**16-17 May 2019 • Sofia, Bulgaria**

**Submission:**21 February 2019 •

**Notification:**11 March 2019 •

**Final Version:**1 April 2019

# 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.

The book presents the most interesting results in the theoretical research in the area of generalized nets, obtained after 1991 year, when the book *"Generalized Nets"* was published.

## Table of contents

- Preface

- Chapter 1. Definitions of generalized net

- On the concept of GN
- Algorithms for transition and GN functioning
- First example: A GN model of a train station
- Short discussion on the use of GNs
- GNs and the other types of Petri nets
- Second example: GN and a Kolmogorov machine

- Chapter 2. Reduced generalized nets

- Definition of reduced GN
- Formal definition of a *-GN
- Third example: A GN-model of a subscribers' traffic of communication switching systems
- Fourth example: GN models of biological processes

- Chapter 3. Conservative extensions of generalized nets

- First conservative extensions of GNs
- Intuitionistic fuzzy GNs of type 1
- Intuitionistic fuzzy GNs of type 2
- Colour GNs
- GNs with interval activation time
- GNs with complex structure
- GNs with global memory
- GNs with optimization components
- GNs with additional clocks
- GNs with stop-conditions
- Opposite GNs

- GNs with tokens duration of "life"
- GNs with tokens possessing enhanced memory capabilities
- Two new types of intuitionistic fuzzy GNs
- Four versions of GNs with special types of initial tokens' characteristics
- First version of а GN with special types of initial tokens' characteristics
- Second version of а GN with special types of initial tokens' characteristics
- Third version of а GN with special types of initial tokens' characteristics
- Fourth and fifth versions of а GN with special types of initial tokens characteristics

- GNs in which the tokens obtain variables as characteristics
- Modified GNs
- GNs with three-dimensional structure
- 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

- Operations and relations over GNs
- An inductive definition of the concept of а GN
- А property of the GNs
- On Hadamard's Correctness Principle

- Chapter 5. Operator aspect of the theory of generalized nets

- Operators over GNs
- Self-modifying GNs
- Sixth Example: GN models in medicine
- GN model of the human body
- GN model of the gastrointestinal system of the human body

- Chapter 6. Methodological aspect of the theory of generalized nets

- How to construct а GN
- How to check GN validity
- Algorithms for constructing of GNs on base of case studies
- First algorithm
- Second algorithm
- Third algorithm
- Fourth algorithm
- Fifth algorithm

- А GN describing the process of learning of а GN

- Chapter 7. Appendices

- Appendix 1: Index matrix
- Appendix 2: Intuitionistic fuzzy logics and intuitionistic fuzzy sets

- Bibliography
- Subject index