On Generalized Nets Theory

On Generalized Nets Theory is a book by Krassimir Atanassov, published in September 2007 in the series "Bulgarian Academic Monographs" of "Professor Marin Drinov" Academic Publishing House. ISBN 978-954-322-237-7.

Table of contents

 * Preface


 * Chapter 1. Definitions of generalized net :
 * 1) On the concept of GN
 * 2) Algorithms for transition and GN functioning
 * 3) First example: A GN model of a train station
 * 4) Short discussion on the use of GNs
 * 5) GNs and the other types of Petri nets
 * 6) Second example: GN amd a Kolmogorov machine


 * Chapter 2. Reduced generalized nets :
 * 1) Definition of reduced GN
 * 2) Formal definition of a *-GN
 * 3) Third example: A GN-model of a subscribers' traffic of communication switching systems
 * 4) Fourth example: GN models of biological processes


 * Chapter 3. Conservative extensions of generalized nets :
 * 1) First conservative extensions of GNs
 * 2) Intuitionistic fuzzy GNs of type 1
 * 3) Intuitionistic fuzzy GNs of type 2
 * 4) Colour GNs
 * 5) GNs with interval activation time
 * 6) GNs with complex structure
 * 7) GNs with global memory
 * 8) GNs with optimization components
 * 9) GNs with additional clocks
 * 10) GNs with stop-conditions
 * 11) Opposite GNs
 * 12) GNs with tokens duration of "life"
 * 13) GNs with tokens possessing enllanced memory capabilities
 * 14) Two new types of intuitionistic fuzzy GNs
 * 15) Four versions of GNs with special types of initial tokens' characteristics
 * 16) First version of а GN with special types of initial tokens' characteristics
 * 17) Second version of а GN with special types of initial tokens' characteristics
 * 18) Third version of а GN with special types of initial tokens' characteristics
 * 19) Fourth and fifth versions of а GN with special types of initial tokens characteristics
 * 20) GNs in wllich the tokens obtain variables as characteristics
 * 21) Modified GNs
 * 22) GNs with three-dimensional structure
 * 23) Fifth example: GN, representing the functioning and the results of the work of а fuzzy Petri net


 * Chapter 4. Algebraic aspect of the theory of generalized nets :
 * 1) Operations and relations over GNs
 * 2) An inductive definition of the concept of а GN
 * 3) А property of the GNs
 * 4) On Hadamard's Correctness Principle


 * Chapter 5. Operator aspect of the theory of generalized nets :
 * 1) Operators over GNs
 * 2) Self-modifying GNs
 * 3) Sixth Example: GN models in medicine
 * 4) GN model of the human body
 * 5) GN model of the gastrointestinal system of the human body


 * Chapter 6. Methodological aspect of the theory of generalized nets :
 * 1) How to construct а GN
 * 2) How to check GN validity
 * 3) Algorithms for constructing of GNs оп ЬаБе of case studies
 * 4) First algorithm
 * 5) Second algorithm
 * 6) Third algorithm
 * 7) Fourth algorithm
 * 8) Fifth algorithm
 * 9) А GN describing the process of learning of а GN


 * Chapter 7. Appendices :
 * 1) Appendix 1: Index matrix
 * 2) Appendix 2: Intuitionistic fuzzy logics and intuitionistic fuzzy sets


 * Bibliography
 * Subject index