The objective of this paper is to establish the relationship between fuzzy approximation operators and fuzzy transformation systems. We show that for each upper/lower fuzzy transformation system there exits a fuzzy approximation space induced by a fuzzy reflexive relation and vice-versa.

The objective of this paper is to establish the relationship between fuzzy approximation operators and fuzzy transformation systems. We show that for each upper fuzzy transformation system there exists a fuzzy reflexive approximation space and vice-versa. We further establish such relationship between lower fuzzy transformation systems and fuzzy reflexive approximation spaces under the condition that the underline lattice structure satisfies double negation law.

This paper is about the study of F -transforms based on overlap and grouping maps, residual and co-residual implicator over complete lattice from both constructive and axiomatic approaches. Further, the duality, basic properties, and the inverse of proposed F -transforms have been studied, and axiomatic characterizations of proposed direct F -transforms are investigated.

The objective of this paper is to establish the relationship between L-valued approximation spaces and L-valued transformation systems. We show that for each L-valued upper/lower fuzzy transformation system there exist an L-valued reflexive approximation space and vice versa. In between, we study the concept of L-valued natural transformations.

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