Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets

Trillas et al. (1999, Soft computing, 3 (4), 197–199) and Trillas and Cubillo (1999, On non-contradictory input/output couples in Zadeh's CRI proceeding, 28–32) introduced the study of contradiction in the framework of fuzzy logic because of the significance of avoiding contradictory outputs in inference processes. Later, the study of contradiction in the framework of Atanassov's intuitionistic fuzzy sets (A-IFSs) was initiated by Cubillo and Castiñeira (2004, Contradiction in intuitionistic fuzzy sets proceeding, 2180–2186). The axiomatic definition of contradiction measure was stated in Castiñeira and Cubillo (2009, International journal of intelligent systems, 24, 863–888). Likewise, the concept of continuity of these measures was formalized through several axioms. To be precise, they defined continuity when the sets ‘are increasing’, denominated continuity from below, and continuity when the sets ‘are decreasing’, or continuity from above. The aim of this paper is to provide some geometrical construction methods for obtaining contradiction measures in the framework of A-IFSs and to study what continuity properties these measures satisfy. Furthermore, we show the geometrical interpretations motivating the measures.

Obtaining contradiction measure on intuitionistic fuzzy sets from fuzzy connectives

In a previous paper, we proposed an axiomatic model for measuring self-contradiction in the framework of Atanassov fuzzy sets. This way, contradiction measures that are semicontinuous and completely semicontinuous, from both below and above, were defined. Although some examples were given, the problem of finding families of functions satisfying the different axioms remained open. The purpose of this paper is to construct some families of contradiction measures firstly using continuous t-norms and t-conorms, and secondly by means of strong negations. In both cases, we study the properties that they satisfy. These families are then classified according the different kinds of measures presented in the above paper.

Probabilidades imprecisas: intervalar, fuzzy e fuzzy intuicionista

The idea of considering imprecision in probabilities is old, beginning with the Booles George work, who in 1854 wanted to reconcile the classical logic, which allows the modeling of complete ignorance, with probabilities. In 1921, John Maynard Keynes in his book made explicit use of intervals to represent the imprecision in probabilities. But only from the work ofWalley in 1991 that were established principles that should be respected by a probability theory that deals with inaccuracies. With the emergence of the theory of fuzzy sets by Lotfi Zadeh in 1965, there is another way of dealing with uncertainty and imprecision of concepts. Quickly, they began to propose several ways to consider the ideas of Zadeh in probabilities, to deal with inaccuracies, either in the events associated with the probabilities or in the values of probabilities. In particular, James Buckley, from 2003 begins to develop a probability theory in which the fuzzy values of the probabilities are fuzzy numbers. This fuzzy probability, follows analogous principles to Walley imprecise probabilities. On the other hand, the uses of real numbers between 0 and 1 as truth degrees, as originally proposed by Zadeh, has the drawback to use very precise values for dealing with uncertainties (as one can distinguish a fairly element satisfies a property with a 0.423 level of something that meets with grade 0.424?). This motivated the development of several extensions of fuzzy set theory which includes some kind of inaccuracy. This work consider the Krassimir Atanassov extension proposed in 1983, which add an extra degree of uncertainty to model the moment of hesitation to assign the membership degree, and therefore a value indicate the degree to which the object belongs to the set while the other, the degree to which it not belongs to the set. In the Zadeh fuzzy set theory, this non membership degree is, by default, the complement of the membership degree. Thus, in this approach the non-membership degree is somehow independent of the membership degree, and this difference between the non-membership degree and the complement of the membership degree reveals the hesitation at the moment to assign a membership degree. This new extension today is called of Atanassov s intuitionistic fuzzy sets theory. It is worth noting that the term intuitionistic here has no relation to the term intuitionistic as known in the context of intuitionistic logic. In this work, will be developed two proposals for interval probability: the restricted interval probability and the unrestricted interval probability, are also introduced two notions of fuzzy probability: the constrained fuzzy probability and the unconstrained fuzzy probability and will eventually be introduced two notions of intuitionistic fuzzy probability: the restricted intuitionistic fuzzy probability and the unrestricted intuitionistic fuzzy probability

Intuitionistic fuzzy Choquet integral operator-based approach for black-start decision-making

Determining the optimal of black-start strategies is very important for speeding the restoration speed of a power system after a global blackout. Most existing black-start decision-making methods are based on the assumption that all indexes are independent of each other, and little attention has been paid to the group decision-making method which is more reliable. Given this background, the intuitionistic fuzzy set and further intuitionistic fuzzy Choquet integral operator are presented, and a black-start decision-making method based on this integral operator is presented. Compared to existing methods, the proposed algorithm cannot only deal with the relevance among the indexes, but also overcome some shortcomings of the existing methods. Finally, an example is used to demonstrate the proposed method. © 2012 The Institution of Engineering and Technology.

A Study Of Frames In The Fuzzy And Intuitionist Fuzzy Contexts

The fuzzy set theory has a wider scope of applicability than classical set theory in solving various problems. Fuzzy set theory in the last three decades as a formal theory which got formalized by generalizing the original ideas and concepts in classical mathematical areas and as a very powerful modeling language, that can cope with a large fraction of uncertainties of real life situations. In Intuitionistic Fuzzy sets a new component degree of non membership in addition to the degree of membership in the case of fuzzy sets with the requirement that their sum be less than or equal to one. The main objective of this thesis is to study frames in Fuzzy and Intuitionistic Fuzzy contexts. The thesis proved some results such as ifµ is a fuzzy subset of a frame F, then µ is a fuzzy frame of F iff each non-empty level subset µt of µ is a subframe of F, the category Fuzzfrm of fuzzy frames has products and the category Fuzzfrm of fuzzy frames is complete. It define a fuzzy-quotient frame of F to be a fuzzy partition of F, that is, a subset of IF and having a frame structure with respect to new operations and study the notion of intuitionistic fuzzy frames and obtain some results and introduce the concept of Intuitionistic fuzzy Quotient frames. Finally it establish the categorical link between frames and intuitionistic fuzzy topologies.

Fuzzy sets in distributed traffic control

The task of controlling urban traffic requires flexibility, adaptability and handling uncertain information spread through the intersection network. The use of fuzzy sets concepts convey these characteristics to improve system performance. This paper reviews a distributed traffic control system built upon a fuzzy distributed architecture previously developed by the authors. The emphasis of the paper is on the application of the system to control part of Campinas downtown area. Simulation experiments considering several traffic scenarios were performed to verify the capabilities of the system in controlling a set of coupled intersections. The performance of the proposed system is compared with conventional traffic control strategies under the same scenarios. The results obtained show that the distributed traffic control system outperforms conventional systems as far as average queues, average delay and maximum delay measures are concerned.

Epidemiological Models of Directly Transmitted Diseases: An Approach via Fuzzy Sets Theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modeling and measuring the spatial relation "along": Regions, contours and fuzzy sets

The analysis of spatial relations among objects in an image is an important vision problem that involves both shape analysis and structural pattern recognition. In this paper, we propose a new approach to characterize the spatial relation along, an important feature of spatial configurations in space that has been overlooked in the literature up to now. We propose a mathematical definition of the degree to which an object A is along an object B, based on the region between A and B and a degree of elongatedness of this region. In order to better fit the perceptual meaning of the relation, distance information is included as well. In order to cover a more wide range of potential applications, both the crisp and fuzzy cases are considered. In the crisp case, the objects are represented in terms of 2D regions or ID contours, and the definition of the alongness between them is derived from a visibility notion and from the region between the objects. However, the computational complexity of this approach leads us to the proposition of a new model to calculate the between region using the convex hull of the contours. On the fuzzy side, the region-based approach is extended. Experimental results obtained using synthetic shapes and brain structures in medical imaging corroborate the proposed model and the derived measures of alongness, thus showing that they agree with the common sense. (C) 2011 Elsevier Ltd. All rights reserved.

Von Fuzzy-Sets zu Computing-with-Words

Dieser Artikel bietet einen Überblick über die Entwicklung und Zusammenhänge der einzelnen Elemente der Fuzzy-Logik, wovon Fuzzy-Set-Theorie die Grundlage bildet. Die Grundproblematik besteht in der Handhabung von linguistischen Informationen, die häufig durch Ungenauigkeit gekennzeichnet sind. Die verschiedenen technischen Anwendungen von Fuzzy-Logik bieten eine Möglichkeit, intelligentere Computersysteme zu konstruieren, die mit unpräzisen Informationen umgehen können. Solche Systeme sind Indizien für die Entstehung einer neuen Ära des Cognitive-Computing, di in diesemArtikel ebenfalls zur Sprache kommt. Für das bessere Verständnis wird der Artikel mit einem Beispiel aus der Meteorologie (d. h. Schnee in Adelboden) begleitet.

Supplementarity measures on fuzzy sets.

In this paper, we commence the study of the so called supplementarity measures. They are introduced axiomatically and are then related to incompatibility measures by antonyms. To do this, we have to establish what we mean by antonymous measure. We then prove that, under certain conditions, supplementarity and incompatibility measuresare antonymous. Besides, with the aim of constructing antonymous measures, we introduce the concept of involution on the set made up of all the ordered pairs of fuzzy sets. Finally, we obtain some antonymous supplementarity measures from incompatibility measures by means of involutions.