We analyze the use of the composition of mappings as a fuzzy conjunction between indexes of inclusion. Instead of the general approach of the φ-index of inclusion, we consider a fresh approach that computes the φ-index of inclusion when restricted to a join-subsemilattice of indexes of inclusion. Under this restriction, we identify a certain join-subsemilattice which has a biresiduated structure when composition is interpreted as conjunction. The main consequence of this biresiduated structure is a representation theorem of biresiduated lattices on the unit interval in terms of the composition and subsets of indexes of inclusion.

We continue our research line on the analysis of the properties of the f-indexes of inclusion and contradiction; in this paper, specifically, we show that both notions can be related by means of the, conveniently reformulated, Aristotelian square of opposition. We firstly show that the extreme cases of the f-indexes of inclusion and contradiction coincide with the vertexes of the Aristotelian square of opposition in the crisp case; then, we allocate the rest of f-indexes in the diagonals of the extreme cases and we prove that the Contradiction, Contrariety, Subcontrariety, Subalternation and Superalternation relations also hold between the f-indexes of inclusion and contradiction.

In this short communication, we refute the conjecture by Fodor and Yager from [5] that the class of inclusion measures proposed by Kitainik coincides with that of inclusion measures based on contrapositive fuzzy implications. In particular, we show that the conjecture only holds when the considered universe of discourse is finite.

We continue studying the properties of the f-index of inclusion and show that, given a fixed pair of fuzzy sets, their f-index of inclusion can be linked to a fuzzy conjunction which is part of an adjoint pair. We also show that, when this pair is used as the underlying structure to provide a fuzzy interpretation of the modus ponens inference rule, it provides the maximum possible truth-value in the conclusion among all those values obtained by fuzzy modus ponens using any other possible adjoint pair.

This paper analyzes the possibility of defining fuzzy association rules by means of direct quantiles F-transforms. The set of fuzzy association rules is used in a fuzzy inference system, defined by means of the inverse quantile F-transform. The obtained inference system reminds the Takagi-Sugeno one due to the use of a weighted sum to perform the inference. However, there is an important difference: the output is a fuzzy set and, as a result, we require the use of a defuzzification procedure. In addition, in this paper we prove experimentally that the fuzzy set obtained as the output of the proposed inference system is related to a probability distribution.

In this work we present a sufficient condition to guarantee the existence of stable models of residuated logic programs with constrain. Such condition is based on another result already published in the literature that guarantees the existence of stable models independently of the syntax. Specifically, it states that if the set of truth values is the unit interval [0,1] and the connectives continuous, then every logic program without constrains has stable models.

A cheap personal camera is a perfect device that allows us to test algorithms for video enhancement. In this paper we present a cascade of filters based on a fuzzy representation of images. This representation tries to capture the uncertainty underlying in the intensity of a pixel by means of a fuzzy set. The cascade of filters is compared with the corresponding standard filters: blurring, sharpening and image averaging. Besides, experimentally we show that our approach provides similar results with a significant reduction of the computational time.

The paper explores Bilinear Interpolation applied to image enlargement after a fuzzification pre-processing. On the one hand, and from a theoretical point of view, we show some interesting relationships between Bilinear Interpolation and the Fuzzification. On the other hand, from an applied point of view we apply the interpolation obtained to enlargement and show that the obtained results are firstly, faster and secondly, comparable with the standard interpolation procedures.

We present a top-k algorithm for retrieving tuples according to the order provided by a ranking function that belongs to a subclass of non-monotonic functions. The ranking functions are defined with the values where the maximum score is achieved. We test the proposed algorithm on various real and artificial data with varying variable ranges and different nonmonotonic ranking functions.

In this paper, we present a way to represent contradiction between fuzzy sets. This representation is given in terms of the notion of f-weak-contradiction. Unlike other approaches, we do not define contradiction just by using one of the relations of f-weak-contradiction but by considering the whole set of relations. This consideration avoids the need to fix an operator beforehand in order to take into account all the information between two fuzzy sets. As a result, we characterize the contradiction between fuzzy sets and define a family of measures of contradiction satisfying four interesting properties: symmetry; antitonicity; if the intersection is empty, then the measure is one; and if there is an element in the intersection with degree of membership 1, then the measure is zero.

The theory of fuzzy property-oriented concept lattices is a formal tool for modeling and processing incomplete knowledge in information systems. This paper relates this research topic to that of mathematical morphology, a theory whose scope is to process and analyze images and signals. Consequently, the theory developed in the concept lattice framework can be used in these particular settings.

In this work we elaborate on the notion of contradiction between fuzzy sets introduced by Trillas et al in a fuzzy logic context. Our approach is parametric in that the operator used to define contradiction is rather a variable than a constant introduced prior to the analysis of contradiction. We give several motivations to consider weaker operators than the usual involutive negations, and obtain some preliminary results which validate this proposal.

Recent approaches have shown that the measurement of the amount of inconsistent information contained in a logic theory can be useful to infer positive information. This paper deals with the definition of measures of inconsistency in the residuated-logic-programming paradigm under the fuzzy answer set semantics. This fuzzy framework provides a soft mechanism to control the amount of information inferred and, thus, controlling the inconsistencies by modifying slightly the truth values of some rules.

Inconsistency in the framework of general resid-uated logic programs can be, somehow, decomposed into two notions: incoherence and instability. In this work, we focus on the measure of instability of normal residuated programs. Some measures were already provided and initial results obtained in terms of the amount of information that have to be discarded in order to recover stability; in this paper, our interest is focused precisely on the case in which stability can be recovered by adding information to our program.

In this paper we continue analyzing the introduction of negation into the framework of residuated logic programming [18], [19]; specifically, we focus on extended programs, in which strong negation is introduced. The classical approach to extended logic programs consists in considering negated literals as new, independent, ones and, then apply the usual monotonic approach (based on the fix-point semantics and the TPoperator); if the least fix-point so obtained is inconsistent, then the approach fails and no meaning is attached to the program. This paper introduces several approaches to considering consistence (under the term coherence) into a fuzzy setting, and studies some of their properties.