# Horizontal Fuzzy Numbers for Solving Quadratic Fuzzy Equation

• Marek Landowski
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 889)

## Abstract

The paper presents method for solving the quadratic equation with fuzzy coefficients. Based on the horizontal fuzzy numbers the solution of fuzzy quadratic equation can be obtained. Solutions with horizontal fuzzy numbers are multidimensional. Obtained solutions are compared with results of standard fuzzy arithmetic. In examples was shown that results with standard fuzzy arithmetic are overestimated or underestimated. Method with horizontal fuzzy numbers generates the granule of information about the solution. Obtained granule gives full information about the solution. Moreover, the granule of information gives possibility to indicate the crisp quadratic equation for crisp value of the solution.

## Keywords

Fuzzy quadratic equation Fuzzy number Horizontal fuzzy number Fuzzy arithmetic RDM arithmetic Uncertainty theory Artificial intelligence

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