The objective of this chapter is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership functions and rough membership functions, between core and support of fuzzy set theory and lower and upper appro...

Interval type-2 fuzzy set (IT2FS) offers interesting avenue to handle high order information and uncertainty in decision support system (DSS) when dealing with both extrinsic and intrinsic aspects of uncertainty. Recently, multiple attribute decision making (MADM) problems with interval type-2 fuzzy information have received increasing attentions both from researchers and practitioners. As a re...

In this paper, subtractive clustering method is combined with least squares estimation algorithms to pre-identify a type-1 Takagi-Sugeno-Kang (TSK) fuzzy model from input/output data. Then the type-2 fuzzy theory is used to expand the type-1 model to a type-2 model. A sensitivity analysis is used to ascertain how a type-1 TSK model output depends upon the pre-initialized parameters and determin...

A novel contrast image enhancement of fingerprint images using intuitionistic type II fuzzy set theory is recommended in this work. The method of Hamacher T co-norm(S norm) which generates a new membership function with the help of upper and lower membership function of type II fuzzy set. The finger print identification is one of the very few techniques employed in forensic science to aid crimi...

A novel contrast image enhancement of fingerprint images using intuitionistic type II fuzzy set theory is recommended in this work. The method of Hamacher T co-norm(S norm) which generates a new membership function with the help of upper and lower membership function of type II fuzzy set. The finger print identification is one of the very few techniques employed in forensic science to aid crimi...

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system (FLS). In order to make the type-2 FLS reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and probability type reduce reasoning method for the interval-valued FLS are developed. We have...

Choquet-integral-based evaluation models are proposed. The evaluation parameters – fuzzy measures – are assigned from a fuzzy rule table. There are three variations in this model: TF-, BP-, and AV-type models. The TF-type model is a natural extension of ordinal Choquet integrals. The BP-type model involves an evaluation using a reference point. The AV-type model involves a neutral evaluation me...

In this paper, we proposed another new form of type-2 fuzzy data points(T2FDPs) that is perfectly normal type-2 data points(PNT2FDPs). These kinds of brand-new data were defined by using the existing type-2 fuzzy set theory(T2FST) and type-2 fuzzy number(T2FN) concept since we dealt with the problem of defining complex uncertainty data. Along with this restructuring, we included the fuzzificati...

Text Classification is an important research field in information retrieval and text mining. The main task in text classification is to assign text documents in predefined categories based on documents’ contents and labeled-training samples. Since word detection is a difficult and time consuming task in Persian language, Bayesian text classifier is an appropriate approach to deal with different...

AND ITS APPLICATION by YU QIU Under the Direction of Yanqing Zhang ABSTRACT In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system. In order to make the type-2 fuzzy logic system reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and a new ...