Representing images by means of interval-valued fuzzy sets. Application to stereo matching

Stereo matching tries to find correspondences between locations in a pair of displaced images of the same scene in order to extract the underlying depth information. Pixel correspondence estimation suffers from occlusions, noise or bias. In this work, we introduce a novel approach to represent images by means of interval-valued fuzzy sets to overcome the uncertainty due to the above mentioned problems. Our aim is to take advantage of this representation in the stereo matching algorithm. The image interval-valued fuzzification process that we propose is based on image segmentation in a different way to the common use of segmentation in stereo vision. We introduce interval-valued fuzzy similarities to compare windows whose pixels are represented by intervals. In the experimental analysis we show the goodness of this representation in the stereo matching problem. The new representation together with the new similarity measure that we introduce shows a better overall behavior with respect to other very well-known methods.

Aggregation for Atanassov's intuitionistic and interval valued fuzzy sets: the median operator

Atanassov's intuitionistic fuzzy sets (AIFS) and interval valued fuzzy sets (IVFS) are two generalizations of a fuzzy set, which are equivalent mathematically although different semantically. We analyze the median aggregation operator for AIFS and IVFS. Different mathematical theories have lead to different definitions of the median operator. We look at the median from various perspectives: as an instance of the intuitionistic ordered weighted averaging operator, as a Fermat point in a plane, as a minimizer of input disagreement, and as an operation on distributive lattices. We underline several connections between these approaches and summarize essential properties of the median in different representations.

A construction method of interval-valued fuzzy sets for image processing

In this work we present a new construction method of IVFSs from Fuzzy Sets. We use these IVFSs for image processing. Concretely, in this contribution we introduce a new image magnification algorithm using IVFSs. This algorithm is based on block expansion and it is characterized by its simplicity.

Color image magnification with interval-valued fuzzy sets

In this work we present a simple magnification algorithm for color images. It uses Interval-Valued Fuzzy Sets in such a way that every pixel has an interval membership constructed from its original intensity and its neighbourhood's one. Based on that interval membership, a block is created for each pixel, so this is a block expansion method.

A new method for deriving priority weights by extracting consistent numerical-valued matrices from interval-valued fuzzy judgement matrix

It is important to derive priority weights from interval-valued fuzzy preferences when a pairwise comparative mechanism is used. By focusing on the significance of consistency in the pairwise comparison matrix, two numerical-valued consistent comparison matrices are extracted from an interval fuzzy judgement matrix. Both consistent matrices are derived by solving the linear or nonlinear programming models with the aid of assessments from Decision Makers (DMs). An interval priority weight vector from the extracted consistent matrices is generated. In order to retain more information hidden in the intervals, a new probability-based method for comparison of the interval priority weights is introduced. An algorithm for deriving the final priority interval weights for both consistent and inconsistent interval matrices is proposed. The algorithm is also generalized to handle the pairwise comparison matrix with fuzzy numbers. The comparative results from the five examples reveal that the proposed method, as compared with eight existing methods, exhibits a smaller degree of uncertainty pertaining to the priority weights, and is also more reliable based on the similarity measure. © 2014 Elsevier Inc. All rights reserved.

Interval-based and fuzzy set-based approaches to modeling of fuzzy inference systems with the local monotonicity property

Even though the importance of the local monotonicity property for function approximation problems is well established, there are relative few investigations addressing issues related to the fulfillment of the local monotonicity property in Fuzzy Inference System (FIS) modeling. We have previously conducted a preliminary study on the local monotonicity property of FIS models, with the assumption that the extrema point(s) (i.e., the maximum and/or minimum point(s)) is either known precisely or totally unknown. However, in some practical situations, the extrema point(s) can be known imprecisely (as an interval or a fuzzy set). In this paper, the imprecise information is exploited to construct an FIS model that fulfills the local monotonicity property. A procedure to estimate the extrema point(s) of a function is devised. Applicability of the findings to a datadriven modeling problem is further demonstrated.

Truth Values in t-norm based Systems Many-valued FUZZY Logic

In t-norm based systems many-valued logic, valuations of propositions form a non-countable set: interval [0,1]. In addition, we are given a set E of truth values p, subject to certain conditions, the valuation v is v=V(p), V reciprocal application of E on [0,1]. The general propositional algebra of t-norm based many-valued logic is then constructed from seven axioms. It contains classical logic (not many-valued) as a special case. It is first applied to the case where E=[0,1] and V is the identity. The result is a t-norm based many-valued logic in which contradiction can have a nonzero degree of truth but cannot be true; for this reason, this logic is called quasi-paraconsistent.

Parental leave regulations and the persistence of the male breadwinner model: Using fuzzy-set ideal type analysis to assess gender equality in an enlarged Europe

his paper uses fuzzy-set ideal type analysis to assess the conformity of European leave regulations to four theoretical ideal typical divisions of labour: male breadwinner, caregiver parity, universal breadwinner and universal caregiver. In contrast to the majority of previous studies, the focus of this analysis is on the extent to which leave regulations promote gender equality in the family and the transformation of traditional gender roles. The results of this analysis demonstrate that European countries cluster into five models that only partly coincide with countries’ geographical proximity. Second, none of the countries considered constitutes a universal caregiver model, while the male breadwinner ideal continues to provide the normative reference point for parental leave regulations in a large number of European states. Finally, we witness a growing emphasis at the national and EU levels concerning the universal breadwinner ideal, which leaves gender inequality in unpaid work unproblematized.

Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

Kuznetsov independence of variables X and Y means that, for any pair of bounded functions f(X) and g(Y), E[f(X)g(Y)]=E[f(X)] *times* E[g(Y)], where E[.] denotes interval-valued expectation and *times* denotes interval multiplication. We present properties of Kuznetsov independence for several variables, and connect it with other concepts of independence in the literature; in particular we show that strong extensions are always included in sets of probability distributions whose lower and upper expectations satisfy Kuznetsov independence. We introduce an algorithm that computes lower expectations subject to judgments of Kuznetsov independence by mixing column generation techniques with nonlinear programming. Finally, we define a concept of conditional Kuznetsov independence, and study its graphoid properties.

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

Fuzzy set Theory and Quantum Chemistry

Es discuteixen breument algunes consideracions sobre l'aplicació de la Teoria dels Conjunts difusos a la Química quàntica. Es demostra aqui que molts conceptes químics associats a la teoria són adequats per ésser connectats amb l'estructura dels Conjunts difusos. També s'explica com algunes descripcions teoriques dels observables quàntics es potencien tractant-les amb les eines associades als esmentats Conjunts difusos. La funció densitat es pren com a exemple de l'ús de distribucions de possibilitat al mateix temps que les distribucions de probabilitat quàntiques