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| Winter M. — Goguen Categories: A Categorical Approach to L-Fuzzy Relations |
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| Предметный указатель |
 -cut Theorem 51 99 122
0-1 crisp 48
Adjoint 13 47 65 167
Adjoint, lower 13 15 47 65
Adjoint, upper 13
Adjoint, upper left 15 47
Adjoint, upper right 15 47 65
Allegory 57
Allegory, distributive 63
Allegory, division 65
Allegory, representable 58 95
Antimorphism 11 25 75 111—112 126—127 131 134 140
antisymmetric 5
Antitone 6 16 25 63 68
Approximate equality 171
Arrow category 94
Arrow category with cuts 122
Arrow category, representable 95
Associative 2 9 40 163
atom 22
Bijection 3 60
Bijective 2 60
Boolean algebra 20 85 93 99
Boolean values 3
Brouwerian lattice 18 43 68
Brouwerian lattice, complete 43 68
Brouwerian lattice, proper 147
Cartesian product 2
Category 55
Category arrow 94
Category arrow with cuts 122
Category arrow, representable 95
Category, Dedekind 68 94
Category, Goguen 128
Category, Goguen, representable 139
Category, locally small 56 68
class 55
Cloos 40 160
Closed set 23
Closg 40
Closure operation 11 14
Coclosure operation 11
Commutative 9 40
Complement 1 20
complete 10
Completely irreducible 22
composition 2 52 57 164
Consistent 9
continuous 10 24 32 40
Contractive 11
Control rule 176
CONVERSE 58
Converse operation 58
Conversion 2
Crisp 48 95
Crisp, 0-1 crisp 48
Crisp, l-crisp 81
Crisp, s-crisp 81
Crispness 48
Cut 48
Decision module 170 179
Dedekind category 68 94
Dedekind category, simple 71 106
Dedekind category, uniform 70 102
Defuzzification 170 179
Difference 1
Distributive 17 63
Domain 2
Endofunction 11 24
Endorelation 2
Environment 87 144
equation 87 144
Extensive 11
Faithful 56
Field 56
Filter 32
Filter, maximal 33
Filter, prime 33
Filter, prime, complete 35
Filter, principal 32
Fixed point 23
Fixed point theorem 24
Fixed point, induction 25 27 29
Fixed point, least 23 27
Formula 86
full 56
Function 2
Function, antitone 6 16 25 63 68
Function, contractive 11
Function, extensive 11
Function, idempotent 11
Function, linear 56
Function, monotone 6 11 16
functor 56
Functor, faithful 56
Functor, full 56
Fuzzification 142 170 176
Fuzzy controller 142 169
Galois correspondence 13 49
Goguen category 128
Goguen category, representable 139
Greatest element 7
Greatest lower bound 7
Heyting algebra 18
Heyting algebras 18
Homogenous relation 2
Homomorphism 3 9 11 19 56 58 65 68 95 130
Homomorphism, Brouwerian lattice 19
Homomorphism, continuous 10
Homomorphism, lattice 11
Homomorphism, lattice, complete 11
Homomorphism, lower co-semilattice 9
Homomorphism, lower co-semilattice, complete 10
Homomorphism, lower semilattice 9
Homomorphism, lower semilattice, complete 10
Homomorphism, upper co-semilattice 10
Homomorphism, upper co-semilattice, complete 10
Homomorphism, upper semilattice 9
Homomorphism, upper semilattice, complete 10
I-indexed product 3
Ideal relation 48 79
Idempotent 9 11
Identity 2
Image 2
Injection 74 173
Injection, crisp 173
Injective 2 60
Intensifying modifier 170
Intersection 1
interval 185
Irreducible 22
Irreducible, completely 22
Isomorphic 3
Isomorphism 3 56
Join 8
Kernel 48 94
Kernel operation 11 14 108
l-crisp 81
Lattice 10
Lattice, atomic 23
Lattice, complete 10
Lattice, completely distributive 17
Lattice, completely downwards-distributive 17
Lattice, completely upwards-distributive 17
Lattice, distributive 17 63
| Lattice, proper 35 147
Lattice, sublattice 10
Lattice, sublattice, complete 10
Lattice-ordered operator set 40
Lattice-ordered operator set, commutative 40
Lattice-ordered operator set, complete 40
Lattice-ordered semigroup 40 52
Lattice-ordered semigroup, commutative 40
Lattice-ordered semigroup, complete 40
Least element 7
Least upper bound 7
Left residual 65
Linear 5
Linear element 8 79
Linear function 56
Linguistic entity 170
Linguistic modifier 170
Linguistic variable 170
Locally small 56 68
Loos 40 52 150
Losg 40 163
Lower adjoint 65
Lower bound 7 170
Lower bound, greatest 7
Lukasiewicz 171
MAP 60
Meet 7
Modifier 170
Modifier, intensifying 170
Modifier, ordering-based 170
Modifier, weakening 170
Modular law 58
Monotone 6 9 16
Morphism 55
Natural numbers 3
Object 55
Ordering 5 170
Ordering-based modifier 170
Partial identity 61 72
POSET 5
Poset, linear 5
Power set 2
Pre-functor 57 69 130
Predicate 1 24
Predicate, admissible 24
Predicate, continuous 24
Projection 75 142
Pseudo-complement 20
Pseudo-Representation Theorem 136
RANGE 2
Real numbers 3
Reflexive 5
Relation 2 43 57
Relation, antisymmetric 5
Relation, approximate equality 171
Relation, bijective 2 60
Relation, composition 2
Relation, converse 2
Relation, crisp 48 95
Relation, domain 2
Relation, endorelation 2
Relation, homogeneous 2
Relation, ideal 48 79
Relation, identity 2
Relation, image 2
Relation, injective 2 60
Relation, L-fuzzy 43
Relation, ordering 5
Relation, ordering, reversed 6
Relation, partial identity 61 72
Relation, range 2
Relation, reflexive 5
Relation, scalar 48 79
Relation, scalar, linear 79
Relation, sliceable 110
Relation, source 2 43
Relation, surjective 2 60
Relation, symmetric idempotent 75
Relation, target 2 43
Relation, total 2 60
Relation, transitive 5
Relation, univalent 2 60
Relational product 75 142
Relational sum 74 142
Relative pseudo-complement 18
Representable 58 95 139
Residual, left 65
Residual, right 65
Residuated operations 15 18 47 167
Reversed ordering 6
Right residual 65
Rule base 170 176
s-crisp 81
scalar 48 79
Scalar, linear 79
Semilattice 7
Semilattice, complete 7
Semilattice, lower 7
Semilattice, upper 8
Set 1
Set, cartesian product 2
Set, closed 23
Set, complement 1
Set, comprehension 1
Set, difference 1
Set, intersection 1
Set, power set 2
Set, union 1
Set-theoretic injection 74
Set-theoretic projection 75
SIMPLE 71 106
Sliceable 110
Source 2 43
Splitting 75 142
Sublattice 10
Subsemilattice 8
Subsemilattice, lower 8
Subsemilattice, upper 8
Support 48 94
Surjective 2 60
Symmetric idempotent relation 75
Symmetric quotient 65
t-conorm 40 52 155
T-norm 40 52 154 171
TARGET 2 43
Tarski-rule 70
Term 86
total 2 60
Transitive 5
Triangular fuzzy set 171
Ultrafilter 33
uniform 70 102
union 1
UNIT 75
Unit interval 3
Univalent 2 60
Upper bound 7 170
Upper bound, least 7
Upper right adjoint 65
Validity 88
Value 88
Vector space 56
Weakening modifier 170
Zermelo — Fraenkel 1 56
ZF 1 56
ZFC 1
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