$Rsb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $Rsb{0}$-algebras and the category of t...

A fixed point theorem of Hadzic [5] is generalized to locally convex spaces and the new result is applied to extend a recent result on invariant approximation of Jungck and Sessa [8] and Mukherjee and Som [11] for non-convex condition of domain and without affineness condition of mappings. Some known results [1], [6], [13] and [16] are also extended and improved. A property known as Property Γ ...

In this article we are presenting two new classes of t-norm and t-conorm based generalized means with weights. We are going to test usability of these measures which we get by combining classes of t-norms and t-conorms to the generalized mean operator. Since we are using the generalized mean we have an additional parameter that controls the power which the argument values are raised. Dombi and ...

T he properties of large conductance C a2+-dependent K + channels in smooth muscle cells (smc) isolated from norm al and atherosclerotic hum an aorta were studied using the patch-clam p technique. It was shown tha t smc from norm al hum an aorta possess a homogeneous population of norm al C a2+-dependent K + channels. In atherosclerotic aorta two kinetically different types of these channels co...

As it was shown in [7], Monoidal t-norm based logic (MTL) is a logic of left-continuous t-norms. In other words, this means that MTL enjoys the standard completeness theorem. In this paper we present a different proof of this theorem. In fact, we prove even more since we show that MTL is complete w.r.t. the class of standard MTL-algebras with finite congruence lattices or equivalently with fini...

A dialogue game based approach to the problem of providing a deeper semantic foundation for t-norm based fuzzy logics is explored. In particular, various versions, extensions and alternatives to Robin Giles’s dialogue and betting game for Lukasiewicz logic are re-visited and put in the context of other foundational research in logic. It emerges that dialogue games cover a wide range of topics r...

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

It is known that the monoidal t-norm based logic (MTL) and many of its schematic extensions are decidable. The usual way how to prove decidability of some schematic extension of MTL is to show that the corresponding class of algebras of truth values has the finite model property (FMP) or the finite embeddability property (FEP). However this method does not work for the extensions whose correspo...

In this paper we prove the strong standard completeness of interval-valued monoidal t-norm based logic (IVMTL) and some of its extensions. For other extensions we show that they are not strong standard complete. We also give a local deduction theorem for IVMTL and other extensions of interval-valued monoidal logic. Similar results are obtained for interval-valued fuzzy logics expanded with Baaz...

The notion of feasibility, applicable in various areas related to logic, is arguably of gradual nature—some tasks are more feasible than others. The possibility of modeling a gradual notion of feasibility in t-norm logics is brought forward and illustrated on the gradual notions of feasible number, feasible knowledge, feasible formula, and feasible computability.