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Keywords
(2)
Fuzzy Equivalence Relation
Triangular Number
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(1)
Fuzzy sets and systems: theory and applications
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Fuzzy groups, fuzzy functions and fuzzy equivalence relations
Fuzzy groups, fuzzy functions and fuzzy equivalence relations,10.1016/S01650114(03)003014,Fuzzy Sets and Systems,Mustafa Demirci,Jordi Recasens
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Fuzzy groups, fuzzy functions and fuzzy equivalence relations
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Citations: 15
)
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Mustafa Demirci
,
Jordi Recasens
To each fuzzy subgroup a
fuzzy equivalence relation
is associated and it is proved that a fuzzy subgroup is normal if and only if the operation of the group is compatible with its associated fuzzy equivalence relation.In the definition of fuzzy subgroup only the subset is fuzzy whilst the group operation remains crisp. In an opposite direction, another structure can be constructed maintaining crisp the basic set X of the group and fuzzifying the group operation. When in addition it is imposed to the fuzzy operation to be compatible with a given fuzzy equivalence relation, this structure is called a vague group. The results of the paper allow us to associate a vague group to every fuzzy subgroup μ in such a way that it can be interpreted as the fuzzy quotient group X/μ.Special attention is paid to normal fuzzy groups and vague groups of the additive group (R,+) of the real numbers.Two examples related to triangular numbers illustrating the results of the paper are provided.
Journal:
Fuzzy Sets and Systems  FSS
, vol. 144, no. 3, pp. 441458, 2004
DOI:
10.1016/S01650114(03)003014
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Citation Context
(6)
...Indeed, M. Demirci and J. Recasens proposed in [
9
] a fuzzy subgroup to be a group (X; ~ ), where ~ (a;b;c) denotes the degree to which c = a b. An even more fuzzier algebraic structure is one were both the elements belongs to the underlying set to a degree and the result of the operation is the \real" result up to some degree...
Apostolos Syropoulos
.
Fuzzy Chemical Abstract Machines
...10414347/08/$25.00 2008 IEEE Published by the IEEE Computer Society see [27], [28], [29], [
30
], and [31]...
Robert Nowicki
.
On Combining NeuroFuzzy Architectures with the Rough Set Theory to So...
...A conceptual origin of our proposed MFFLSE may be found in Sasaki [14], Demirci [8][9], Demirci and Recasens [
10
] discusses the general properties of “Fuzzy Functions” from a perspective of mathematical theory...
B. Turksen
.
Mixed Fuzzy Functions
...Although there are many variations of fuzzy functions in the literature [16],[17],[46], a conceptual origin of our proposed FFLSE may be found in Demirci [12][
14
] where the general properties of “Fuzzy Functions” from the perspective of mathematical theory is discussed...
I. Burhan
,
et al.
Comparison of Fuzzy Functions with Fuzzy Rule Base Approaches
...For other works on combining the rough set and fuzzy set theories see [2], [3], [4], [
6
] and [11]...
Robert Nowicki
.
RoughNeuroFuzzy System with MICOG Defuzzification
References
(11)
UPPER AND LOWER APPROXIMATIONS OF FUZZY SETS
(
Citations: 52
)
D. BOIXADER
,
J. JACAS
,
J. RECASENS
Journal:
International Journal of General Systems  INT J GEN SYSTEM
, vol. 29, no. 4, pp. 555568, 2000
Searching for Meaning on Defuzzification
(
Citations: 3
)
Jordi Recasens
,
Dionis Boixader
,
Joan Jacas
Journal:
International Journal of Uncertainty, Fuzziness and Knowledgebased Systems  IJUFKS
, vol. 7, no. 5, pp. 475482, 1999
Vague Groups
(
Citations: 11
)
Mustafa Demirci
Journal:
Journal of Mathematical Analysis and Applications  J MATH ANAL APPL
, vol. 230, no. 1, pp. 142156, 1999
Fuzzy functions and their fundamental properties
(
Citations: 27
)
Mustafa Demirci
Journal:
Fuzzy Sets and Systems  FSS
, vol. 106, no. 2, pp. 239246, 1999
Fuzzy Functions and Their Applications
(
Citations: 24
)
Mustafa Demirci
Journal:
Journal of Mathematical Analysis and Applications  J MATH ANAL APPL
, vol. 252, no. 1, pp. 495517, 2000
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Citations
(15)
Fuzzy relation equations and reduction of fuzzy automata
(
Citations: 4
)
Miroslav Ciric
,
Aleksandar Stamenkovic
,
Jelena Ignjatovic
,
Tatjana Petkovic
Journal:
Journal of Computer and System Sciences  JCSS
, vol. 76, no. 7, pp. 609633, 2010
MyhillNerode type theory for fuzzy languages and automata
Jelena Ignjatovic
,
Miroslav Ciric
,
Stojan Bogdanovic
,
Tatjana Petkovic
Journal:
Fuzzy Sets and Systems  FSS
, vol. 161, no. 9, pp. 12881324, 2010
Algebras of fuzzy sets
(
Citations: 2
)
I. Bosnjak
,
R. Madarász
,
G. Vojvodic
Journal:
Fuzzy Sets and Systems  FSS
, vol. 160, no. 20, pp. 29792988, 2009
Uniform fuzzy relations and fuzzy functions
(
Citations: 1
)
Miroslav Ciric
,
Jelena Ignjatovic
,
Stojan Bogdanovic
Journal:
Fuzzy Sets and Systems  FSS
, vol. 160, no. 8, pp. 10541081, 2009
Similarity Based Fuzzy Interpolation Applied to CAGD
Joan Jacas
,
Amadeu Monreal
,
Jordi Recasens
Conference:
European Society for Fuzzy Logic and Technology  EUSFLAT
, pp. 16961701, 2009