Fuzzy higher type information granules from an uncertainty measurement

Design and development of brain emotional learning based adaptive membership functions for type-2 fuzzy systems

This paper presents the design and development of Brain Emotional Learning based adaptive Type-2 Fuzzy Systems for control of dynamical systems. The BEL controller belongs to the class of bio inspired controllers, as its architecture is based on limbic system of human brain and is capable of providing solutions for complex real time problems. In this work, dynamics of Brain Emotional Learning are used for the adaptation of membership functions in the design of Type-2 Fuzzy Logic Controllers. The stability of the overall system is analysed through Lyapunov Yakubovich’s criteria. The proposed approach is validated on the benchmark system such as inverted pendulum, CSTR and Ship heading control through simulation and in real-time environment using OPAL RT OP5600.

A Two-Stage Approach for Constructing Type-2 Information Granules

In this article, we are concerned with the formation of type-2 information granules in a two-stage approach. We present a comprehensive algorithmic framework which gives rise to information granules of a higher type (type-2, to be specific) such that the key structure of the local granular data, their topologies, and their diversities become fully reflected and quantified. In contrast to traditional collaborative clustering where local structures (information granules) are obtained by running algorithms on the local datasets and communicating findings across sites, we propose a way of characterizing granular data (formed) by forming a suite of higher type information granules to reveal an overall structure of a collection of locally available datasets. Information granules built at the lower level on a basis of local sources of data are weighted by the number of data they represent while the information granules formed at the higher level of hierarchy are more abstract and general, thus facilitating a formation of a hierarchical description of data realized at different levels of detail. The construction of information granules is completed by resorting to fuzzy clustering algorithms (more specifically, the well-known Fuzzy C-Means). In the formation of information granules, we follow the fundamental principle of granular computing, viz., the principle of justifiable granularity. Experimental studies concerning selected publicly available machine-learning datasets are reported.

Granular Fuzzy Modeling Guided Through the Synergy of Granulating Output Space and Clustering Input Subspaces

As an augmentation of classic fuzzy models, granular fuzzy models (GFMs) have been applied to many fields being in rapport with experimental data, models, and users. However, most of the existing methods used to construct GFMs are based on the principle of optimal allocation of information granularity, which requires that a numeric model be provided in advance. In this paper, a straightforward and convincing modeling method is proposed to directly construct GFM on a basis of experimental data. The method first granulates the output space to form some interval information granules with distinct semantics and then uses them to partition the entire input space into a series of input subspaces. Subsequently, an initial GFM is emerged by using "If-Then" rules to relate with those interval information granules positioned in the output space and structures expressed in prototypes that are produced by clustering individual input subspaces. Further, the initial GFM is also refined by continuously migrating prototypes in individual input subspaces. The experimental studies using the synthetic dataset and several real-world datasets are reported. They offer a useful insight into the feasibility and effectiveness of the proposed modeling method and reveal the impact of parameters on the performance of the ensuing GFMs. An application example is also presented to exhibit the advantages of the resulting GFM.

Study of speciation and spatial variation of pollutants in Anzali Wetland (Iran) using linear regression, Kriging and multivariate analysis

Multivariate statistical techniques and geostatistical methods are among the important tools used in surface water quality management. They are widely used in interpreting data, identifying the pollution sources, understanding the spatial variation of parameters, and determining the places of monitoring stations. Therefore, in this study, spatial variation of water quality and pollutants in the Anzali Wetland water (Iran) was evaluated using multivariate statistical and Kriging methods. The values of different water quality parameters measured in six stations in the wetland water were subjected to cluster analysis (CA) and principal component analysis (PCA). Cluster analysis reduced the number of stations from six to four. The results of PCA showed that industrial and agricultural pollution sources could be responsible for the Anzali Wetland water quality. Then, the spatial variation maps of the PCA scores were generated using Kriging geostatistical method in the geographical information system (GIS) to investigate the pollution sources affecting the wetland parts. These maps illustrated that a great part of the wetland body was under the effect of agricultural sources, while the industrial sources affected the outlet and central parts. Finally, a comparison between two models (multiple linear regression (MLR) and Kriging) was made to assess their ability in predicting water quality parameters in the study area. The results showed the improvement of prediction using MLR, which was by 25%-97%, compared with Kriging. The results of the present study can be effectively used in the planning and implementation of future monitoring networks in the Anzali Wetland and other similar aquatic systems.