Lattice fuzzy transforms from the perspective of mathematical morphology

被引：28
作者：
Sussner, Peter [1 ]
机构：
[1] Univ Estadual Campinas, Dept Appl Math, BR-13083859 Campinas, SP, Brazil
来源：
FUZZY SETS AND SYSTEMS | 2016年 / 288卷
关键词：
Lattice fuzzy transform; Residuated lattice; Mathematical morphology on complete lattices; L-fuzzy mathematical morphology; Adjunction; Erosion; Dilation; Opening; Closing; Structuring element; Structuring function; THEORETICAL FOUNDATIONS; INFORMATION; SYSTEMS; SETS;
D O I：
10.1016/j.fss.2015.09.018
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The compositions of direct and inverse fuzzy transforms constitute powerful tools in knowledge extraction and representation that have been applied to a large variety of problems in computational intelligence as well as in image processing and computer vision. Fuzzy transforms (FTs) have linear as well as lattice-based versions. In this paper, we extend the latter FTs, known as lattice FTs, and relate these operators and their underlying mathematical structures to the ones of mathematical morphology (MM), in particular to the ones of MM on complete lattices and L-fuzzy MM. (C) 2015 Elsevier B. V. All rights reserved.
引用
收藏
页码：115 / 128
页数：14
相关论文
共 64 条
  • [1] [Anonymous], 2000, Principles of Applied Mathematics: Transformation and Approximation
  • [2] [Anonymous], 2010, Intuitionistic Fuzzy Sets: Theory and Applications
  • [3] [Anonymous], 2012, Formal concept analysis: mathematical foundations
  • [4] [Anonymous], 2002, INTRODUCTION, DOI DOI 10.1017/CBO9780511809088
  • [5] [Anonymous], 2003, STUD FUZZINESS SOFT
  • [6] [Anonymous], 1988, Image analysis and mathematical morphology
  • [7] DECOMPOSITION OF MAPPINGS BETWEEN COMPLETE LATTICES BY MATHEMATICAL MORPHOLOGY .1. GENERAL LATTICES
    BANON, GJF
    BARRERA, J
    [J]. SIGNAL PROCESSING, 1993, 30 (03) : 299 - 327
  • [8] Bargiela A., 2003, Granular Computing: An Introduction
  • [9] Concept lattices of isotone vs. antitone Galois connections in graded setting: Mutual reducibility revisited
    Belohlavek, Radim
    Konecny, Jan
    [J]. INFORMATION SCIENCES, 2012, 199 : 133 - 137
  • [10] Birkhoff G., 1993, Lattice Theory, V3rd ed.
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