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Goguen categories : a categorical approach to l-fuzzy relations
Winter, Michael, Ph. D.

اطلاعات کتابشناختی

Goguen categories : a categorical approach to l-fuzzy relations
Author :   Winter, Michael, Ph. D.
Publisher :   Springer,
Pub. Year  :   2007
Subjects :   Fuzzy relational calculus.
Call Number :   ‭QA 9 .65 .W786 2007

جستجو در محتوا

ترتيب

فهرست مطالب

  • CONTENTS (7)
  • INTRODUCTION (9)
  • 1. SETS, RELATIONS, AND FUNCTIONS (13)
  • 2. LATTICES (16)
    • 2.1 Galois correspondences and residuated operations (24)
    • 2.2 Distributive lattices (28)
    • 2.3 Brouwerian lattices (29)
    • 2.4 Boolean algebras (31)
    • 2.5 Special elements (33)
    • 2.6 Fixed points (34)
    • 2.7 The complete Brouwerian lattice of antimorphisms (36)
    • 2.8 Filters (42)
    • 2.9 Lattice-ordered semigroups (51)
  • 3. L-FUZZY RELATIONS (53)
    • 3.1 Basic operations and properties (53)
    • 3.2 Crispness (58)
    • 3.3 Operations derived from lattice-ordered semigroups (62)
  • 4. CATEGORIES OF RELATIONS (65)
    • 4.1 Categories (65)
    • 4.2 Allegories (67)
    • 4.3 Distributive allegories (73)
    • 4.4 Division allegories (75)
    • 4.5 Dedekind categories (78)
    • 4.6 Relational constructions in Dedekind categories (84)
    • 4.7 The Dedekind category of antimorphisms (85)
    • 4.8 Scalars and crispness in Dedekind categories (89)
    • 4.9 Schröder categories (95)
    • 4.10 Formal languages of relational categories (96)
  • 5. CATEGORIES OF L-FUZZY RELATIONS (103)
    • 5.1 Arrow categories (104)
    • 5.2 The arrow category of antimorphisms (122)
    • 5.3 Arrow categories with cuts (132)
    • 5.4 The arrow category with cuts of antimorphisms (136)
    • 5.5 Goguen categories (137)
    • 5.6 The Goguen category of antimorphisms (141)
    • 5.7 Representation of Goguen categories (144)
    • 5.8 Boolean-based Goguen categories (149)
    • 5.9 Equations in Goguen categories (152)
    • 5.10 Operations derived from lattice-ordered semigroups (160)
  • 6. FUZZY CONTROLLERS IN GOGUEN CATEGORIES (179)
    • 6.1 The Mamdani approach to fuzzy controllers (179)
    • 6.2 Linguistic entities and variables (180)
    • 6.3 Fuzzification (186)
    • 6.4 The rule base (186)
    • 6.5 Decision module (189)
    • 6.6 Defuzzification (189)
    • 6.7 Proving properties of a controller (192)
    • 6.8 Discussion of the approach (204)
  • INDEX (206)
    • A (206)
    • B (206)
    • C (206)
    • D (207)
    • E (207)
    • F (207)
    • G (207)
    • H (207)
    • I (207)
    • J (207)
    • K (207)
    • L (207)
    • M (208)
    • N (208)
    • O (208)
    • P (208)
    • R (208)
    • S (208)
    • T (208)
    • U (208)
    • V (209)
    • W (209)
    • Z (209)
  • SYMBOLS (210)
  • REFERENCES (212)
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