This paper presents an edge-detection method that is based on the morphological gradient technique and generalized type-2 fuzzy logic. The theory of alpha planes is used to implement generalized type-2 fuzzy logic for edge detection. For the defuzzification process, the heights and approximation methods are used. Simulation results with a type-1 fuzzy inference system, an interval type-2 fuzzy inference system, and with a generalized type-2 fuzzy inference system for edge detection are presented. The proposed generalized type-2 fuzzy edge-detection method was tested with benchmark images and synthetic images. We used the merit of Pratt measure to illustrate the advantages of using generalized type-2 fuzzy logic.

In this paper, a modification of the Sugeno integral with interval type-2 fuzzy logic is proposed. The modification includes changing the original equations of the Sugeno Measures and the Sugeno integral that were initially proposed for type-1 fuzzy logic. The proposed modification enables calculation of the interval type-2 Sugeno integral for combining multiple source of information with a higher degree of uncertainty than with the traditional type-1 Sugeno integral. The advantages of the interval type-2 Sugeno integral are illustrated by reporting improved recognition rates in benchmark face databases. This new concept could also be a useful tool in other areas of applications. Also, the improvement provided by the type-2 integral is verified to be statistically significant in the recognition results for complex face databases (like the FERET database) when compared with the type-1 Sugeno integral. The proposed Sugeno integral is used to combine the modules' outputs of a modular neural network for face recognition. Simulation results show that the interval type-2 Sugeno integral is able to improve the recognition rate for the benchmark face databases. Recognition results are better or comparable to results produced by alternative approaches present in the literature reported for the same benchmark problems.

A hybrid approach composed by different types of fuzzy systems, such as the Type-1 Fuzzy Logic System (T1FLS), Interval Type-2 Fuzzy Logic System (IT2FLS) and Generalized Type-2 Fuzzy Logic System (GT2FLS) for the dynamic adaptation of the alpha and beta parameters of a Bee Colony Optimization (BCO) algorithm is presented. The objective of the work is to focus on the BCO technique to find the optimal distribution of the membership functions in the design of fuzzy controllers. We use BCO specifically for tuning membership functions of the fuzzy controller for trajectory stability in an autonomous mobile robot. We add two types of perturbations in the model for the Generalized Type-2 Fuzzy Logic System to better analyze its behavior under uncertainty and this shows better results when compared to the original BCO. We implemented various performance indices; ITAE, IAE, ISE, ITSE, RMSE and MSE to measure the performance of the controller. The experimental results show better performances using GT2FLS then by IT2FLS and T1FLS in the dynamic adaptation the parameters for the BCO algorithm.