Weak and directional monotonicity of functions on Riesz spaces to fuse uncertain data

Sesma‐Sara, Mikel; Mesiar, Radko; Bustince, Humberto

doi:10.1016/j.fss.2019.01.019

Cited by 27 publications

(8 citation statements)

References 50 publications

(59 reference statements)

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“…There exist more relaxed forms of monotonicity in the literature, such as ordered directional monotonicity 17 and strengthened ordered directional monotonicity 12 . Additionally, pointwise directional monotonicity has also been proposed 18 and the concepts of weak and directional monotonicity have been extended to more general frameworks such as interval‐valued functions, among other 13 …”

Section: Notation and Preliminariesmentioning

confidence: 99%

“…Another research topic that has attracted the interest of many researchers in the framework of aggregation functions is that of relaxing the monotonicity condition that is required in the definition of an aggregation function. To that end, various relaxed forms of monotonicity have been presented in the literature: weak monotonicity, 10 directional monotonicity, 11 as well as some other extensions 12,13 …”

Section: Introductionmentioning

confidence: 99%

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ℱ‐homogeneous functions and a generalization of directional monotonicity

Santiago

Sesma‐Sara

Fernández

et al. 2022

Int J of Intelligent Sys

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A function that takes n numbers as input and outputs one number is said to be homogeneous whenever the result of multiplying each input by a certain factor λ yields the original output multiplied by that same factor. This concept has been extended by the notion of abstract homogeneity, which generalizes the product in the expression of homogeneity by a general function g and the effect of the factor λ by an automorphism. However, the effect of parameter λ remains unchanged for all the input values. In this study, we generalize further the condition of abstract homogeneity by introducing MJX-tex-caligraphicnormalℱ‐homogeneity, which is defined with respect to a family of functions, enabling a different behavior for each of the inputs. Next, we study the properties that are satisfied by this family of functions and, moreover, we link this concept with the condition of directional monotonicity, which is a trendy property in the framework of aggregation functions. To achieve that, we generalize directional monotonicity by MJX-tex-caligraphicnormalℱ directional monotonicity, which is defined with respect to a family of functions MJX-tex-caligraphicnormalℱ and a family of vectors MJX-tex-caligraphicscriptV. Finally, we show how the introduced concepts could be applied in two different problems of computer vision: a snow detection problem and image thresholding improvement.

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Section: Notation and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

ℱ‐homogeneous functions and a generalization of directional monotonicity

Santiago

Sesma‐Sara

Fernández

et al. 2022

Int J of Intelligent Sys

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“…In this work we will focus on bounded convex sublattices of vector-lattices (also called Riesz spaces [17]). Therefore, we have that any convex combination of elements of the set belongs to the set.…”

Section: Preliminariesmentioning

confidence: 99%

OWA Operators Based on Admissible Permutations

Paternain

Jin

Mesiar

et al. 2019

2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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In this work we propose a new OWA operator defined on bounded convex posets of a vector-lattice. In order to overcome the non-existence of a total order, which is necessary to obtain a non-decreasing arrangement of the input data, we use the concept of admissible permutation. Based on it, our proposal calculates the different ways in which the input vector could be arranged, always respecting the partial order. For each admissible arrangement, we calculate an intermediate value which is finally collected and averaged by means of the arithmetic mean. We analyze several properties of this operator and we give some counterexamples of those properties of aggregation functions which are not satisfied.

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“…Weak and directional monotonicity have been extended to more general frameworks, such as lattices, intervals, intuitionistic fuzzy values, etc. in [20].…”

Section: Introductionmentioning

confidence: 99%

Local Properties of Strengthened Ordered Directional and Other Forms of Monotonicity

Sesma‐Sara

Miguel

Mesiar

et al. 2019

Advances in Intelligent Systems and Computing

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In this study we discuss some of the recent generalized forms of monotonicity, introduced in the attempt of relaxing the monotonicity condition of aggregation functions. Specifically, we deal with weak, directional, ordered directional and strengthened ordered directional monotonicity. We present some of the most relevant properties of the functions that satisfy each of these monotonicity conditions and, using the concept of pointwise directional monotonicity, we carry out a local study of the discussed relaxations of monotonicity. This local study enables to highlight the differences between each notion of monotonicity. We illustrate such differences with an example of a restricted equivalence function.

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Weak and directional monotonicity of functions on Riesz spaces to fuse uncertain data

Cited by 27 publications

References 50 publications

ℱ‐homogeneous functions and a generalization of directional monotonicity

ℱ‐homogeneous functions and a generalization of directional monotonicity

OWA Operators Based on Admissible Permutations

Local Properties of Strengthened Ordered Directional and Other Forms of Monotonicity

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