The Type-2 fuzzy set (T2 FS) is widely used for efficient control uncertainties, such as noise sensitivity in the fuzzy set. In addition, unsupervised machine learning requires a clustering parameter value in advance, and may affect clustering performance according to prior information such as the number and size of clusters. In this case, the fuzzifier value m to be applied is the most important factor in improving the accuracy of data. Therefore, in this paper, we intend to perform clustering to automatically acquire the determination of m1 and m2 values that depended on existing repeated experiments. To this end, in order to increase efficiency on deriving appropriate fuzzifier value, we used the Interval type-2 possibilistic fuzzy Cmeans (IT2PFCM), clustering method to classify a given pattern. In Efficient IT2PFCM method, used for clustering, we propose an algorithm that derives suitable fuzzifier values for each data. These values also extract information from each data point through the histogram approach and Gaussian Curve Fitting method. Using the extracted information, two adaptive fuzzifier value m1 and m2 are determined. Obtained values apply the new lowest and highest membership values. In addition, it is possible to form an appropriate fuzzy area on each cluster by only taking advantage of the characteristics of IT2PFCM, which reduces uncertainty. This doesn't only improve the accuracy of clustering of measured sensor data, but can also be used without additional procedures such as data labeling or the provision of prior information. It is also efficient at monitoring numerous sensors, managing and verifying sensor data collected in real time such as smart cities. Eventually, in this study, the proposed method is to improve IT2PFCM performance on accurate and quick clustering of large amount of complex data such as Internet of Things (IoT).

Type-2 fuzzy sets are preferred over type-1 sets as they are capable of addressing uncertainty more efficiently. The fuzzifier values play pivotal role in managing these uncertainties; still selecting appropriate value of fuzzifiers has been a tedious task. Generally, based on observation particular value of fuzzifier is chosen from a given range of values. In this paper we have tried to adaptively compute suitable fuzzifier values of interval type-2 possibilistic fuzzy c-means (IT2 PFCM) for a given data. Information is extracted from individual data points using histogram approach and this information is further processed to give us the two fuzzifier values m 1 and m 2 . These obtained values are bounded within some upper and lower bounds based on interval type-2 fuzzy sets.

In this paper, we propose a hybrid approach towards multiple kernels interval type-2 possibilistic fuzzy C-means(PFCM) based on interval type-2 possibilistic fuzzy c-means(IT2PFCM) and possibilistic fuzzy c-means using multiple kernels(PFCM-MK). In case of noisy data or overlapping cluster prototypes, fuzzy C-means gives poor performance in comparison to possibilistic fuzzy C-means(PFCM). Moreover, to address the uncertainty associated with fuzzifier parameter m, interval type-2 possibilistic fuzzy C-means(PFCM) is used. Most of the practical data available are complex and non-linearly separable. In such cases using Gaussian kernels proves helpful. Therefore, in order to overcome all these issues, we have integrated multiple kernels possibilistic fuzzy C-means(PFCM) into interval type-2 possibilistic fuzzy C-means(IT2PFCM) and propose the idea of multiple kernels based interval type-2 possibilistic fuzzy C-means(IT2PFCM-MK).