertile for new discoveries. This paper will introduce some of these fields of research with the expectation that there will be tremendous advances in the next decade. Some of these fields are already matured with key problems still unsolved while others are nebulous at this time in history. I will address three arithmetic fields: the mul...

New Tools in Fuzzy Arithmetic with Fuzzy Numbers

We present new tools for fuzzy arithmetic with fuzzy numbers, based on the parametric representation of fuzzy numbers and new fuzzy operations, the generalized difference and the generalized division of fuzzy numbers. The new operations are described in terms of the parametric LR and LU representations of fuzzy numbers and the corresponding algorithms are described. An application to the soluti...