Interval type-2 fractional fuzzy inference systems: Towards an evolution in fuzzy inference systems

Abstract

Following type-1 fractional fuzzy inference systems presented recently as the new generation of fuzzy inference systems, interval type-2 fractional fuzzy inference systems (IT2FFISs) as a leap further ahead in the evolution of fuzzy inference systems (FISs) are introduced in this article. The IT2FFISs, which are outlined in this article, add to the armamentarium of FISs some particular concepts such as interval type-2 fractional membership functions, type-2 fractional translation rule, type-2 fracture index, the concept of switching, the entanglement, the degeneracy concept, and so forth. An IT2FFIS exploits not only the tolerance for the uncertainty in the interpretation of the meaning of a word, but also the relevance between the quality and quantity levels of the given information to infer an answer to an inference query. The IT2FFISs make an increase in machine intelligence quotient possible by an increase in the range of FISs order rather than their type. Moreover, the synergy of the concepts coming with various modes of IT2FFISs such as the aggressive mode opens a gate to a space of fuzzy systems outputs which used to be indiscoverable. Furthermore, it is demonstrated that as the type-2 fracture index approaches zero, the space of IT2FFISs outputs contracts and eventually it coincides the space of IT2FISs output when the fracture index is equal to zero. It is also proved that, provided a particular order of the IT2FFIS is taken into account, independent of the problem in question, a typical IT2FIS never leads to results which are more satisfactory than those obtained by the IT2FFIS corresponding to the typical IT2FIS.