Aggregation with dependencies: Capacities and fuzzy integrals

Beliakov, Gleb; Divakov, D. V.

doi:10.1016/j.fss.2021.03.009

Cited by 11 publications

(3 citation statements)

References 67 publications

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“…Not for large n, which is usual in the MADM, there are schemes for the numerical solving of this problem in real time. Recent studies contrary to our approach to fuzzy measure identification in the interactive MADM environment can be found in [64][65][66][67][68].…”

Section: Associated Probabilities' Identification By Pair Interaction Indexes Of Attributes and Attributes' Importance Valuesmentioning

confidence: 99%

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Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

Sirbiladze

2021

Mathematics

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In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms (Tp,Spq) and (Tmin,Smax) are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes.

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Section: Associated Probabilities' Identification By Pair Interaction Indexes Of Attributes and Attributes' Importance Valuesmentioning

confidence: 99%

“…PFD and NFD measures reflect as pairs of expert evaluations α disc ij = (p ij , n ij ) from the interval [0,1] 2 . For our goal we selected the more convenient one [64]:…”

Section: Discrimination Q-rung Picture Linguistic Measures In Madmmentioning

confidence: 99%

Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

Sirbiladze

2021

Mathematics

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“…They are defined by means of a capacity, i.e., a normalized fuzzy measure. Aggregating the criteria information by using these functions allows the decision maker to model interaction between criteria and, therefore, overcome biased effects provided by redundancy in the decision data [17], [18]. However, the drawback in such approaches lies in the parameters identification, mainly because the number of capacity coefficients exponentially increases with the number of criteria.…”

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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High-Order Non-uniform Grid Scheme for Numerical Analysis of Shortest Queue Control Problem with a Small Parameter

Vasilyev,

Bouatta,

Kanzitdinov

et al. 2023

Lecture Notes in Networks and Systems

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Aggregation with dependencies: Capacities and fuzzy integrals

Cited by 11 publications

References 67 publications

Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

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

High-Order Non-uniform Grid Scheme for Numerical Analysis of Shortest Queue Control Problem with a Small Parameter

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