Quantitative orness for lattice OWA operators

Aggregation functions are mathematical operators that merge given data in order to obtain a global value that preserves the information given by the data as much as possible. In most practical applications, this value is expected to be between the infimum and the supremum of the given data, which is guaranteed only when the aggregation functions are idempotent. Ordered weighted averaging (OWA) operators are particular cases of this kind of function, with the particularity that the obtained global value depends on neither the source nor the expert that provides each datum, but only on the set of values. They have been classified by means of the orness-a measurement of the proximity of an OWA operator to the OR-operator. In this paper, the concept of orness is extended to the framework of idempotent aggregation functions defined both on the real unit interval and on a complete lattice with a local finiteness condition.

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“…A quantitative orness was defined in [8] in the following way for any OWA operator defined on (L, ≤ L , T, S). Definition 8 ([8]).…”

Section: Remark 6 Note That Any Finite Lattice Satisfies Condition (mentioning

confidence: 99%

“…On the one hand, a qualitative orness has been defined for OWA operators when the lattice L is finite [4]. On the other hand, when the lattice satisfies a weaker locally-finiteness condition, each OWA operator may be assigned a quantitative orness [8].…”

Section: Introductionmentioning

confidence: 99%

Orness For Idempotent Aggregation Functions

Legarreta

Lizasoain

Mardones-Pérez

2017

Axioms

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“…To elaborate this, Kishore et al provide an axiomatic definition of orness with more plausible features and better categorization. Recently, Paternain et al introduced a quantitative measure of orness for OWA operator on the basis of its proximity to the OR operator.…”

Section: Introductionmentioning

confidence: 99%

“…From the practical application viewpoint, the orness measure has also attracted many researchers and some of the recent publications are strong evidence of it. For example, Dujmovíc investigated the orness and andness as the mean of the overall importance of arguments.…”

Section: Introductionmentioning

confidence: 99%

On the orness of Bonferroni mean and its variants

Figueira

Das

2019

Int J Intell Syst

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This article addresses orness measures to reflect the orlike degree of the Bonferroni mean (BM) and its variants. Some properties of these operators associated with their orness measures are portrayed analytically. However, the general orness measure involves the multiple integrals with the integral fold number being the number of the aggregated elements and as a result, the computation becomes complicated when the number of the aggregated elements is large. Furthermore, the analytical formula of the orness measure often cannot be obtained. For this reason, this study concentrates on Monte Carlo simulation to validate the result. We estimate the two parameters of the BM for a predefined orness value and a fixed length of the input vector. Besides the theoretical study of orness measure related to BM and its variants, the article also explores the simulation-based results. To support this, we provide four numerical examples. K E Y W O R D S aggregation operator, Bonferroni mean, decision-making, Monte Carlo simulation, orness measure

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“…Marques Pereira and Ribeiro 25 investigated mixture operators and their aggregation, and Li 26 investigated the multiattribute decision-making method based on generalized OWA operators with intuitionistic fuzzy sets. Paternain et al 27 proposed a new OWA operators defined on any complete lattice endowed with a t-nor and a t-conorm. Marichal 28 investigated tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral.…”

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confidence: 99%

Monotonic argument-dependent OWA operators

Zeng

2018

Int. J. Intell. Syst.

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The ordered weighted averaging (OWA) operator introduced by Yager is one of the most popular aggregation technique. In this paper, we develop two kinds of argument‐dependent OWA (DOWA) operators including the pessimistic‐dependent OWA (PE‐DOWA) operator and optimistic‐dependent OWA (OP‐DOWA) operator, that point out that the PE‐DOWA operator is decreasing and the OP‐DOWA operator is increasing, and investigate some properties of our proposed monotonic DOWA operators in detail. Furthermore, we introduce the concept of original function in which a gradient vector generates the weights of the PE‐DOWA and OP‐DOWA operators. Meanwhile, we propose two classes of original functions including summing‐type original function and multiplying‐type original function and investigate the sufficient monotonic conditions for the DOWA operators generated by the original functions. Finally, we discuss the characteristics and properties of our proposed DOWA operators in detail and use a numerical example to illustrate the flexibility of our proposed operators.

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Quantitative orness for lattice OWA operators

Cited by 20 publications

References 24 publications

Orness For Idempotent Aggregation Functions

Orness For Idempotent Aggregation Functions

On the orness of Bonferroni mean and its variants

Monotonic argument-dependent OWA operators

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