Abstract
In this short communication we generalize the definition of type-2 fuzzy tolerance relation and consequently the type-2 fuzzy G-tolerance relation in type-2 fuzzy sets. The type-2 fuzzy G-tolerance relation helps in finding the type-2 fuzzy G-equivalence relation. Moreover, we have studied the notion of type-2 fuzzy tolerance relation in abstract algebra.
Highlights
Type-2 fuzzy sets are relatively new in the world of fuzzy sets and systems
The advantage of type-2 fuzzy sets is that they are helpful in some cases where it is difficult to find the exact membership functions for a fuzzy sets
We have studied the concept of type-2 fuzzy tolerance relation in abstract algebra
Summary
Type-2 fuzzy sets are relatively new in the world of fuzzy sets and systems. They were originally introduced in 1975 by L. These newer fuzzy sets were thought of as an extension of the already popular fuzzy sets ( labelled type-1) to include additional uncertainties in the set. The advantage of type-2 fuzzy sets is that they are helpful in some cases where it is difficult to find the exact membership functions for a fuzzy sets. We have studied the concept of type-2 fuzzy tolerance relation in abstract algebra. We have discussed type-2 fuzzy G-tolerance relation and type-2 fuzzy G-equivalence relation in Section (3). Section (5) describes type-2 fuzzy tolerance relation in algebraic structures
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