In this paper we summarize our results obtained recently on continuous triangular norms that are migrative with respect to an arbitrary continuous triangular norm. We start with the original notion of migrativity and completely describe all continuous migrative triangular norms. Since the migrative property excludes both idempotent and nilpotent t-norm classes, the characterization and construc...

Introducing more types of integrals will provide more choices todeal with various types of objectives and components in real problems. Firstly,in this paper, a (T) fuzzy integral, in which the integrand, the measure andthe integration result are all multi-valued, is presented with the introductionof T-norm and T-conorm. Then, some classical results of the integral areobtained based on the prope...

and Applied Analysis 3 As a result of 2.2 we obtain, for each x, y ∈ 0, 1 , T ( x, y ) ≤ T x, 1 x, T ( x, y ) ≤ T ( 1, y ) y. 2.5 Since, for all x, y ∈ 0, 1 , trivially T x, y ≥ 0 TD x, y , we get for an arbitrary t-norm T , TD ≤ T ≤ TM. 2.6 That is, TD is weaker and TM is stronger than any other t-norms. Also since TL < TP , we obtain the following ordering for four basic t-norms TD < TL < TP ...

The above norm induces a metric d where d(f, g) = ‖f − g‖p. Note that d(f, g) = 0 if and only if f = g a.e. μ, in which case we identify f with g. The Lp norm, like all worthy norms, satisfies the triangle inequality: ‖f + g‖p ≤ ‖f‖p + ‖g‖p ; this is precisely Minkowski’s inequality. For random variables X, Y defined on the same probability space and having finite p’th moments, Minkowski’s ineq...

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to ...

 Minimum and maximum operators are two well-known t-norm and s-norm used frequently in fuzzy systems. In this paper, two different types of fuzzy inequalities are simultaneously studied where the convex combination of minimum and maximum operators is applied as the fuzzy relational composition. Some basic properties and theoretical aspects of the problem are derived and four necessary and suffi...

We are interested in generalizations of the concepts of t-norm and t-conorm. In a companion chapter in this volume [14] we have presented a family of hypert-norms ∧q and a family of hyper-t-conorms ∨p. The prefix hyper is used to indicate multi-valued operations, also known as hyperoperations (see [5, 14]), i.e. operations which map pairs of elements to sets of elements. See [14] for the constr...

This paper discusses the property of local finiteness for t-norm monoids and extensions of them. The focus is (i) on t-norm bimonoids, which are of interest in the context of weighted automata, (ii) on those extensions of t-norm monoids which are reducts of t-algebras, i.e. of the basic semantic entities for the (fuzzy) logics of left-continuous and of continuous t-norms, and (iii) on extension...

In fuzzy logic in wider sense t norms got a prominent r ole in recent times In many valued logic the Lukasiewicz systems the G odel sytems and also the product logic are t norm based The present paper discusses the more general problem of the adequate axiomatizability for such t norm based logical systems in general survey ing results of the last years