Interval Subsethood Measures with Respect to Uncertainty for the Interval-Valued Fuzzy Setting

Pękala, Barbara; Bentkowska, Urszula; Sesma‐Sara, Mikel; Fernández, Javier; Lafuente, Julio; Altalhi, Abdulrahman H.; Knap, Maksymilian; Bustince, Humberto; Pintor, Jesus Maria

doi:10.2991/ijcis.d.200204.001

Cited by 15 publications

(5 citation statements)

References 39 publications

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“…) is called a similarity measure for i = 1, ..., n.. To construct interval-valued similarity, we need interval aggregation functions ( [21], [22], [23]) and an inclusion measure (precedence indicator) ( [29], cf. [31]) that take into account the width of the intervals, that is, the uncertainty. is a similarity measure.…”

Section: B Interval-valued Fuzzy Set Theorymentioning

confidence: 99%

Federated Similarity-Based Learning with Incomplete Data

Pekala,

Szkola,

Dyczkowski

et al. 2023

2023 IEEE International Conference on Fuzzy Systems (FUZZ)

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Section: B Interval-valued Fuzzy Set Theorymentioning

confidence: 99%

Federated Similarity-Based Learning with Incomplete Data

Pekala,

Szkola,

Dyczkowski

et al. 2023

2023 IEEE International Conference on Fuzzy Systems (FUZZ)

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“…Before we get to the main issue that interests us, that is, the equivalence measures we recall two different notions of a precedence indicator which use linear or partial order and uncertainty measure 37 . Both of them pay attention to the width of the intervals, as this width is seen as a way to measure the uncertainty related to the interval, and which we denote by

w

, where

w (α) = \overset{α}{true} - \underset{α}{true} for α \in L^{I} .

The precedence indicators can be used to build subsethood or inclusion measures which have been discussed in axiomatic or constructive ways.…”

Section: Fuzzy Settingmentioning

confidence: 99%

“…Other examples of the construction of strengthened precedence indicators one may find in the paper by Pȩkala et al 37 …”

Section: Fuzzy Settingmentioning

confidence: 99%

“…An operation

E_{\land_{z}} (α, β) = ({, \begin{array}{lc} [1 - w MathClass-open(α MathClass-close), 1], & α = β, \\ bold0, & otherwise \end{array})

MJX-tex-caligraphicnormalℬ

‐equivalence, where

MJX-tex-caligraphicnormalℬ

is a representable IV t‐norm

T_{I V}

in the case of

\leq_{L^{I}}

, created by

MJX-tex-caligraphicscriptA = \land

in (12) (

\land ≫ T_{I V}

). Then we have

MJX-tex-caligraphicnormalℬ

‐transitivity of

σ_{z}

(see, Reference [37], Proposition 4). Moreover

E_{\land_{z}} = E_{{A_{m e a n}^{0}}_{z}},

where

A_{m e a n}^{0} (α, β) = ({, \begin{array}{ll} bold0, & α = bold0 o r β = bold0, \\ A_{m e a n}, & otherwise \end{array})

and

E_{{A_{m e a n}^{0}}_{z}}

A_{m e a n}^{0}

‐equivalence measure with respect to

\leq_{X Y}

created by

MJX-tex-caligraphicscriptA = A_{m e a n}^{0}

…”

Section: Equivalence Measurementioning

confidence: 99%

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Interval‐valued equivalence measures respecting uncertainty in image processing

et al. 2021

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A new concept of equivalence between intervals and the induced indistinguishability between interval‐valued (IV) fuzzy sets are proposed and considered. A new notion of the degree of IV equivalence is presented where partial or linear orders and the width of intervals are involved reflecting uncertainty. Furthermore, construction methods of the considered equivalences are provided and the relation between them and other notions of IV equivalences are studied. Finally, a methodology to apply the proposed equivalences in the field of image processing is shown, along with an illustrative example.

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“…Subsethood measures have many applications on family of fuzzy sets and decision-making problems. Besides the former studies about them, these measures have been applied on many real-life problems lately for many different sets in the family of fuzzy sets (Köseoğlu & Şahin, 2019;Pękala et al, 2020;Peng et al, 2017;Şahin & Küçük, 2015;Zadrożny et al, 2021;Köseoğlu, 2021).…”

Section: Introduction Girişmentioning

confidence: 99%

Subsethood measure for picture fuzzy sets and its applications on multicriteria decision making

KÖSEOĞLU

2022

Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Picture fuzzy set is a direct generalization of intuitionistic fuzzy set and is therefore more capable of dealing with uncertainty while working on real life problems. The concept of inclusion is a subject that is frequently studied in family of fuzzy sets and has many applications in real life problems. Therefore, in this work, the measuring degree of inclusion between picture fuzzy sets is introduced. For this purpose, firstly axioms for subsethood measure are given and then a subsethood measure based on a distance measure for picture fuzzy sets is proposed. Then, a numerical example is provided to illustrate the applicability and usefulness of the presented measure. Finally, results are compared with the existing methods and aggregation operator to show validity of subsethood measure for PFS.

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Interval Subsethood Measures with Respect to Uncertainty for the Interval-Valued Fuzzy Setting

Cited by 15 publications

References 39 publications

Federated Similarity-Based Learning with Incomplete Data

Federated Similarity-Based Learning with Incomplete Data

Interval‐valued equivalence measures respecting uncertainty in image processing

Subsethood measure for picture fuzzy sets and its applications on multicriteria decision making

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