Interval-Valued Atanassov Intuitionistic OWA Aggregations Using Admissible Linear Orders and Their Application to Decision Making

Miguel, Laura De; Bustince, Humberto; Pękala, Barbara; Bentkowska, Urszula; Silva, Ivanosca Da; Bedregal, Benjamín R. C.; Mesiar, Radko; Ochoa, Gustavo

doi:10.1109/tfuzz.2016.2543744

Cited by 43 publications

(7 citation statements)

References 24 publications

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“…Originally they were introduced in the context of interval-valued fuzzy sets by H. Bustince et al in [11] and since then they have been widely used [12,14,40,48]. Lately, such notion was studied in other types of fuzzy sets, such as interval-valued intuitionistic fuzzy sets [18,20,21], hesitant fuzzy sets [31,32], multidimensional fuzzy sets [19] and n-dimensional fuzzy sets [22].…”

Section: Introductionmentioning

confidence: 99%

Aggregation functions on n-dimensional ordered vectors equipped with an admissible order and an application in multi-criteria group decision-making

Milfont¹,

Mezzomo²,

Bedregal³

et al. 2021

Preprint

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n-Dimensional fuzzy sets are a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0, 1] increasingly ordered, called n-dimensional intervals. The set of n-dimensional intervals is denoted by L n ([0, 1]). This paper aims to investigate semi-vector spaces over a weak semifield and aggregation functions concerning an admissible order on the set of n-dimensional intervals and the construction of aggregation functions on L n ([0, 1]) based on the operations of the semi-vector spaces. In particular, extensions of the family of OWA and weighted average aggregation functions are investigated. Finally, we develop a multi-criteria 1 group decision-making method based on n-dimensional aggregation functions with respect to an admissible order and give an illustrative example.

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Section: Introductionmentioning

confidence: 99%

Aggregation functions on n-dimensional ordered vectors equipped with an admissible order and an application in multi-criteria group decision-making

Milfont¹,

Mezzomo²,

Bedregal³

et al. 2021

Preprint

Self Cite

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“…Accordingly, many extensions of the OWA operators based on fuzzy numbers have been developed. Miguel et al extended the OWA operators based on the definition of admissible order for interval‐valued Atanassov intuitionistic fuzzy sets. Merigã et al presented the fuzzy generalized ordered weighted averaging (FGOWA) operator that is an extension of the GOWA operator in fuzzy environment.…”

Section: Introductionmentioning

confidence: 99%

Density‐clusters ordered weighted averaging op erat or based on generalized trapezoidal fuzzy numbers

Wang

2019

Int J Intell Syst

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To the problem of multi-attribute decision making with fuzzy numbers, this paper proposes a new type of operator called the density-clusters ordered weighted averaging (OWA) operator based on generalized trapezoidal fuzzy (GTF) numbers. This operator is abbreviated as the GTF-DOWA operator. A primary characteristic of the GTF-DOWA operator is that it considers the implicit structure of the GTF numbers to be aggregated by grouping the numbers to various local clusters. We discuss the grouping methods of the GTF numbers using the centroids of the numbers. The cluster weights are determined by the combined consideration of the decision maker's attitude and the scale of each local cluster. In addition, we discuss the primary properties of the GTF-DOWA operator. Finally, a numerical example regarding the selection of optimal alternative is provided. The aggregations of the GTF-DOWA operator are compared with those of the weighted arithmetic averaging (WAA) operator and the OWA operator based on GTF numbers to illustrate the validity of the GTF-DOWA operator. K E Y W O R D Scluster weights, generalized trapezoid fuzzy number, GTF-DOWA operator, OWA operator, uncertain multi-attribute decision making

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“…Email: laura.demiguel@unavarra.es have studied the generalization of OWA operator to other spaces (De Miguel et al 2017; Wang and Xu 2016;Wei et al 2016;Merigó and Casanovas 2010;Yager 2009;Jin, Mesiar, and Yager 2019;Paternain et al 2019). The extension of OWA operators to interval-valued fuzzy sets has been studied in (Bustince et al 2013) and in (De Miguel et al 2016) by defining a linear order between the real intervals. In a complementary way, OWA operators are generalized in (Lizasoain and Moreno 2013;Mesiar et al 2018) to fuzzy sets that take values on a complete lattice (L, ≤ L ), even in the case where the order ≤ L is not linear on L. In this work, we investigate the lattice I m as a mathematical model to deal with the different partitions of a continuous and bounded range.…”

Section: Introductionmentioning

confidence: 99%

Orness for real m-dimensional interval-valued OWA operators and its application to determine a good partition

Miguel

Paternain

Lizasoain

et al. 2019

International Journal of General Systems

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Ordered Weighted Averaging (OWA) operators are a profusely applied class of averaging aggregation functions, i.e., operators that always yield a value between the minimum and the maximum of the inputs. The orness measure was introduced to classify the behavior of the OWA operators depending on the weight vectors. Defining a suitable orness measure is an arduous task when we deal with OWA operators defined over more intricate spaces, such us intervals or lattices. In this work we propose a suitable definition for the orness measure to classify OWA operators defined on the set of m dimensional intervals taking real values in [0, 1]. The orness measure is applied to decide which is the best partition of a continuous range that should be divided into four linguistic labels. This example shows the good behavior of the proposed orness measure.

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Interval-Valued Atanassov Intuitionistic OWA Aggregations Using Admissible Linear Orders and Their Application to Decision Making

Cited by 43 publications

References 24 publications

Aggregation functions on n-dimensional ordered vectors equipped with an admissible order and an application in multi-criteria group decision-making

Aggregation functions on n-dimensional ordered vectors equipped with an admissible order and an application in multi-criteria group decision-making

Density‐clusters ordered weighted averaging op erat or based on generalized trapezoidal fuzzy numbers

Orness for real m-dimensional interval-valued OWA operators and its application to determine a good partition

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