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1. Towards interval uncertainty propagation control in bivariate aggregation processes and the introduction of width-limited interval-valued overlap functions

Author

Asmus, Tiago da Cruz, Dimuro, Graçaliz Pereira, Bedregal, Benjamín, Sanz, José Antonio, Mesiar, Radko, and Bustince, Humberto

Subjects
Computer Science - Artificial Intelligence
Abstract

Overlap functions are a class of aggregation functions that measure the overlapping degree between two values. Interval-valued overlap functions were defined as an extension to express the overlapping of interval-valued data, and they have been usually applied when there is uncertainty regarding the assignment of membership degrees. The choice of a total order for intervals can be significant, which motivated the recent developments on interval-valued aggregation functions and interval-valued overlap functions that are increasing to a given admissible order, that is, a total order that refines the usual partial order for intervals. Also, width preservation has been considered on these recent works, in an intent to avoid the uncertainty increase and guarantee the information quality, but no deeper study was made regarding the relation between the widths of the input intervals and the output interval, when applying interval-valued functions, or how one can control such uncertainty propagation based on this relation. Thus, in this paper we: (i) introduce and develop the concepts of width-limited interval-valued functions and width limiting functions, presenting a theoretical approach to analyze the relation between the widths of the input and output intervals of bivariate interval-valued functions, with special attention to interval-valued aggregation functions; (ii) introduce the concept of $(a,b)$-ultramodular aggregation functions, a less restrictive extension of one-dimension convexity for bivariate aggregation functions, which have an important predictable behaviour with respect to the width when extended to the interval-valued context; (iii) define width-limited interval-valued overlap functions, taking into account a function that controls the width of the output interval; (iv) present and compare three construction methods for these width-limited interval-valued overlap functions., Comment: submitted

Published
2021

7. <inline-formula><tex-math notation="LaTeX">$dC_{F}$</tex-math></inline-formula>-Integrals: Generalizing C<inline-formula><tex-math notation="LaTeX">$_{F}$</tex-math></inline-formula>-Integrals by Means of Restricted Dissimilarity Functions

Author

Wieczynski, Jonata, Lucca, Giancarlo, Dimuro, Gracaliz P., Borges, Eduardo N., Sanz, Jose A., Asmus, Tiago da Cruz, Fernandez, Javier, and Bustince, Humberto

Abstract

The Choquet integral (CI) is an averaging aggregation function that has been used, e.g., in the fuzzy reasoning method (FRM) of fuzzy rule-based classification systems (FRBCSs) and in multicriteria decision making in order to take into account the interactions among data/criteria. Several generalizations of the CI have been proposed in the literature in order to improve the performance of FRBCSs and also to provide more flexibility in the different models by relaxing both the monotonicity requirement and averaging conditions of aggregation functions. An important generalization is the $C_{F}$-integrals, which are preaggregation functions that may present interesting nonaveraging behavior depending on the function $F$ adopted in the construction and, in this case, offering competitive results in classification. Recently, the concept of d-Choquet integrals was introduced as a generalization of the CI by restricted dissimilarity functions (RDFs), improving the usability of CIs, as when comparing inputs by the usual difference may not be viable. The objective of this article is to introduce the concept of $dC_{F}$-integrals, which is a generalization of $C_{F}$-integrals by RDFs. The aim is to analyze whether the usage of $dC_{F}$-integrals in the FRM of FRBCSs represents a good alternative toward the standard $C_{F}$-integrals that just consider the difference as a dissimilarity measure. For that, we consider six RDFs combined with five fuzzy measures, applied with more than 20 functions $F$. The analysis of the results is based on statistical tests, demonstrating their efficiency. Additionally, comparing the applicability of $dC_{F}$-integrals versus $C_{F}$-integrals, the range of the good generalizations of the former is much larger than that of the latter.

Published
2023
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8. Avaliação de um método de transformação de valores crisp em valores fuzzy

Author

de Mattos, Viviane Leite Dias, Asmus, Tiago da Cruz, Machado, Cátia Maria dos Santos, Silvestre, Ismael Batista Maidana, and Korb, Matheus Muller

Subjects
Eng. da Qualidade
Abstract

O presente estudo analisa o comportamento de um método de transformação de valores crisp em valores fuzzy triangulares em um processo de avaliação de características de qualidade sensoriais, procedimento bastante usual na indústria de alimentos. Foram analisados resultados de características sensoriais, obtidos a partir de uma avaliação de juízes, que foram interpretados como valores crisp e valores fuzzy. Para ordenação dos números fuzzy foram utilizados três métodos: Kaufmann-Grupta, Yager e Chang. Na análise desenvolvida foram utilizados os testes estatísticos de Friedman e de Wilcoxon e o coeficiente de Kendall, além de técnicas gráficas e analíticas utilizadas em estudos exploratórios de dados, sendo constatado que a métrica é modificada com a transformação e bastante influenciada por algumas propriedades dos dados. Também foi constatado que o método de ordenação interfere na interpretação dos resultados, que foram similares para os métodos de Kaufmann-Grupta e de Yager, mas diferentes para o método Chang.

Published
2015

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