d-XC Integrals: On the Generalization of the Expanded Form of the Choquet Integral by Restricted Dissimilarity Functions and Their Applications

Wieczynski, Jonata; Fumanal-Idocin, Javier; Lucca, Giancarlo; Borges, Eduardo Nunes; Asmus, Tiago da Cruz; Emmendorfer, Leonardo Ramos; Bustince, Humberto; Dimuro, Graçaliz Pereira

doi:10.1109/tfuzz.2022.3176916

Cited by 19 publications

(8 citation statements)

References 41 publications

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“…) and δ(y, z) ≤ δ(x, z). From these functions (RDFs), Bustince et al [27] recently generalized the standard Choquet integral by substituting the difference operator by an RDF, introducing the d-Choquet [30].…”

Section: Background Theorymentioning

confidence: 99%

“…From the expanded standard Choquet integral and the d-Choquet integral, Wieczynski et al [30] introduced the d-XChoquet integral as in the following definition.…”

Section: D-xchoquet Integralsmentioning

confidence: 99%

“…The d-XChoquet integral properties were studied in [30]. In that work the authors have showed the properties for each of the d-XChoquet integrals in Table I.…”

Section: D-xchoquet Integralsmentioning

confidence: 99%

“…Then, Wieczynski et al [29] introduced the dC F -integrals, a generalization of the Choquet integral by means of two functions, F and RDFs. More recently, Wieczynski et al [30] have proposed a generalization of the expanded form of the standard Choquet integral using RDFs, called d-XC integrals, with application to multi-criteria decision making problems and also in a motorimagery brain computer interface framework.…”

Section: Introductionmentioning

confidence: 99%

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Applying d-XChoquet integrals in classification problems

Wieczynski

Lucca

Borges

et al. 2022

2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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Several generalizations of the Choquet integral have been applied in the Fuzzy Reasoning Method (FRM) of Fuzzy Rule-Based Classification Systems (FRBCS's) to improve its performance. Additionally, to achieve that goal, researchers have searched for new ways to provide more flexibility to those generalizations, by restricting the requirements of the functions being used in their constructions and relaxing the monotonicity of the integral. This is the case of CT-integrals, CC-integrals, CF-integrals, CF1F2-integrals and dCF-integrals, which obtained good performance in classification algorithms, more specifically, in the fuzzy association rule-based classification method for high-dimensional problems (FARC-HD). Thereafter, with the introduction of Choquet integrals based on restricted dissimilarity functions (RDFs) in place of the standard difference, a new generalization was made possible: the d-XChoquet (d-XC) integrals, which are ordered directional increasing functions and, depending on the adopted RDF, may also be a pre-aggregation function. Those integrals were applied in multi-criteria decision making problems and also in a motor-imagery brain computer interface framework. In the present paper, we introduce a new FRM based on the d-XC integral family, analyzing its performance by applying it to 33 different datasets from the literature.

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Section: Background Theorymentioning

confidence: 99%

“…From the expanded standard Choquet integral and the d-Choquet integral, Wieczynski et al [30] introduced the d-XChoquet integral as in the following definition.…”

Section: D-xchoquet Integralsmentioning

confidence: 99%

“…The d-XChoquet integral properties were studied in [30]. In that work the authors have showed the properties for each of the d-XChoquet integrals in Table I.…”

Section: D-xchoquet Integralsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Applying d-XChoquet integrals in classification problems

Wieczynski

Lucca

Borges

et al. 2022

2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

Self Cite

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“…Similarly, the C T -integral can be applied to multi-criteria decision-making problems; see [17]. Other generalizations of the Choquet integral have seen use in problems involving multi-criteria decision-making (see [18,19]). In this paper, we focus on multi-criteria decision-making problems.…”

Section: Introductionmentioning

confidence: 99%

CT-Integral on Interval-Valued Sugeno Probability Measure and Its Application in Multi-Criteria Decision-Making Problems

Hong

Shang

Gong

2022

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It is well known that the complexity of the decision-making environment frequently coexists with the diversity of linguistic information in the decision-making process. In order to solve this kind of uncertain multi-criteria decision-making problem, reasonable measures and integrals should be established. In this paper, the discrete expression of the CT-integral on the interval-valued Sugeno probability measure is proposed. The CT-integral is the Choquet integral when the t-norm is T(x,y)=xy in the CT-integral and is a pre-aggregation function. Then, the CT-integral on interval-valued Sugeno probability measure is applied to solve end-of-life (EOL) strategy in order to determine multi-criteria decision-making problems. Compared with the general Choquet integral, the method proposed in this paper significantly improves the calculation process, that is, the calculation is simpler and the amount of calculation is smaller. A case study was performed in order to validate the effectiveness of this conclusion.

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