mathematics

Krassimir Atanassov

Krassimir Atanassov is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Krassimir Atanassov rather than just read about it. In short: Krassimir Todorov Atanassov (Bulgarian: Красимир Тодоров Атанасов; 23 March 1954, Burgas, Bulgaria) is a Bulgarian mathematician, Academician of the Bulgarian Academy of Sciences (2021). He is best known for introducing the concepts of Generalized nets and Intuitionistic fuzzy sets, which are extensions of the concepts of Petri nets and fuzzy sets, respectively.

Key takeaways

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Reference excerpt

Krassimir Todorov Atanassov (Bulgarian: Красимир Тодоров Атанасов; 23 March 1954, Burgas, Bulgaria) is a Bulgarian mathematician, Academician of the Bulgarian Academy of Sciences (2021). He is best known for introducing the concepts of Generalized nets and Intuitionistic fuzzy sets, which are extensions of the concepts of Petri nets and fuzzy sets, respectively.

Biography Krassimir Atanassov graduated mathematics in the Sofia University, Sofia, in 1978, and defended his PhD in 1986. He became Doctor of Technical (computer) Sciences in 1997, with a doctor thesis on Generalized nets, and three years later defended a second higher doctorate, Doctor of Mathematical Sciences, with a thesis in the other field of his scientific interest - intuitionistic fuzzy sets. Since 1995 he has been working in the Centre of Biomedical Engineering at the Bulgarian Academy of Sciences, which in 2010 was merged into the Institute of Biophysics and Biomedical Engineering. In 1998, he became full professor and in 2012 was elected Corresponding member of the Bulgarian Academy of Sciences. In 2013, he was awarded the "Pythagoras" Award for considerable contribution to science (Technical Sciences), awarded by the Ministry of Education and Science of Bulgaria. In 2013, he was elected Fellow of the International Fuzzy Systems Association.

Expertise Other research activities of Professor Atanassov are: Editor-in-Chief of:

"Notes on Intuitionistic Fuzzy Sets" (since 1995) "Notes on Number Theory and Discrete Mathematics" (since 1995) "Advanced Studies in Contemporary Mathematics" (since 2001) "Annual of the Informatics Section", Union of Bulgarian Scientists (since 2008) "Proceedings of the Jangjeon Mathematical Society" (since 2002) Member of the Editorial Boards of:

"New Mathematics and Natural Computation" (since 1999) "Italian Journal of Pure and Applied Mathematics" (since 2002) "International Journal Bioautomation" (since 2008)

Research

Generalized nets In 1983 Atanassov introduced the object "Generalized Net" and investigated its basic properties, as well as some of its applications in artificial intelligence, systems theory, medicine, economics, transportation, chemical industry and others. He was the engine of the theoretical research on the area of Generalized nets, and promoted much of the applied research. He has defined a lot of operations and relations over generalized nets, part of which have analogues in the theory of ordinary Petri nets. However, the topological and logical operators he has introduced have no analogue in Petri nets theory.

Intuitionistic fuzzy sets The other fundamental field of research interest for Atanassov are Fuzzy sets, defined by Lotfi Zadeh, which he significantly extended by launching the concept of "Intuitionistic Fuzzy Sets" and investigated their basis properties. He has also initiated the applications of Intuitionistic fuzzy sets in expert systems, systems theory, decision making and others. He has studied and defined a lot of operations and relations over intuitionistic fuzzy sets, part of which have analogues in the theory of fuzzy sets. Without analogues in traditional fuzzy set theory are the operators on modal, topological, level, which Atanassov introduced and researched. Intuitionistic fuzzy sets are also often referred to in the literature as "Atanassov fuzzy sets" or "Atanassov intuitionistic fuzzy sets".

Bibliography Monographs in Generalized nets

Atanassov K., Generalized Nets, World Scientific, Singapore, New Jersey, London, 1991. Atanassov K., Introduction in the Theory of the Generalized Nets" (Burgas, Pontica Print, 1992; in Bulgarian) Shannon A., J. Sorsich, K. Atanassov. Generalized Nets in Medicine. "Prof. M. Drinov" Academic Publishing House, Sofia, 1996. Atanassov K., Generalized Nets and Systems Theory, "Prof. M. Drinov" Academic Publishing House, Sofia, 1997. Atanassov K., M. Daskalov, P. Georgiev, S. Kim, Y. Kim, N. Nikolov, A., Shannon, J. Sorsich. Generalized Nets in Neurology. "Prof. M. Drinov" Academic Publishing House, Sofia, 1997. Shannon A., J. Sorsich, K. Atanassov, N. Nikolov, P. Georgiev. Generalized Nets in General and Internal Medicine. Vol. 1. "Prof. M. Drinov" Academic Publishing House, Sofia, 1998. Atanassov K., Generalized Nets in Artificial Intelligence. Vol. 1: Generalized nets and Expert Systems, "Prof. M. Drinov" Academic Publishing House, Sofia, 1998. Atanassov K., H. Aladjov. Generalized Nets in Artificial Intelligence. Vol. 2: Generalized nets and Machine Learning. "Prof. M. Drinov" Academic Publishing House, Sofia, 1998. Shannon A., J. Sorsich, K. Atanassov, N. Nikolov, P. Georgiev. Generalized Nets in General and Internal Medicine. Vol. 2. "Prof. M. Drinov" Academic Publishing House, Sofia, 1999. Shannon, A., J. Sorsich, K. Atanassov, N. Nikolov, P. Georgiev. Generalized Nets in General and Internal Medicine. Vol. 3. "Prof. M. Drinov" Academic Publishing House, Sofia, 2000. Atanassov, K., A. Shannon, C. Wong. Generalized Nets and Cognitive Science. KvB Visual Concepts Pty Ltd, Monograph No. 2, Sydney, 2000. Shannon, A., J. Sorsich, K. Atanassov, V. Radeva. Generalized Net Interpretations of Ivan Dimirtov's Informational Theory of Diseases. "Prof. M. Drinov" Academic Publishing House, Sofia, 2001. Sorsich J., A. Shannon, K. Atanassov. Generalized Net in Child Neurology. "Prof. M. Drinov" Academic Publishing House, Sofia, 2002. Atanassov, K., G. Gluhchev, S. Hadjitodorov, A. Shannon, V. Vassilev. Generalized Nets and Pattern Recognition. KvB Visual Concepts Pty Ltd, Monograph No. 6, Sydney, 2003. Shannon A., O. Roeva, T. Pencheva, K. Atanassov. Generalized Nets Modelling of Biotechnological Processes. "Prof. M. Drinov" Academic Publishing House, Sofia, 2004. Shannon, A., D. Langova-Orozova, E. Sotirova, I. Petrounias, K. Atanassov, M. Krawczak, P. Melo-Pinto, T. Kim. Generalized Net Modelling of University Processes. KvB Visual Concepts Pty Ltd, Monograph No. 7, Sydney, 2005. Monographs in Intuitionistic fuzzy sets

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Worked examples

Example 1 — a first encounter with Krassimir Atanassov

Start with the simplest possible case. Write down what Krassimir Atanassov claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Krassimir Atanassov before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Krassimir Atanassov ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Krassimir Atanassov

In research: Krassimir Atanassov appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Krassimir Atanassov in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Krassimir Atanassov is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1954 births, 20th-century Bulgarian mathematicians, 21st-century Bulgarian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Krassimir Atanassov outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Krassimir Atanassov in 20 minutes

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Close the page and write down what Krassimir Atanassov means in your own words.
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Frequently asked questions

What is Krassimir Atanassov in simple terms?

Why does Krassimir Atanassov matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Krassimir Atanassov?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Krassimir Atanassov.