General design method of hedge-algebras-based fuzzy controllers and an application for structural active control

Hedge algebras (HAs) theory has been extensively developed with many effective applications in different fields of fuzzy theory such as data mining, fuzzy database system, fuzzy reasoning, and so on. We propose here a general design method of hedge-algebras-based fuzzy controllers (HACs) for a potential application in structural active control. The proposed method utilizes inherent order relationships between words in a word-domain to express the semantics of words instead of using fuzzy sets. This qualitative word semantics determines the so-called semantically quantifying mappings (SQMs), which are order-isomorphisms and map words of variable into numeric values, by only giving values of the fuzziness parameter of the variable. It is demonstrated that HAC and optimal HACs can be designed using this method for the active control of a structure, which is subjected to excitations of some different earthquakes. Simulation results show that the proposed method is simple, transparent and efficient in reducing the pick storey drift as well as the pick absolute acceleration of the structure. Moreover, computation time of HACs is significantly lower than that of ordinary fuzzy controllers.