Aggregation of Interacting Criteria in Land Combat Vehicle Selection by Using Fuzzy Measures

Beliakov, Gleb; Cao, Thang; Mak‐Hau, Vicky

doi:10.1109/tfuzz.2021.3135972

Cited by 9 publications

(2 citation statements)

References 46 publications

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“…In this approach, which stems from the multiattribute value theory (MAVT), non-redundancy among criteria is an expected property [2] and a cornerstone underlying the use of linear aggregation operators. However, intercriteria relations are often observed in practical scenarios [3], [4], which has been motivating the development of novel aggregation strategies that can, for instance, deal with redundant criteria so to avoid double counting of the same latent factor driving two different criteria [5]- [9].…”

Section: Introductionmentioning

confidence: 99%

A novel unsupervised capacity identification approach to deal with redundant criteria in multicriteria decision making problems

Pelegrina,

Duarte

2024

Preprint

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The use of the Choquet integral in multicriteria decision making problems has gained attention in the last two decades. Despite of its usefulness, there is the issue of how to define the Choquet integral parameters, called capacity coefficients, specially the ones associated with coalitions of criteria. A possible approach to address this issue is based on unsupervised learning, which aims to define such parameters with the goal of mitigating undesirable effects provided by intercriteria relations. However, current unsupervised approaches present some drawbacks, as there is no guarantee that the parameters are equally prioritized in the learning procedure. In this paper, we propose a novel unsupervised capacity identification approach which ensures a fair learning for all parameters. Moreover, in comparison with the existing methods, our proposal is less complex in terms of optimization, as it is based on a linear formulation. Experimental results in both synthetic and real datasets attest the applicability of our proposal.

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Section: Introductionmentioning

confidence: 99%

A novel unsupervised capacity identification approach to deal with redundant criteria in multicriteria decision making problems

Pelegrina,

Duarte

2024

Preprint

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“…Special classes of aggregation functions are distinguished in the literature. These include t-norms [12], [13], OWA operators [14], [15], fuzzy measures [16], polynomial function [17], order-2 fuzzy sets [18], or fuzzy generalized unified aggregation operator [19]. There are also granular models, see [20], [21].…”

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confidence: 99%

Quadrature-Inspired Generalized Choquet Integral in an Application to Classification Problems

Karczmarek,

Dolecki,

Powroznik

et al. 2023

IEEE Access

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Correct classification remains a challenge for researchers and practitioners developing algorithms. Even a minor enhancement in classification quality, for instance, can significantly boost the effectiveness of detecting conditions or anomalies in safety data. One solution to this challenge involves aggregating classification results. This process can be executed effectively as long as the aggregation function is appropriately chosen. One of the most efficient aggregation operators is the Choquet integral. Furthermore, there exist numerous generalizations and extensions of the Choquet integral in the existing literature. In this study, we conduct a comprehensive analysis and evaluation of a novel approach for deriving an aggregate classification. The aggregation process applied to various classifiers is based on enhancements to the Choquet integral. These novel expressions draw inspiration from Newton-Cotes quadratures and other well-known formulae from numerical analysis. In contrast to previous approaches that exploit the generalization of the Choquet integral, our approach requires the utilization of two or three adjacent values associated with the membership of a specific element in different classes. This enables the use of more efficient enhancements in terms of accuracy measurement. Specifically, the t-norm following the integral symbol can be effectively replaced by mathematical expressions used in executing numerical integration formulae. This leads to more precise results and aligns with the concept of numerical integration. Furthermore, in a series of experiments, we thoroughly assess the performance of the proposed approach in terms of classification accuracy. We analyze the strengths and weaknesses of the new approach and establish the experimental settings that can be applied to similar tasks. In the series of experiments, we have demonstrated that the proposed Quadrature-Inspired Generalized Choquet Integral (QIGCI) can either outperform previous enhancements of the Choquet integral or at least achieve a similar level of accuracy measurement. However, we also highlight scenarios where previous approaches can still be a suitable choice. The number of QIGCI-based aggregation models that outperform others is convincing, indicating that this approach is worthy of consideration. INDEX TERMSAggregation, anomaly detection, Choquet integral, generalized Choquet integral, numerical quadratures, many classifiers, pre-aggregation functions I. INTRODUCTION T HE The problem of classification has recently become one of the most significant challenges in theoretical and applied computer science. It arises in various contexts such as image analysis, anomaly detection, and tabular data recognition. Especially in the past decade, this task has seen

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Choquet integral‐based measures of economic welfare and species diversity

Beliakov

Liu

2021

Int J of Intelligent Sys

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Measures of diversity, spread and inequality can be important indicators in domains as diverse as ecology, economics and health. One of the key characteristics of such indices is the Pigou–Dalton (P‐D) principle, also known as the principle of progressive transfers, whereby proportional redistribution from larger to smaller arguments should increase (or decrease, depending on the context) the overall measure of social or economic welfare, diversity and so on. Previous studies have identified the ordered weighted averaging operators as being appropriate for welfare measurement, subject to conditions on the weighting vectors. We propose the Choquet integral, defined with respect to a capacity or fuzzy measure, as a candidate for defining nonsymmetric measures of welfare. This allows for importance and interaction to be modelled between inputs while still satisfying the P‐D principle. We extend the buoyancy concept to fuzzy measures and characterise the resulting classes of buoyant and antibuoyant fuzzy measures. We then turn to the problem of optimisation of the Choquet integral subject to linear constraints, which in the case of antibuoyant fuzzy measures permits an efficient linear programming solution.

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Aggregation of Interacting Criteria in Land Combat Vehicle Selection by Using Fuzzy Measures

Cited by 9 publications

References 46 publications

A novel unsupervised capacity identification approach to deal with redundant criteria in multicriteria decision making problems

A novel unsupervised capacity identification approach to deal with redundant criteria in multicriteria decision making problems

Quadrature-Inspired Generalized Choquet Integral in an Application to Classification Problems

Choquet integral‐based measures of economic welfare and species diversity

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