Ordered Directionally Monotone Functions: Justification and Application

被引：44

作者：

Bustince, Humberto ^{[1
,2
]}

Barrenechea, Edurne ^{[1
,2
]}

Sesma-Sara, Mikel ^{[1
,2
]}

Lafuente, Julio ^{[3
]}

Pereira Dimuro, Gracaliz ^{[2
]}

Mesiar, Radko ^{[4
,5
]}

Kolesarova, Anna ^{[6
]}

机构：

[1] Univ Publ Navarra, Pamplona 31006, Spain

[2] Inst Smart Cities, Pamplona 31006, Spain

[3] Univ Publ Navarra, Pamplona 31006, Spain

[4] Slovak Univ Technol Bratislava, Fac Civil Engn, Dept Math & Descript Geometry, Bratislava 81107, Slovakia

[5] Univ Ostrava, Inst Res & Applicat Fuzzy Modelling, CZ-70103 Ostrava, Czech Republic

[6] Slovak Univ Technol Bratislava, Inst Informat Engn Automat & Math, Bratislava 81237, Slovakia

来源：

IEEE TRANSACTIONS ON FUZZY SYSTEMS | 2018年 / 26卷 / 04期

关键词：

Aggregation function; edge detection; function-based monotonicity; ordered directionally monotone function; weak monotonicity; SUBSETHOOD MEASURES; OVERLAP INDEXES; FUZZY; CONSTRUCTION; OPERATORS;

D O I：

10.1109/TFUZZ.2017.2769486

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper, we introduce the notion of ordered directionally monotone function as a type of function which allows monotonicity along different directions in different points. In particular, these functions take into account the ordinal size of the coordinates of the inputs in order to fuse them. We show several examples of these functions and we study their properties. Finally, we present an illustrative example of an application which justifies the introduction and the study of the concept of ordered directional monotonicity.

引用

页码：2237 / 2250

页数：14

共 50 条

[41] NOWHERE MONOTONE FUNCTIONS
WEIL, CE
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 56 (APR) : 388 - 389
[42] CHARACTERIZATION OF MONOTONE FUNCTIONS
ORNSTEIN, D
ILLINOIS JOURNAL OF MATHEMATICS, 1971, 15 (01) : 73 - &
[43] MONOTONE MULTIPLICATIVE FUNCTIONS
COHEN, JM
AMERICAN MATHEMATICAL MONTHLY, 1989, 96 (06): : 512 - 513
[44] Convergence of monotone functions
Heinich, H
Lootgieter, JC
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1996, 322 (09): : 869 - 874
[45] ON FUNCTIONS THAT ARE MONOTONE ON NO INTERVAL
SALAT, T
AMERICAN MATHEMATICAL MONTHLY, 1981, 88 (10): : 754 - 755
[46] Monotone Boolean functions
Korshunov, AD
RUSSIAN MATHEMATICAL SURVEYS, 2003, 58 (05) : 929 - 1001
[47] ON QUOTIENT OF MONOTONE FUNCTIONS
MOTT, TE
AMERICAN MATHEMATICAL MONTHLY, 1963, 70 (02): : 195 - &
[48] Monotone functions and maps
Saugata Basu
Andrei Gabrielov
Nicolai Vorobjov
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2013, 107 : 5 - 33
[49] Estimating monotone functions
Low, MG
Kang, YG
STATISTICS & PROBABILITY LETTERS, 2002, 56 (04) : 361 - 367
[50] MONOTONE DECREASING FUNCTIONS
MOURANT, WJ
AMERICAN MATHEMATICAL MONTHLY, 1968, 75 (08): : 915 - &

← 1 2 3 4 5 →