Primeness in Quantales

In this paper we propose a new concept of primeness in quantales. It is proved that this concept coincide with classical definition in commutative quantales, but no longer valid in the noncommutative setting. Also, the notions of strong and uniform strong primeness are investigated

Mathematical morphology for two valued gray-scale images with undefined information

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Interval additive generators of interval t-norms and interval t-conorms

The aim of this paper is to introduce the concepts of interval additive generators of interval t-norms and interval t-conorms, as interval representations of additive generators of tnorms and t-conorms, respectively, considering both the correctness and the optimality criteria. The formalization of interval fuzzy connectives in terms of their interval additive generators provides a more systematic methodology for the selection of interval t-norms and interval t-conorms in the various applications of fuzzy systems. We also prove that interval additive generators satisfy the main properties of additive generators discussed in the literature

Analyzing the relationship between interval-valued D-Implications and interval-valued QL-Implications

The aim of this work is to analyze the relationship between interval QLimplications and their contrapositions named interval D-implications.In order to achieve this aim, the commutative classes relating to these concepts are studied.We also analyze under which conditions the main properties corresponding to punctual D-implications and QL-implications are still valid when an interval-based fuzzy approach,on the best interval representation, is considered

Interval-Valued D-Implications

The aim of this work is to introduce the concepts of interval Dimplications and automorphisms, analyzing their main properties and establishing the relation between them. Also, interval D-implications are related with punctual D-implications and automorphisms

On interval fuzzy S-implications

This paper presents an analysis of interval-valued S-implications and interval-valued automorphisms, showing a way to obtain an interval-valued S-implication from two S-implications, such that the resulting interval-valued S-implication is said to be obtainable. Some consequences of that are: (1) the resulting interval-valued S-implication satisfies the correctness property, and (2) some important properties of usual S-implications are preserved by such interval representations. A relation between S-implications and interval-valued Simplications is outlined, showing that the action of an interval-valued automorphism on an interval-valued S-implication produces another interval-valued S-implication

‎On Generalized Mixture Functions

In the literature it is very common to see problems in which it is necessary to aggregate a set of data into a single one‎. ‎An important tool able to deal with these issues is the aggregation functions‎, ‎which we can highlight as the OWA functions‎. ‎However‎, ‎there are other functions that are also capable of performing these tasks‎, ‎such as the preaggregation function and mixture functions‎. ‎In this paper we investigate two special types of functions‎, ‎the Generalized Mixture functions and Bounded Generalized Mixture functions‎, ‎which generalize both OWA and Mixture functions‎. ‎We also prove some properties‎, ‎constructions and examples of these functions‎. ‎Both the Generalized and Bounded Generalized Mixture functions are developed in such a way that the weight vectors are variables that depend on the input vector‎, ‎which generalizes the aggregation functions‎: ‎ Minimum‎, ‎Maximum‎, Arithmetic Mean and Median, ‎and are extensively used in image processing‎. ‎Finally‎, ‎we propose a Generalized Mixture function‎, ‎denoted by $\mathbf{H}$‎, ‎and we show that $\mathbf{H}$ satisfies a series of properties in order to apply this function in an illustrative example of application‎: ‎The image reduction process‎