Imprecise choices can be described using either a probabilistic or a fuzzy formalism. No relation between them has been studied so far. In this contribution we present a connection between the two formalisms that strongly makes use of fuzzy implication operators and t-norms. In this framework, Luce’s Choice Axiom turns out to be a special case when the product t-norm is considered and other sim...

The law of importation for fuzzy implications is studied and it is solved for S, R, QL and D-implications derived from uninorms. Along this study many new solutions of this property appears different from those already known for implications derived from t-norms and t-conorms.

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...

Propositional fuzzy logics given by a combination of a continuous SBL t-norm with finitely many idempotents and of an involutive negation are investigated. A characterization of continuous t-norms which, in combination with different involutive negations, yield either isomorphic algebras or algebras with distinct and incomparable sets of propositional tautologies is presented.

We study some boolean-like laws with iterative variables in Fuzzy Logic. We show that beyond the classical De Morgan triplets of connectives described by t-norms, t-conorms and strong negations there are interesting models with infinite solutions and surprising situations where there are none.

So far, computational complextity of the general formula for the extended t-norm does not allow to construct fuzzy logic systems of type-2 other than interval type. In this paper, we derive new formulae for extended t-norms for arguments with Gaussian and piecewise-Gaussian membership functions basing on our original theorems.

and Applied Analysis 3 a vector space from various points of view 28–30 . In particular, Bag and Samanta 31 , following Cheng and Mordeson 32 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 33 . They established a decomposition theorem of a fuzzy norm into a family of crisp norms and investigated some properties of fuzzy normed ...

In recent years many Fuzzy Description Logics (FDLs) based on infinite t-norms have been proved to be undecidable. On the other hand, several FDLs based on finite t-norms, not only have been proved to be decidable, but they have been proved to belong to the same complexity classes as the corresponding crisp DLs. In light of such results, a question that naturally arises is whether the finite-va...

In this article, we introduce the idea of normality and translation Q-intuitionistic fuzzy subgroups with respect to norms (t-norm T t-conorm C) some interesting results them are given. Conditions for level cut subsets explored provided. Finally, investigate by using group homomorphisms investigated.

In the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. Then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.