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.

In this contribution, we first introduce the concept of metrical T-norm-based similarity measure for hesitant fuzzy sets (HFSs) {by using the concept of T-norm-based distance measure}. Then,the relationship of the proposed {metrical T-norm-based} similarity {measures} with the {other kind of information measure, called the metrical T-norm-based} entropy measure {is} discussed. The main feature ...

Extensions of monoidal t-norm logic MTL and related fuzzy logics with truth stresser modalities such as globalization and “very true” are presented here both algebraically in the framework of residuated lattices and proof-theoretically as hypersequent calculi. Completeness with respect to standard algebras based on t-norms, embeddings between logics, decidability, and the finite embedding prope...

Finding strongly standard complete axiomatizations for t-norm based fuzzy logics (i.e. complete for deductions with infinite sets of premises w.r.t. semantics on the real unit interval [0, 1]) is still an open problem in general, even though results are already available for some particular cases like some infinitary logics based on a continuous t-norm or certain expansions of Monoidal t-norm b...

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.