Two New Defuzzification Methods Useful for Different Fuzzy Arithmetics

One of the many reasons why a human searches for new solutions is inspiration for innovation perceived in natural processes and phenomena. The authors of the paper present new algorithms for the defuzzyfication block which is the final process of the fuzzy controller (fuzzy control systems), for which a defuzzyfied value controls a given object. The presented new methods are: Golden Ratio (GR) and Mandala Factor (MF). The first of them uses the ancient Golden Ratio rule which is known, among others, from the Fibonacci sequence. The second proposal is based on the interpretation of drawing technique used in Asia, consisting in arranging pictures of color sand grains. In Tibetan Buddhism this technique is known as Mandala, a symbol of perfection and harmony. The interpretation of the perfection symbol and the Golden Ratio method in this paper has been referenced to other methods used in the defuzzyfication process, including weight averange method, centroid and mean of maxima. The scene for solutions presented here is provided by the ordered fuzzy numbers (OFN) theory which allows to use both the trend of a given phenomena, as well as more precisely wield mathematical methods. A special property of the proposed methods is their sensitivity to the OFN number order. This means that MF and GR operators applied to the numbers of the same shape but of opposite orders would result in different defuzzyfication values. The paragraph relating to discussion on the research includes a comparison of the existing defuzzyfication operators as regards the sensitivity to order.