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Several results on set-valued possibilistic distributions

Ivan Kramosil, Milan Daniel (2015)

Kybernetika

When proposing and processing uncertainty decision-making algorithms of various kinds and purposes, we more and more often meet probability distributions ascribing non-numerical uncertainty degrees to random events. The reason is that we have to process systems of uncertainties for which the classical conditions like σ -additivity or linear ordering of values are too restrictive to define sufficiently closely the nature of uncertainty we would like to specify and process. In cases of non-numerical...

Software cost estimation with fuzzy inputs: Fuzzy modelling and aggregation of cost drivers

Miguel-Ángel Sicilia, Juan-J. Cuadrado-Gallego, Javier Crespo, Elena García Barriocanal (2005)

Kybernetika

Parametric software cost estimation models are well-known and widely used estimation tools, and several fuzzy extensions have been proposed to introduce a explicit handling of imprecision and uncertainty as part of them. Nonetheless, such extensions do not consider two basic facts that affect the inputs of software cost parametric models: cost drivers are often expressed through vague linguistic categories, and in many cases cost drivers are better expressed in terms of aggregations of second-level...

Special issue: WUPES’12

Jiřina Vejnarová, Václav Kratochvíl (2014)

Kybernetika

This special issue of the Kybernetika Journal arose from the 9th workshop on uncertainty processing, WUPES’12, held in Mariánské Lázně, Czech Republic, in September 2012. In the selection process for this special issue, we tried to capture the rich variety of the presented methodological approaches. The quality of the selected papers was judged by reviewers in accord with the usual practice of Kybernetika. After a careful selection, 7 papers were included in the special issue. There are, however,...

Systems of possibilistic regressions: a case study in ecological inference.

Sergio Donoso, Nicolás Marín, M. Amparo Vila (2005)

Mathware and Soft Computing

This work introduces how possibilistic regression can be used in the case of non symmetrical triangular membership functions, building a system of regressions, so that suitable restrictions for each particular problem can be incorporated. We apply this methodology to the problem of ecological inference, in particular to the estimation of the electoral transition matrix. An experimentation with several examples shows the benefits of the new approach.

The irrelevant information principle for collective probabilistic reasoning

Martin Adamčík, George Wilmers (2014)

Kybernetika

Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, error , as being optimal in the context of a single agent whose subjective probabilistic knowledge base is consistent. In particular Paris and Vencovská completely characterised the error inference process by means of an attractive set of axioms which an inference process should satisfy. More recently the second author extended the Paris-Vencovská axiomatic approach...

Topological Interpretation of Rough Sets

Adam Grabowski (2014)

Formalized Mathematics

Rough sets, developed by Pawlak, are an important model of incomplete or partially known information. In this article, which is essentially a continuation of [11], we characterize rough sets in terms of topological closure and interior, as the approximations have the properties of the Kuratowski operators. We decided to merge topological spaces with tolerance approximation spaces. As a testbed for our developed approach, we restated the results of Isomichi [13] (formalized in Mizar in [14]) and...

Totally coherent set-valued probability assessments

Angelo Gilio, Salvatore Ingrassia (1998)

Kybernetika

We introduce the concept of total coherence of a set-valued probability assessment on a family of conditional events. In particular we give sufficient and necessary conditions of total coherence in the case of interval-valued probability assessments. Some relevant cases in which the set-valued probability assessment is represented by the unitary hypercube are also considered.

Towards a linguistic description of dependencies in data

Ildar Batyrshin, Michael Wagenknecht (2002)

International Journal of Applied Mathematics and Computer Science

The problem of a linguistic description of dependencies in data by a set of rules R_k: “If X is T_k then Y is S_k” is considered, where T_k’s are linguistic terms like SMALL, BETWEEN 5 AND 7 describing some fuzzy intervals A_k. S_k’s are linguistic terms like DECREASING and QUICKLY INCREASING describing the slopes p_k of linear functions y_k = p_{k}x + q_k approximating data on A_k. The decision of this problem is obtained as a result of a fuzzy partition of the domain X on fuzzy intervals A_k,...

Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets

Mohammed-Amine Abchir, Isis Truck (2013)

Kybernetika

In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera and Martínez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the...

Transitive decomposition of fuzzy preference relations: the case of nilpotent minimum

Susana Díaz, Susana Montes, Bernard De Baets (2004)

Kybernetika

Transitivity is a fundamental notion in preference modelling. In this work we study this property in the framework of additive fuzzy preference structures. In particular, we depart from a large preference relation that is transitive w.r.t. the nilpotent minimum t-norm and decompose it into an indifference and strict preference relation by means of generators based on t-norms, i. e. using a Frank t-norm as indifference generator. We identify the strongest type of transitivity these indifference and...

Twofold integral and multi-step Choquet integral

Yasuo Narukawa, Vicenç Torra (2004)

Kybernetika

In this work we study some properties of the twofold integral and, in particular, its relation with the 2-step Choquet integral. First, we prove that the Sugeno integral can be represented as a 2-step Choquet integral. Then, we turn into the twofold integral studying some of its properties, establishing relationships between this integral and the Choquet and Sugeno ones and proving that it can be represented in terms of 2-step Choquet integral.

Vagueness and its representations: a unifying look.

Maciej Wygralak (1998)

Mathware and Soft Computing

Using the notion of a vaguely defined object, we systematize and unify different existing approaches to vagueness and its mathematical representations, including fuzzy sets and derived concepts. Moreover, a new, approximative approach to vaguely defined objects will be introduced and investigated.

Variations on undirected graphical models and their relationships

David Heckerman, Christopher Meek, Thomas Richardson (2014)

Kybernetika

We compare alternative definitions of undirected graphical models for discrete, finite variables. Lauritzen [7] provides several definitions of such models and describes their relationships. He shows that the definitions agree only when joint distributions represented by the models are limited to strictly positive distributions. Heckerman et al. [6], in their paper on dependency networks, describe another definition of undirected graphical models for strictly positive distributions. They show that...

Visual anomaly detection via soft computing: a prototype application at NASA.

Jesús A. Domínguez, Steven J. Klinko (2003)

Mathware and Soft Computing

A visual system prototype that detects anomalies or defects in real time under normal lighting operating conditions was built for NASA at the Kennedy Space Center (KSC). The system prototype is basically a learning machine that integrates the three elements of soft computing, Fuzzy Logic (FL), Artificial Neural Network (ANN), and Genetic Algorithm (GA) schemes to process the image, run the learning process, and finally detect the anomalies or defects. The system acquires the image, performs segmentation...

Yager’s classes of fuzzy implications: some properties and intersections

Michał Baczyński, Balasubramaniam Jayaram (2007)

Kybernetika

Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [Yager2004] has introduced two new classes of fuzzy implications called the f -generated and g -generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the h -generated implications. In this article we discuss in detail some properties of the above mentioned classes of fuzzy implications and we describe their relationships amongst...

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