Fuzzy dissimilarities and the fuzzy Choquet integral of triangular fuzzy numbers on [0,1]

被引：0

作者：

de Hierro, A. F. Roldan Lopez ^{[1
]}

Cruz, A. ^{[2
]}

Santiago, R. H. N. ^{[3
]}

Roldan, C. ^{[1
]}

Garcia-Zamora, D. ^{[4
]}

Neres, F. ^{[5
]}

Bustince, H. ^{[6
]}

机构：

[1] Univ Granada, Dept Stat & Operat Res, Granada, Spain

[2] Univ Fed Rio Grande do Norte, Inst Metropole Digital, Natal, RN, Brazil

[3] Univ Fed Rio Grande do Norte, Dept Informat & Matemat Aplicada, Natal, RN, Brazil

[4] Univ Jaen, Dept Comp, Jaen, Spain

[5] Univ Fed Rural Semi Arido, Dept Ciencia & Tecnol, Caraubas, Caraubas, RN, Brazil

[6] Univ Publ Navarra, Dept Estadist Informat & Matemat, Pamplona, Spain

来源：

FUZZY SETS AND SYSTEMS | 2025年 / 505卷

关键词：

Choquet integral; Fuzzy number; Dissimilarity; Ranking; Alpha-ordering; Binary relation; RESTRICTED EQUIVALENCE FUNCTIONS; AGGREGATION;

D O I：

10.1016/j.fss.2025.109277

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Having in mind the huge amount of data daily registered in the world, it is becoming increasingly important to summarize the information included in a data set. In Statistics and Computer Science, this task is successfully carried out by aggregation functions. One of the most widely applied methodologies of aggregating data is the Choquet integral. The main aim of this paper is to introduce an appropriate notion of Choquet integral in the context of fuzzy numbers. To do this, we face three challenges: the underlying uncertainty when handling fuzzy numbers, the way to order fuzzy numbers by appropriate binary relations and the way to compute the dissimilarity among fuzzy numbers. Illustrative examples are given by involving the alpha-order on the family of all triangular fuzzy numbers with support on [0, 1].

引用

页数：29

共 28 条

[1] A fuzzy regression model based on finite fuzzy numbers and its application to real-world financial data
Alfonso, G.
Lopez de Hierro, A. F. Roldan
Roldan, C.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 318 : 47 - 58
[2] Simplifying the Search for Effective Ranking of Fuzzy Numbers
Ban, Adrian I.
Coroianu, Lucian
[J]. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2015, 23 (02) : 327 - 339
[3] Bede B, 2013, STUD FUZZ SOFT COMP, V295, P1, DOI 10.1007/978-3-642-35221-8
[4] Beliakov G., 2007, Aggregation Functions: A Guide for Practitioners, DOI DOI 10.1007/978-3-540-73721-6
[5] How different are ranking methods for fuzzy numbers? A numerical study
Brunelli, Matteo
Mezei, Jozsef
[J]. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2013, 54 (05) : 627 - 639
[6] Relationship between restricted dissimilarity functions, restricted equivalence functions and normal EN-functions:: Image thresholding invariant
Bustince, H.
Barrenechea, E.
Pagola, M.
[J]. PATTERN RECOGNITION LETTERS, 2008, 29 (04) : 525 - 536
[7] d-Choquet integrals: Choquet integrals based on dissimilarities
Bustince, H.
Mesiar, R.
Fernandez, J.
Galar, M.
Paternain, D.
Altalhi, A.
Dimuro, G. P.
Bedregal, B.
Takac, Z.
[J]. FUZZY SETS AND SYSTEMS, 2021, 414 : 1 - 27
[8] A Historical Account of Types of Fuzzy Sets and Their Relationships
Bustince, Humberto
Barrenechea, Edurne
Pagola, Miguel
Fernandez, Javier
Xu, Zeshui
Bedregal, Benjamin
Montero, Javier
Hagras, Hani
Herrera, Francisco
De Baets, Bernard
[J]. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2016, 24 (01) : 179 - 194
[9] Chakraverty S., 2019, Concepts of Soft Computing, DOI DOI 10.1007/978-981-13-7430-23
[10] Choquet G., 1953, ANN LINSTITUT FOURIE, V5, P131, DOI DOI 10.5802/AIF.53

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