Space Missions Engineering Laboratory

Fuzzy Logic

The Fuzzy Logic (FL) is a tool for modelling under imprecise and qualitative information, easily translated into a quantitative formulation useful for automation. Generally speaking it could be inserted in the Experts Systems category that contains all the agents that work on a precompiled Knowledge Base (a set of logical rules) thanks to an inference motor to obtain consequence from real premises. The main difference is that FL rules are vague and not crisp and they are activated in parallel and not sequentially. The inference motor, however, makes the system visible to the user and modifiable.

The Fuzzy Logic, based on the Fuzzy Sets theory firstly proposed by Lofti Zadeh, represents an extension of the predicate calculus to deal with uncertainty related to the truth of a generic predicate. The Aristotle’s logic greatly exploits the non contradiction and third excluded principles to deal with deductive reasoning: a variable cannot simultaneously belong to a set A and to the complementary set non-A; the union of the A and non-A sets represents the whole universe. Those axioms make difficult modelling several real situations for which the membership of a given variable to a specific set is actually not so crisp.  The Fuzzy Sets overcome the Boolean Aristotelian axioms letting the variables belonging simultaneously to different classes no more exclusive. The membership to clashing sets is given by a degree of truth, tuned through a specific membership function. It has to be noted that the Fuzzy Theory is definitely different from the probabilistic approach: Probability does not overcome the True-False paradigm and a Boolean logic is still applied; the FL, even whenever an event occurred, maintains the multi-valued logic to judge it.

The FL methodology is nowadays widely diffused and exploited; it is typically applied to model phenomena occurring under a certain level of uncertainty and qualitative knowledge. Environments related to decision making and deduction mechanisms are typically faced by applying such a techniques, such as the robust model identification, the diagnosis (with a second order predicate calculus for the abduction), the general decision making processes, the classification problem typically occurring in the image processing possibly connected with the autonomous navigation and control problem for robots,  the adaptive control for dynamic systems.



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