This paper introduces the implicative derivations and gives some of their characterizations on MTL-algebras. Furthermore, we provide representation MTL-algebras by obtain Boolean algebra via all derivations. Finally, explore relationship between derivation other operators show that there exists a bijection sets multiplier IMTL-algebras. The results this can common properties in t-norm-based fuz...

MTL-algebras are algebraic structures for the Esteva-Godo monoidal tnorm based logic (MTL), a many-valued propositional calculus that formalizes the structure of the real interval [0, 1], induced by a left-continuous t-norm. Given a complete MTL-algebra X , we define the weak forcing value |φ|X and the forcing value [φ]X , for any formula φ of MTL in X . We establish some arithmetical propertie...

After dropping the implication-like operation and reversing the order, an MTL-algebra becomes a partially ordered structure (L;≤,⊕, 0, 1) based on the single addition-like operation ⊕. Furthermore, ⊕ may be restricted to a partial, but cancellative addition + without loss of information. We deal in this paper with the case that the resulting partial algebra (L;≤,+, 0, 1) is embeddable into the ...

We present the preliminary design for a C++ template library to enable the compositional construction of matrix classes suitable for high performance numerical linear algebra computations. The library based on our interface definition — the Matrix Template Library (MTL) — is written in C++ and consists of a small number of template classes that can be composed to represent commonly used matrix ...

We present a generic programming methodology for expressing data structures and algorithms for high-performance numerical linear algebra. As with the Standard Template Library [14], our approach explicitly separates algorithms from data structures, allowing a single set of numerical routines to operate with a wide variety of matrix types, including sparse, dense, and banded. Through the use of ...

Active libraries can be defined as libraries which play an active part in the compilation, in particular, the optimisation of their client code. This paper explores the implementation of an active dense linear algebra library by delaying evaluation of expressions built using library calls, then generating code at runtime for the compositions that occur. The key optimisations in this context are...

byJeremy G. Siek This thesis describes a generic programming methodology for expressing data struc-tures, algorithms, and optimizations for numerical linear algebra. A high-performanceimplementation of this approach, the Matrix Template Library (MTL), is also described.The goal of the MTL is to facilitate development of higher-level libraries and applicationsfor scientif...

The logic MTL, Monoidal t-norm based logic was presented by F. Estva and L. Godo and discuss several properties of MTL-algebra in [6] The Boolean logic (BL) was introduced by P. Hajek and discuss the properties in [1].The fuzzy reasoning and implication operators was discussed by Ying in ([2],[3]). A proper logical system for fuzzy propositional calculus and a innovative arithmetical configurat...

The Archimedean property is one of the most beautiful axioms of the classical arithmetic and some of the methods of constructing the field of real numbers are based on this property. It is well-known that every Archimedean `-group is abelian and every pseudo-MV algebra is commutative. The aim of this paper is to introduce the Archimedean property for pseudo-MTL algebras and FLw-algebras. The ma...

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...