By Leticia Cervantes, Oscar Castillo

This publication specializes in the fields of fuzzy common sense, granular computing and likewise contemplating the regulate sector. those components can interact to resolve quite a few keep watch over difficulties, the belief is this mixture of components might let much more complicated challenge fixing and higher effects. during this booklet we try the proposed procedure utilizing benchmark difficulties: the complete flight keep watch over and the matter of water point keep watch over for a three tank procedure. whilst fuzzy good judgment is used it make it effortless to played the simulations, those fuzzy platforms aid to version the habit of a true platforms, utilizing the bushy platforms fuzzy principles are generated and with this may generate the habit of any variable looking on the inputs and linguistic worth. therefore this paintings considers the proposed structure utilizing fuzzy platforms and with this increase the habit of the complicated regulate problems.

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**Additional info for Hierarchical Type-2 Fuzzy Aggregation of Fuzzy Controllers **

**Example text**

2 Statistical Comparison Using the Empirical Type-2 Fuzzy System and a Type-2 Fuzzy System Using Genetic Algorithm It is important to consider a comparison between the empirical type-2 fuzzy system and the type-2 fuzzy system designed using a genetic algorithm, because is necessary to know if a signiﬁcant difference exist when a genetic algorithm is applied to the type-2 fuzzy system design. 18. 000, GL = 29 Deviation std. Mean of std. 000, GL = 29 Deviation std. Mean of std. 000, GL = 30 Mean Deviation std.

1 Statistical Comparison Using Type-1 Fuzzy System Without Optimization and Type-1 Fuzzy System Using Genetic Algorithm Individual valve plot of valve 1 with the type-1 fuzzy systems and the type-1 fuzzy system with genetic algorithm is shown in Fig. 13. 000, GL = 29 Mean Deviation std. Mean of std. 000, GL = 29 Mean Deviation std. Mean of std. 000, GL = 30 Mean Deviation std. Mean of std. 000, GL = 29 Mean Deviation std. Mean of std. 000, GL = 31 Mean Deviation std. Mean of std. 0073 least as extreme as the one that really was obtained and GL is the degrees of freedom.

Fig. 1 Simulation Results in the First Case of Study 39 Fig. 26 Individual value plot of valve 20 Fig. 27 Individual value plot of valve 32 Individual value plot of valve 32 with the type-1 fuzzy system and the type-2 fuzzy system is shown in Fig. 27. Result in tables (Sect. 1) shown that, there is statistical evidence to say that there is a signiﬁcant difference in the results presented with regards to granular type-2 (more than 95 % conﬁdence). In other words, the type-2 fuzzy system with granular computing generated a signiﬁcant increase in the controller to have better control.