## 1 Introduction  
Classification is one of the most important and challenging machine learning tasks. As the main goal is to investigate similarities between groups of objects, the classification accuracy strongly depends on the initial data sets used for training. There are a lot of issues to be handled, such as unbalanced or biased training data, but also incomplete or vague information which is often the case for real data. A lot of research was done to address this problem, especially using fuzzy classification and by extending to type-2 fuzzy sets as well. For example, recently in [1], a new fuzzy reasoning method for an interval type-2 fuzzy classification system including cluster-based rules was introduced. Authors propose to incorporate the introduced reasoning procedure with a new Possibility-based fuzzy measure to handle uncertainty of cluster centers in an interval type-2 fuzzy rule-based classification system. In [2], a robust sparse representation for classification of medical images is proposed based on an introduced adaptive type-2 fuzzy dictionary learning. Remote-sensing image classification techniques using type-2 fuzzy sets were introduced [3; 4; 5] where, for example recently, considering the last cited research, a novel robust interval type-2 possibilistic fuzzy clustering model for the classification of complex remote sensing land cover was presented. There are many fuzzy control applications based on the use of type-2 fuzzy sets. Recently, type-2 fuzzy logic system for ergonomic control of indoor environments was proposed [6]. The system calculates the effective working time and time-dependent change in carbon dioxide levels and aims to evaluate ergonomic comfort conditions. The authors proved better system performance using type-2 fuzzy sets for ergonomic control in fuzzy environments. Important medical application was proposed in [7]. An interval type-2 fuzzy stochastic modeling and control strategy to consider the uncertainties of the COVID-19 pandemic in order to control the number of infected people was introduced. A common strategy for fuzzy model parameter tuning is the use of evolutionary algorithms. In [8], authors applied a genetic algorithm to tune the parameters of an interval type-2 fuzzy proportional-derivative controller, in order to track the trajectory of a snake robot in the presence of system uncertainties. In [9; 10], slime mold and particle swarm optimization algorithms were used for parameter tuning of interval type-2 fuzzy controllers, respectively. In [11], the design of membership functions for interval type-2 fuzzy tracking controllers was optimized using a metaheuristic algorithm. In general, type-2 fuzzy sets provide better generalizations [12; 13] as the main assumption here is the additional fuzzification of the membership values of type-1 fuzzy sets involved. Therefore, type-2 fuzzy sets can handle better with imprecise information [14; 15]. Additionally, to deal with information issues, data discovery is used to induce knowledge. Information systems and rough sets, originally introduced by [PERSON] [16; 17; 18], are often used to represent knowledge. Basic mathematical concepts, using rough sets theory to induce fuzzy rules, have been worked on for a long time. In [19], fuzzy learning methods for the automatic generation of membership functions and fuzzy if-then rules from training examples were introduced. Fuzzy decision rules induction was presented in [20] using the tolerance-based rough sets model. Rough sets were used to reduce the dimensionality of complex datasets as preprocessing for fuzzy rule induction [21]. The above guided us to investigate the possible combination of fuzzy reasoning with [PERSON]'s information systems. We have already introduced our concept of a fuzzy information system [22]. This research is a continuation of our previous research, by evolving and combining our concept with the Takagi-Sugeno fuzzy model [23]. Fuzzy information systems introduce a relation between attributes and fuzzy sets [24].