On the Cardinality and Power Set of Fuzzy Sets and Multiple Sets

被引：0
|
作者：
Sanjitha, R. [1 ]
Baiju, T. [1 ]
S. Pai, Sandhya [1 ]
机构：
[1] Manipal Acad Higher Educ, Manipal Inst Technol, Dept Math, Manipal 576104, India
来源：
ADVANCES IN FUZZY SYSTEMS | 2024年 / 2024卷
关键词：
D O I：
10.1155/2024/8465775
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
A multiple set is a generalized version of a fuzzy set that deals with the uncertainty of an object along with its multiplicity. This work is a comparative analysis of the fundamental conclusions based on the cardinality of the classical set and fuzzy set. Several classical results based on fuzzy cardinality are then generalized to multiple set theory. An introduction to the concept of the power set of a multiple set is made, along with some basic results that support it. Furthermore, an extensive analysis of the power set properties of the fuzzy set is also carried out.
引用
收藏
页数：10
相关论文
共 50 条
  • [1] On cardinality and singular fuzzy sets
    Dyczkowski, Krzysztof
    Wygralak, Maciej
    [J]. COMPUTATIONAL INTELLIGENCE: THEORY AND APPLICATIONS, PROCEEDINGS, 2001, 2206 : 261 - 268
  • [2] An Axiomatic Approach to Fuzzy Measures Like Set Cardinality for Finite Fuzzy Sets
    Holcapek, Michal
    [J]. INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS: THEORY AND METHODS, PT 1, 2010, 80 : 505 - 514
  • [3] Questions of cardinality of finite fuzzy sets
    Wygralak, M
    [J]. FUZZY SETS AND SYSTEMS, 1999, 102 (02) : 185 - 210
  • [4] On Ralescu's cardinality of fuzzy sets
    Bartl, Eduard
    Belohlavek, Radim
    [J]. FUZZY SETS AND SYSTEMS, 2025, 498
  • [5] Questions of cardinality of finite fuzzy sets
    [J]. Fuzzy Sets Syst, 2 (185-210):
  • [6] A Bag Theoretic Fuzzy Count and Cardinality of Fuzzy Sets
    Tripathy, B. K.
    Jena, S. P.
    Ghosh, S. K.
    [J]. 2013 IEEE INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE AND COMPUTING RESEARCH (ICCIC), 2013, : 379 - 384
  • [7] Cardinality of Fuzzy Sets and Accumulation of Small Membership
    Bartl, Eduard
    Belohlavek, Radim
    [J]. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2024, 32 (06) : 3779 - 3789
  • [8] Fuzzy sets with triangular norms and their cardinality theory
    Wygralak, M
    [J]. FUZZY SETS AND SYSTEMS, 2001, 124 (01) : 1 - 24
  • [9] A Functional Approach to Cardinality of Finite Fuzzy Sets
    Holcapek, Michal
    [J]. INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS, PT II, 2014, 443 : 234 - 243
  • [10] CARDINALITY OF FUZZY-SETS VIA BAGS
    YAGER, RR
    [J]. MATHEMATICAL MODELLING, 1987, 9 (06): : 441 - 446
12345