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This contribution provides an exhaustive explanation of the graded approach to the monotonicity property (of a fuzzy relation) and its non-graded version. Our framework is algebraic. We present a wide variety of examples to support our claims relating to the well defined notion and suitability for fuzzy rule base applications and moreover, to improve the readability of the following mathematical formulae.

Monotonicity of fuzzy rule bases: On differences between graded and non-graded approaches