Monotonicity of the system function of a SISO FRI system with neutrality and ordering property preserving fuzzy implications

Abstract

The monotonicity of the system function of a fuzzy relational inference (FRI) system is one of the most important issues that need attention. The unavailability of monotonicity of the system function of an FRI system is not desirable in many practical settings. Works existing in the literature have dealt with monotonicity of the system function of an FRI system where fuzzy implications have been widely used and those fuzzy implications are known to come from a residuated lattice structure. Moreover, there are very few studies where monotonicity has been studied under a non-residuated lattice structure. Building on our recent work on monotonicity under a non-residuated setting, in this work, we ensure that the system function of a certain type of FRI system with a Single-Input Single-Output (SISO) implicative rule base and ordering property preserving fuzzy implications is monotonic. Towards doing this, we represent the monotone fuzzy rule base by a fuzzy relation that involves fuzzy implications which satisfy the so-called neutrality property and ordering property, simultaneously. It should be highlighted that this work generalizes the class of fuzzy implications that can be employed in an FRI system without modifying the rule base to ensure the monotonic nature of the system function, giving more choices to the practitioners.