Lucian Coroianu

36018210600

Publications - 10

Wasserstein distance for OWA operators

Lucian Coroianu István Harmati Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2024-05-15

Volume: 484

Issue: Unknown

Page Range: Unknown

Description:

We suggest a distance measure for OWA operators. First we associate an OWA operator with a unique regular increasing monotone quantifier and then define the distance between two OWA operators as the Wasserstein-1 distance between their associated quantifiers.

Open Access: Yes

DOI: 10.1016/j.fss.2024.108931

The median under orness

Lucian Coroianu István Harmati Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2024-04-01

Volume: 481

Issue: Unknown

Page Range: Unknown

Description:

Besides the mean, the median is the most widely used single-valued descriptor of data sets. It is well-known that the orness level of the median operator is 1/2. In this paper we provide approximations of the median operator under a given level of orness. We find the exact optimal weighting vector for the 1-norm approximation problem in all conceivable cases and for 2-norm approximation up to nine aggregates. The analytical results show that if the orness level is not 1/2, then not only the middle, but the extreme values also matter.

Open Access: Yes

DOI: 10.1016/j.fss.2024.108901

Best approximation of OWA Olympic weights under predefined level of orness

Lucian Coroianu István Harmati Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2022-11-05

Volume: 448

Issue: Unknown

Page Range: 127-144

Description:

An ideal type of OWA aggregation operator is the one constructed on the so-called Olympic weights. The orness of this operator is 1/2. Therefore, sometimes we need a trade-off between the desire of having an OWA aggregation operator with weights as close as possible to the Olympic ones and the desire of having a predefined level of orness. In this paper, we choose these optimal weights by minimizing the Euclidean distance to the Olympic weights vector under the constraint of preserving a given level of orness. First, in the case n=4, we propose an iterative algorithm where the optimal solution is given for all possible values of the orness, values that are grouped along a partition of the unit interval. This iterative algorithm will inspire us to deduce the optimal weights in the general case. Consequently, we will obtain the analytical solution of the optimal weights as a function depending on the orness level.

Open Access: Yes

DOI: 10.1016/j.fss.2022.07.009

An Iterative Approach for the Solution of the Constrained OWA Aggregation Problem with Two Comonotone Constraints

Lucian Coroianu Robert Fullér

Publication Name: Information Switzerland

Publication Date: 2022-10-01

Volume: 13

Issue: 10

Page Range: Unknown

Description:

In this paper, first, we extend the analytical expression of the optimal solution of the constrained OWA aggregation problem with two comonotone constraints by also including the case when the OWA weights are arbitrary non-negative numbers. Then, we indicate an iterative algorithm that precisely indicates whether a constraint in an auxiliary problem is either biding or strictly redundant. Actually, the biding constraint (or two biding constraints, as this case also may occur) are essential in expressing the solution of the initial constrained OWA aggregation problem.

Open Access: Yes

DOI: 10.3390/info13100443

Constrained ordered weighted averaging aggregation with multiple comonotone constraints

Lucian Coroianu Marek Gagolewski Robert Fullér Simon James

Publication Name: Fuzzy Sets and Systems

Publication Date: 2020-09-15

Volume: 395

Issue: Unknown

Page Range: 21-39

Description:

The constrained ordered weighted averaging (OWA) aggregation problem arises when we aim to maximize or minimize a convex combination of order statistics under linear inequality constraints that act on the variables with respect to their original sources. The standalone approach to optimizing the OWA under constraints is to consider all permutations of the inputs, which becomes quickly infeasible when there are more than a few variables, however in certain cases we can take advantage of the relationships amongst the constraints and the corresponding solution structures. For example, we can consider a land-use allocation satisfaction problem with an auxiliary aim of balancing land-types, whereby the response curves for each species are non-decreasing with respect to the land-types. This results in comonotone constraints, which allow us to drastically reduce the complexity of the problem. In this paper, we show that if we have an arbitrary number of constraints that are comonotone (i.e., they share the same ordering permutation of the coefficients), then the optimal solution occurs for decreasing components of the solution. After investigating the form of the solution in some special cases and providing theoretical results that shed light on the form of the solution, we detail practical approaches to solving and give real-world examples.

Open Access: Yes

DOI: 10.1016/j.fss.2019.09.006

Minimum of Constrained OWA Aggregation Problem with a Single Constraint

Lucian Coroianu Robert Fullér

Publication Name: Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics

Publication Date: 2019-01-01

Volume: 11291 LNAI

Issue: Unknown

Page Range: 183-192

Description:

In a recent paper we found an analytical formula for the constrained ordered weighted aggregation problem (OWA) when we need to maximize the objective function. In this note we prove that the method works in the case when we need to minimize the objective function. If in the case of the maximization problem we need to rearrange the coefficients in the constrained in nondecreasing order, for the nontrivial minimization problem, it suffice to rearrange them in nonincreasing order.

Open Access: Yes

DOI: 10.1007/978-3-030-12544-8_15

Nguyen type theorem for extension principle based on a joint possibility distribution

Lucian Coroianu Robert Fullér

Publication Name: International Journal of Approximate Reasoning

Publication Date: 2018-04-01

Volume: 95

Issue: Unknown

Page Range: 22-35

Description:

In this paper, first we prove that making abstraction of the output obtained from the interactive extension principle based on a joint possibility distribution, in the case of unimodal fuzzy numbers and when the function that generates the operation is continuous and strictly increasing in each argument restricted to the support of each fuzzy number used in the process, then we can use joint possibility distributions with the property that the left/right side of the output is obtained from the convolution of the values in the left/right side of these fuzzy numbers. Then, considering joint possibility distributions with the aforementioned property, we find an Nguyen type characterization of the level sets of the output based on interactive extension principle, in terms of the level sets of the fuzzy numbers used in the process. These two key results complete well-known results obtained in the case of Zadeh's extension principle and also in the case of triangular norm-based extension principle. As an interesting corollary, in the special case of unimodal fuzzy numbers, the Nguyen theorem can be used to present a new proof concerning necessary and sufficient conditions on the equality of the outputs based on joint possibility distributions, respectively based on Zadeh's extension principle.

Open Access: Yes

DOI: 10.1016/j.ijar.2018.01.007

On the constrained OWA aggregation problem with single constraint

Lucian Coroianu Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2018-02-01

Volume: 332

Issue: Unknown

Page Range: 37-43

Description:

In this note we present a simple proof for the constrained OWA aggregation problem with a single constraint but with variable coefficients.

Open Access: Yes

DOI: 10.1016/j.fss.2017.04.013

Necessary and sufficient conditions for the equality of interactive and non-interactive extensions of continuous functions

Lucian Coroianu Robert Fullér

Publication Name: Fuzzy Sets and Systems

Publication Date: 2018-01-15

Volume: 331

Issue: Unknown

Page Range: 116-130

Description:

In this contribution we find the class of n-dimensional joint possibility distributions with the property that the interactive extension principle coincides with the non-interactive extension principle as long as the interactive operations are determined by continuous functions strictly increasing in each argument. This result completes recent studies by the authors, where the particular case of interactive additions and multiplications versus non-interactive additions and multiplications were investigated. In addition, this time we propose results that also cover the cases when we know the fuzzy numbers only from their membership functions. It means that we eliminated the limitations that appear when we cannot pass from membership function representation to parametric representation of fuzzy numbers. As important new applications, we mention the study on the completely correlated fuzzy numbers. Also of note is that we propose two simple methods to extend bidimensional joint possibility distributions to n-dimensional joint possibility distributions. One method is based on an inductive construction while the other one is based on a pairwise construction.

Open Access: Yes

DOI: 10.1016/j.fss.2017.07.023

Characterization of the level sets for interactive additions

Lucian Coroianu Robert Fullér

Publication Name: Cinti 2016 17th IEEE International Symposium on Computational Intelligence and Informatics Proceedings

Publication Date: 2017-02-07

Volume: Unknown

Issue: Unknown

Page Range: 35-40

Description:

In this paper, on the set of unimodal fuzzy numbers, first we prove that under some minimal assumptions, it suffices to consider only those joint possibility distributions that satisfy that the left/right side of the fuzzy number generated by the interactive addition based on the given joint possibility distribution, is obtained by evaluating only the left/right side of the summands. Then, we will obtain a representation theorem for the level sets of this interactive addition in terms of the level sets of the summands. These results generalize corresponding results for the special case of triangular-norm-based additions.

Open Access: Yes

DOI: 10.1109/CINTI.2016.7846376