NewConcepts Related toNon-Stationary FuzzySets

Inthispaper, formal definitions oftheconcepts relevant tonon-stationary fuzzysetsareprovided, aswellas definitions ofthebasic non-stationary fuzzy setoperators with proofs ofselected properties oftheseoperators. Amongthe novel termsintroduced arethefootprint ofinstantiations, the domain ofinstantiations andthetemporal histogram. Further, we discuss thecorrespondence between non-stationary andtype-2 fuzzysets, andmakethefirst attempt atproposing a setof comparable terms. I.INTRODUCTION Type-2 fuzzysets wereintroduced byZadeh, inhissem- inalpaperof1975(1), inorder topermit 'fuzzy setsin whichthegrades ofmembership arespecified inlinguistic terms'. Unfortunately, their useinpractice waslimited due tothesignificant amountofcomputational complexity in- volved intheir implementation. Morerecently, type-2 fuzzy setsreceived renewed interest, mainly duetotheefforts ofMendel(2), butalso, possibly, duetotheincreases in computational power. Mendel established asetofterms tobe usedwhenworking withtype-2 fuzzy sets and,inparticular, introduced theconcept knownasthefootprint ofuncertainty (3)whichprovides auseful verbal andgraphical description oftheuncertainty captured byanygiven type-2 fuzzy set. As a consequence, manypublications onthetheory and applications oftype-2 fuzzy setsappeared (for example, (4) and(5)).