module over a ring is a general mathematical concept for many examples of mathematicalobjects that can be added to each other and multiplied by scalar numbers.in this paper, we consider a module over a ring as a universe and by using the notion of reference points, we provide local approximations for  subsets of the universe.

in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...

This paper discusses the application of grey numbers for uncertainty representation. It highlights the difference between grey sets and interval-valued fuzzy sets, and investigates the degree of greyness for grey sets. It facilitates the representation of uncertainty not only for elements of a set, but also the set itself as a whole. Our results show that a grey set could be specified for inter...

In real-applications, there may exist many kinds of data (e.g., boolean, categorical, real-valued and set-valued data) and missing data in an information system which is called as a Hybrid Information System (HIS). A new Hybrid Distance (HD) in HIS is developed based on the value difference metric, and a novel fuzzy rough set is constructed by combining the HD distance and the Gaussian kernel. ...

Deep scientific ideas have at least one distinctive property: they can be applied both by philosophers in abstract fundamental debates and by engineers in concrete practical applications. Mathematical approaches to modeling of vagueness also possess this property. Problems connected with vagueness have been discussed at the beginning of XXth century by philosophers, logicians and mathematicians...

As a further extension of the fuzzy set and intuitive set, interval-valued (IIFS) is more effective tool to deal with uncertain problems. However, classical rough based on equivalence relation, which do not apply IIFS. In this paper, we combine IIFS ordered information system obtain (IIFOIS). On basis, three types multiple granulation models dominance relation are established effectively overco...

Many rule induction algorithms are unable to cope with high dimensional descriptions of input features. To enable such techniques to be effective, a redundancy-removing step is usually carried out beforehand. Rough Set Theory (RST) has been used as such a dataset pre-processor with much success, however it is reliant upon a crisp dataset; important information may be lost as a result of quantiz...

In this paper, a novel approach of rough-fuzzy hybridization is proposed for efficient personalized Web retrieval. Variable precision rough set model is used to discover user preference. Fuzzy sets are incorporated to take care of the real-valued weights in each document vector. Discerning keywords are identified to refine a query for more focused representation. To further filter out irrelevan...