Recently it has been shown that in Image Processing, the usual sum and product of the reals are not the only operations that can be used. Several other operations provided by fuzzy logic perform well in this application. We continue this line of research and we propose the use of a pair consisting of a uninorm and an absorbing norm determined by a continuous, strictly increasing generator inste...

In this paper, a set of axioms is given that characterizes those functions I : [0, 1] → [0, 1] for which a left-continuous uninorm U exists in such a way that I is the residual implication derived from U . A characterization for the particular case when U is representable is also given. Keywords— Implication function, left-continuity, residual implication, uninorm.

We consider the interval ]−1, 1[ and intend to endow it with an algebraic structure like a ring. The motivation lies in decision making, where scales that are symmetric w.r.t. 0 are needed in order to represent a kind of symmetry in the behaviour of the decision maker. A former proposal due to Grabisch was based on maximum and minimum. In this paper, we propose to build our structure on t-conor...

In this paper we introduce a slight modification of the definition of migrativity for aggregation functions that allows useful characterization of this property. Among other things, in this context we prove that there are no t-conorms, uninorms or nullnorms that satisfy migrativity (with the product being the only migrative t-norm, as already shown by other authors) and that the only migrative ...

Uninorms as binary operations on the unit interval have been widely applied in the fuzzy set theory. This paper presents some 7 properties of uninorm-like operations for which the underlying operations are given by ordinal sums. If the underlying operations of a uninorm are given by ordinal sums, then the Cartesian product of the union of two arbitrary intervals (one in [0, e] and the other in ...

This paper delves deeply into the recently introduced mathematical morphology based on discrete t-norms. Closing and opening operators and the concepts of open and closed objects are introduced. All the properties satisfied by nilpotent t-norms, even the generalized idempotence, hold too. After that, some experimental results, using comparative measures, on edge detection are showed. Some exper...

The relationship between support vector machines (SVMs) and Takagi–Sugeno–Kang (TSK) fuzzy systems is shown. An exact representation of SVMs as TSK fuzzy systems is given for every used kernel function. Restricted methods to extract rules from SVMs have been previously published. Their limitations are surpassed with the presented extraction method. The behavior of SVMs is explained by means of ...

semi-regular locales are extensions of the classical semiregularspaces. we investigate the conditions such that semi-regularizationis a functor. we also investigate the conditions such that semi-regularizationis a reflection or coreflection.