Towards an Advanced Modelling of Complex Economic Phenomena

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Contents
Introduction
The Paths towards Knowledge
Irruption of Mathematical Spaces on Management Studies
Brief Summary of This Work
A Return to the Origin?
Precedents: Intuitive and Axiomatic Aspects of Topology
Brief Historical Overview of Topology
Some Classical Approaches of Topology
Considerations on the Subject of the Idea of Topology
Elemental Notions in Topological Spaces
Brief Reference to Metric Spaces
Part I: From Pretopology to Uncertain Pretopological
Axiomatics
Chapter 1: Pretopology
1 The Notion of Combinatorial Pretopology .................................................. 3
2 Isotone Pretopological Space....................................................................... 7
3 Distributive Pretopology............................................................................ 10
4 Correspondence between Distributive Pretopology and Reflexive
Graph ......................................................................................................... 12
5 Comparison of Pretopologies..................................................................... 16
6 Lattices of Pretopologies ........................................................................... 19
7 Moore Closing ........................................................................................... 23
Chapter 2: Pretopologies in Uncertainty
1 Axiomatic of an Uncertain Pretopology .................................................... 29
2 Isotonia in Uncertain Pretopologies........................................................... 39
3 Moore's Closing in Uncertainty ................................................................. 46
4 Distributive Uncertain Pretopology ........................................................... 56
5 Uncertain Moore Pretopology ................................................................... 63
6 Brief Final Discussion on Pretopological Spaces ...................................... 67

Part II: Towards an Idea of Uncertain Topological Space
Chapter 3: Topology
1 Genesis of a Topology ............................................................................... 71
2 Topological Space ..................................................................................... 76
3 A Comparative Look at Some Spaces ....................................................... 83
4 The Notion of Neighbourhood................................................................... 89
5 Topology, Open, Closed and Neighbourhoods.......................................... 95
6 Topological Continuity, Open Functions and Closed Functions ............. 100
7 Topological Homeomorphism................................................................. 104
Chapter 4: Uncertain Topological Spaces
1 Some Notions of Uncertain Topology ..................................................... 107
2 The Notion of Neighbourhood in an Uncertain Topological Space......... 121
3 Properties of Uncertain Topologies ......................................................... 128
4 Induction of Deterministic Topologies from Uncertain Topologies ........ 133
5 Process of Obtaining of Boolean Topologies from a Referential of
Fuzzy Subsets .......................................................................................... 142
6 Relationship between Uncertain Topological Spaces .............................. 152
7 Continuous Functional Application in Uncertainty ................................. 164
8 Homeomorphic Applications in Uncertainty ........................................... 177
Part III: Operative Techniques for Economy and Management
Chapter 5: Technical Elements with Topological Support
1 A Topology Named Clan......................................................................... 187
2 The Use of These Topologies in the Area of Management ..................... 192
3 Clans in Uncertainty ................................................................................ 197
4 Neighbourhood of a Clan......................................................................... 209
Chapter 6: Pretopology, Topology and Affinities
1 A Return to Moore's Fuzzy Pretopology ................................................. 217
2 Obtaining of Moore Closing from a Family ............................................ 224
3 Obtaining of Moore Closing through a Relationship............................... 227
4 Establishment of Connections from α-Cuts............................................. 238
5 Generalisation by Means of a Rectangular Fuzzy Relationship .............. 247
6 The Concept of Affinity........................................................................... 252
7 An Application of the Theory of Affinities ............................................. 259
Some Final Considerations .............................................................................. 267
Bibliography...................................................................................................... 273

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关键词：Modelling phenomena Economic Advanced Complex Complex

Zitsing 发表于 2015-2-18 13:05
Contents
Introduction
The Paths towards Knowledge

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