Fuzzy logics based on triangular norms and their corresponding conorms are investigated. An aarmative answer to the question whether in such logics a speciic level of satissability of a set of formulas can be characterized by the same level of satissability of its nite subsets is given. Tautologies, contradictions and contingencies with respect to such fuzzy logics are studied, in particular fo...

xiii Acknowledgements / Agräıments xv

This paper deals with interval-valued fuzzy sets and I-fuzzy sets, Atanassov's intuitionistic fuzzy sets. They are treated in a systematic way as two, formally equivalent, natural extensions of methods of representing incomplete knowledge about sets. We define and investigate triangular norm-based areas of uncertainty of interval-valued fuzzy sets and I-fuzzy sets, and study some properties of ...

In this paper a variation of the fibred semantics of D. Gabbay called plain fibring is proposed, with the aim of combining logics given by matrix semantics. It is proved that the plain fibring of matrix logics is also a matrix logic. Moreover, it is proved that any logic obtained by plain fibring is a conservative extension of the original logics. It is also proposed a simpler version of plain ...

Analytical structure for a fuzzy PID controller is introduced by employing two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. This structure is derived via left and right trapezoidal membership functions for inputs, trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum infere...

5 The paper surveys the present state of knowledge on t-norm based predicate fuzzy logics with their double semantics: standard (the set of truth values being the real interval [0,1]) and general with abstract algebras of truth functions. 7 © 2009 Published by Elsevier B.V.

Recently, in [4], we have discussed the following distributive equation of implications I(x, T1(y, z)) = T2(I(x, y), I(x, z)) over t-representable t-norms, generated from strict t-norms, in interval-valued fuzzy sets theory. In this work we continue these investigations, but with the assumption that T1 is generated from nilpotent t-norms, while T2 is generated from strict t-norms. As a byproduc...

A family of fuzzification schemes is proposed that can be used to transform cardinality-based similarity measures for ordinary sets into similarity measures for fuzzy sets in a finite universe. These schemes are based on the Frank t-norm family and preserve transitivity in the fuzzification process.

A generalization of bags is proposed and fundamental operations are described. That is, a real-valued bag is proposed which is a straightforward generalization of the traditional bags, but is necessary for complementation, and s-norm and t-norm operations. We mainly describe how complementation and s-norms are related. As a result a duality theorem between s-norm and t-norm is obtained. R-bag r...