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Stereo matching is the central problem of stereovision paradigm. Area-based techniques provide the dense disparity maps and hence they are preferred for stereo correspondence. Normalized cross correlation (NCC), sum of squared differences (SSD) and sum of absolute differences (SAD) are the linear correlation measures generally used in the area-based techniques for stereo matching. In this paper, similarity measure for stereo matching based on fuzzy relations is used to establish the correspondence in the presence of intensity variations in stereo images. The strength of relationship of fuzzified data of two windows in the left image and the right image of stereo image pair is determined by considering the appropriate fuzzy aggregation operators. However, these measures fail to establish correspondence of the pixels in the stereo images in the presence of occluded pixels in the corresponding windows. Another stereo matching algorithm based on fuzzy relations of fuzzy data is used for stereo matching in such regions of images. This algorithm is based on weighted normalized cross correlation (WNCC) of the intensity data in the left and the right windows of stereo image pair. The properties of the similarity measures used in these algorithms are also discussed. Experiments with various real stereo images prove the superiority of these algorithms over normalized cross correlation (NCC) under nonideal conditions.

Equivalence relations and orderings are key concepts of mathematics. For both types of relations, formulations within the framework of fuzzy relations have been proposed already in the early days of fuzzy set theory. While similarity (indistinguishability) relations have turned out to be very useful tools, e.g. for the interpretation of fuzzy partitions and fuzzy controllers, the utilization of fuzzy orderings is still lagging far behind, although there are a lot of possible applications, for instance, in fuzzy preference modeling and fuzzy control. The present paper is devoted to this missing link. After a brief motivation, we will critically analyze the existing approach to fuzzy orderings. In the main part, an alternative approach to fuzzy orderings, which also takes the strong connection to gradual similarity into account, is proposed and studied in detail, including several constructions and representation results.

Aggregation processes are fundamental in any discipline where the fusion of information is of vital interest. For aggregating binary fuzzy relations such as equivalence relations or fuzzy orderings, the question arises which aggregation operators preserve specific properties of the underlying relations, e.g. T-transitivity. It will be shown that preservation of T-transitivity is closely related to the domination of the applied aggregation operator over the corresponding t-norm T. Furthermore, basic properties for dominating aggregation operators, not only in the case of dominating some t-norm T, but dominating some arbitrary aggregation operator, will be presented. Domination of isomorphic t-norms and ordinal sums of t-norms will be treated. Special attention is paid to the four basic t-norms (minimum t-norm, product t-norm, Łukasiewicz t-norm, and the drastic product).

This paper introduces strict fuzzy orderings in the framework of similarity-based fuzzy orderings, i.e. where a context of similarity/indistinguishability is given by means of a fuzzy equivalence relation. We consider how to construct strict fuzzy orderings from partial fuzzy orderings and vice versa. The appropriateness of the concepts introduced in this paper is underlined by theoretical results and examples. We observe that the strongest results are achieved if the underlying triangular norm induces an involutive residual negation.

We analyze the main properties of binary relations, defined on a nonempty set, that arise in a natural way when dealing with real-valued functions that satisfy certain classical functional equations on two variables. We also consider the converse setting, namely, given binary relations that accomplish some typical properties, we study whether or not they come from solutions of some functional equation. Applications to the numerical representability theory of ordered structures are also furnished as a by-product. Further interpretations of this approach as well as possible generalizations to the fuzzy setting are also commented. In particular, we discuss how the values taken for bivariate functions that are bounded solutions of some classical functional equations define, in a natural way, fuzzy binary relations on a set.

This paper extends the theory of fuzzy diseases predictions in order to detect the causes of business failure. This extension is justified through the advantages of the reference model and its originality. Moreover, the fuzzy model is completed by this proposal and some parts of it have been published in isolated articles. For this purpose, the fuzzy theory is combined with the OWA operators to identify the factors that generate problems in firms. Also, a goodness index to validate its functionality and prediction capacity is introduced. The model estimates a matrix of economic- financial knowledge based on matrices of causes and symptoms. Knowing the symptoms makes it possible to estimate the causes, and managing them properly, allows monitoring and improving the company’s financial situation and forecasting its future. Also with this extension, the model can be useful to develop suitable computer systems for monitoring companies’ problems, warning of failures and facilitating decision-making.

In this paper, we provide a definition of α-fuzzified lower and upper approximations for fuzzy sets based on the α-cut of fuzzy binary relations. We show that the definition is a proper generalization of the previous one for approximations of crisp sets and compare it with an existing definition in the context of fuzzy tolerance relation.

We use fuzzy logic engineering tools to detect human behavior in the finance arena, specifically in the technical analysis field. Since technical analysis theory consists of indicators used by experts to evaluate stock prices, the new proposed method maps these indicators into new inputs that can be fed into a fuzzy logic system. This system can create an optimum computerized model to evaluate stock price movement. This method relies on human psychology to predict human behavior when certain price movements or certain price formations occur. The success of the system is measured by comparing system output versus stock price movement. The new stock evaluation method is proven to exceed market performance and it can be an excellent tool in the technical analysis field. The flexibility of the system is also demonstrated.

We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0,1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices.The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples.

Two-dimensional (2D) polyacrylamide gel electrophoresis of proteins is a robust and reproducible technique. It is the most widely used separation tool in proteomics. Current efforts in the field are directed at development of tools for expanding the range of proteins accessible with 2D gels. Proteomics was built around the 2D gel. The idea that multiple proteins can be analyzed in parallel grew from 2D gel maps. Proteomics researchers needed to identify interested protein spots by examining the gel. This is time-consuming, labor-extensive, and error-prone process. It is desired that the computer can analyze the proteins automatically by first detecting then quantifying the protein spots in the 2D gel images. In our previous work, we presented a new technique for segmentation of 2D gel images using the fuzzy c-means (FCM) algorithm using the notion of fuzzy relations. In this paper, we will describe the new relational FCM (RFCM) algorithm and use it for automatic protein spots quantification. We will also use two methods to evaluate its performance: the unsupervised evaluation method and comparison with the expert spots quantification.

In this paper we highlight a few features of the semantic gap problem in image interpretation. We show that semantic image interpretation can be seen as a symbol grounding problem. In this context, ontologies provide a powerful framework to represent domain knowledge, concepts and their relations, and to reason about them. They are likely to be more and more developed for image interpretation. A lot of image interpretation systems rely strongly on descriptions of objects through their characteristics such as shape, location, image intensities. However, spatial relations are very important too and provide a structural description of the imaged phenomenon, which is often more stable and less prone to variability than pure object descriptions. We show that spatial relations can be integrated in domain ontologies. Because of the intrinsic vagueness we have to cope with, at different levels (image objects, spatial relations, variability, questions to be answered, etc.), fuzzy representations are well adapted and provide a consistent formal framework to address this key issue, as well as the associated reasoning and decision making aspects. Our view is that ontology-based methods can be very useful for image interpretation if they are associated to operational models relating the ontology concepts to image information. In particular, we propose operational models of spatial relations, based on fuzzy representations.

This paper deals with identification of romanized plaintexts of five Indian Languages - Hindi, Bengali, Manipuri, Urdu and Kashmiri. Fuzzy Pattern Recognition technique has been adopted for identification. Suitable features/characteristics are extracted from training samples of each of these five languages and represented suitably through fuzzy sets. Prototypes in the form of fuzzy sets are constructed for each of these five languages. The identification is based on computation of dissimilarity with prototypes of each of these languages. It is computed using a dissimilarity measure extracted through fuzzy relational matrices. The identifier proposed is independent of dictionary of any of these languages and can even identify plaintext without word break-ups. The identification can be used for automatic segregation of plain texts of these languages while analysing intercepted multiplexed interlieved Speech/Data/Fax communication on RF channel, in a computer network or Internet.

We introduce Restriction Level relations (RL-relations) to represent imprecise relations. The proposal is based on the notion of RL-representation of imprecise properties proposed by the authors as an alternative to fuzzy representations, with the advantage that the ordinary properties of the crisp case are preserved. On this basis we define RL-preference structures and discuss about the properties of this new approach.

We propose a new theoretical background of autoregressive fuzzy associative memories (AFAM). It stems from the theory of fuzzy relation equations and eigen sets of their solutions. We introduce a couple of related AFAM models that share the same fuzzy relation. For one particular couple, we propose a fast algorithm of data retrieval. We characterize the types of noise that can be removed/reduced by the related models of a couple.

The aim of the following paper is to make a diagnosis of firms using the theory developed by Vigier and Terceño [1], an overall approach for analyzing the causes and symptoms of the future economic-financial situations of firms. The methodological postulates of the model are adapted and applied to a group of SMEs in the construction sector for a particular timeline, using the tools and methods of fuzzy logic. By working with multiple qualitative variables and modeling the expert’s knowledge, this methodology overcomes many of the traditional models’ restrictions regarding the treatment of subjectivity and uncertainty. This research shows the results of the estimates of the matrix of economic–financial knowledge, as well as the treatment of causes, taking as a reference the first theoretical approach presented in Terceño et al. [2].