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...

Learning from data streams is a contemporary and challenging issue due to the increasing rate of the size and temporal availability of data, turning traditional learning methods impracticable. This work addresses a structure and introduces a learning approach to train uninorm-based hybrid neural networks using extreme learning concepts. Uninorms bring flexibility and generality to fuzzy neuron ...

An odd Sugihara monoid is a residuated distributive latticeordered commutative idempotent monoid with an order-reversing involution that fixes the monoid identity. The main theorem of this paper establishes a category equivalence between odd Sugihara monoids and relative Stone algebras. In combination with known results, it swiftly determines which varieties of odd Sugihara monoids are [strongl...

Recently the distributive equations involving various classes of aggregation operators have aroused widespread attention because of their importance in the theoretic and applied communities of fuzzy set theory. 2-uninorms and semi-t-operators are two special classes of aggregation operators and have been proved to be useful in many areas such as fuzzy decision making, approximate reasoning and ...

The main ‘philosophical’ outcome of this article is to demonstrate that the structural description of residuated lattices requires the use of the co-residuated setting. A construction, called skew symmetrization, which generalizes the well-known representation of an ordered Abelian group obtained from the positive (or negative) cone of the algebra is introduced here. Its definition requires lea...

Uninorms are a generalization of t-norms and tconorms for which the neutral element is an element of [0,1] which is not necessarily equal to 0 (as for t-norms) or 1 (as for t-conorms). Uninorms on the unit interval are either conjunctive or disjunctive, i.e. they aggregate the pair (0,1) to either 0 or 1. In reallife applications, this kind of aggregation may be counter-intuitive. Atanassov’s i...

Paving is a method for constructing new operations from a given one. We will show that this method can be used to construct associative, commutative and monotone operations from particular given operations (from basic ‘paving stones’). We will discuss properties of the resulting operations by considering different cases of the ‘paving stones’ and the starting position of paving. Finally, we wil...

In intelligent systems where fuzzy rule base and reasoning mechanism are applied, like fuzzy control systems, decision support and expert systems, one of the key issues is the problem of aggregation of information represented by membership functions. Since the pioneering work of Prof. Lotfi Zadeh [21] a great number of fuzzy connectives, aggregation operators have been introduced. The results o...

In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, ...