Theory and Applications of Ordered Fuzzy Numbers by Piotr Prokopowicz

About this book :-
"Theory and Applications of Ordered Fuzzy Numbers: A Tribute to Professor Witold Kosinski" by "Piotr Prokopowicz, Jacek Czerniak, Dariusz Mikolajewski, Lukasz Apiecionek, Dominik Slezak" is a specialized academic book that extends classical fuzzy number theory by introducing "Ordered Fuzzy Numbers (OFNs)". This concept adds information about direction and order, allowing uncertainty to be modeled in a more expressive and realistic way. The book begins with clear theoretical foundations, making it easier to understand how OFNs differ from traditional fuzzy numbers. The author explains the mathematical structure of ordered fuzzy numbers, including their definitions, operations, and algebraic properties. Special attention is given to how ordering improves data interpretation, trend analysis, and reasoning under uncertainty. These theoretical tools are carefully developed to support reliable modeling in complex systems where standard fuzzy approaches may be limited. In the applied sections, the book demonstrates how OFNs can be used in real-world problems such as decision support, economics, control systems, and data analysis. By combining theory with practical examples, it serves researchers and advanced students looking for deeper tools to handle imprecise information. The book strongly contributes to "fuzzy mathematics", "uncertainty modeling", "ordered fuzzy numbers", "decision making", and "applied mathematics".

Book Detail :-
Title: Theory and Applications of Ordered Fuzzy Numbers by Piotr Prokopowicz
Publisher: Springer
Year: 2017
Pages: 330
Type: PDF
Language: English
ISBN-10 #: 331986663X
ISBN-13 #: 978-3319866635
License: CC BY 4.0
Amazon: Amazon

About Author :-
The author , Jacek Czerniak, Dariusz Mikolajewski, Lukasz Apiecionek, and Dominik Slezak are Polish researchers specializing in fuzzy logic, uncertainty modeling, and applied mathematics. Their academic work combines mathematical theory with practical computational methods, focusing on better ways to represent imprecise and directional data in real systems. In Theory and Applications of Ordered Fuzzy Numbers, they jointly develop and apply the concept of ordered fuzzy numbers. Their collaboration advances ordered fuzzy numbers, fuzzy logic, uncertainty modeling, decision making, and applied mathematics, supporting both research and real-world applications.

Book Contents :-
PART-I BACKGROUND OF FUZZY SET THEORY 1. Introduction to Fuzzy Sets 2. Introduction to Fuzzy Systems PART-II THEORY OF ORDERED FUZZY NUMBERS 3. Ordered Fuzzy Numbers: Sources and Intuitions 4. Ordered Fuzzy Numbers: Definitions and Operations 5. Processing Direction with Ordered Fuzzy Numbers 6. Comparing Fuzzy Numbers Using Defuzzificators on OFN Shapes 7. Two Approaches to Fuzzy Implication PART-III EXAMPLES OF APPLICATIONS 8. OFN Capital Budgeting Under Uncertainty and Risk 9. Input-Output Model Based on Ordered Fuzzy Numbers 10. Ordered Fuzzy Candlesticks 11. Detecting Nasdaq Composite Index Trends with OFNs 12. OFN Ant Method Based on TSP Ant Colony Optimization 13. A New OFN Bee Method as an Example of Fuzzy Observance Applied for ABC Optimization 14. Fuzzy Observation of DDoS Attack 15. Fuzzy Control for Secure TCP Transfer 16. Fuzzy Numbers Applied to a Heat Furnace Control 17. Analysis of Temporospatial Gait Parameters 18. OFN-Based Brain Function Modeling

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