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Comparison of classical methods of processing fuzzy information with methods using idea of ordered fuzzy numbers based on general linguistic Mamdani model

Prokopowicz P.

Image Processing & Communications

2006

Vol. 11, no 1

83-90

Model of ordered fuzzy numbers (OFN) was defined and described in [4][5]. For this model simple and effective methods of arithmetical operations were suggested [4] [5] [6] [7]. OFNs representation is quite easy in the implementation as well as operations on them. Thanks to OFNs using we can free ourselves of the situation, in which results of operations on convex fuzzy numbers (classical model) we get "wider- more and more imprecise. In this paper author wants to pay attention on an important ownership of ordered fuzzy numbers - possibility of practical using as convex fuzzy numbers. Results of the simulation of using OFN to steering simplified fuzzy model of moving vehicle were introduced in [9]. Analysis and comparing results of the processing of imprecise information are a main aim of this publication. Were compared here chosen classical methods (aggregation of premises being based on MAX-MIN t-norm and reasoning methods based on Mamdani, Larsen, Łukasiewicz operators) with methods based on OFN. To get possibiy general results analysis were based on the very general linguistic model of Mamdani type fuzzy controller where we are operating on values of the linguistic variable amount so as little", average", "much". Carried analysis this way permits to get scores independent of units. With merit of introducing linguistic value in the form of fuzzy numbers, there is a possibility of straight and free graduating presented notions to the sizes dependent on the context in the any concrete situation.