Comparison of two kinds of fuzzy arithmetic, LR and OFN, applied to fuzzy observation of the cofferdam water level

Jacek M. Czerniak, Wojciech Dobrosielski, Rafal A. Angryk


This paper presents certain important aspects of the fuzzy logic extension, one of which is OFN. It includes basic definitions of that discipline. It also compares fuzzy logic arithmetic with the arithmetic of ordered fuzzy numbers in L-R notation. Computational experiments were based on fuzzy observation of the impounding basin. The results of the study show that there is a connection between the order of OFN number and trend of changes in the environment. The experiment was carried out using computer software developed specially for that purpose. When comparing the arithmetic of fuzzy numbers in L-R notation with the arithmetic of ordered fuzzy numbers on the grounds of the experiment, it has been concluded that with fuzzy numbers it is possible to expand the scope of solutions in comparison to fuzzy numbers in classic form. The symbol of OFN flexibility is the possibility to determine the X number that always satisfies the equation A+X=C, regardless of the value of arguments. Operations performed on OFN are less complicated, as they are performed in the same way regardless the sign of the input data and their results are more accurate in the majority of cases. The promising feature of ordered fuzzy numbers is their lack of rapidly growing fuzziness. Authors expect to see implication of that fact in practice in the near future.


Fuzzy Logic, Fuzzy Number, Ordered Fuzzy Numbers

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