Authors: "Renáta Bartková", "Beloslav Riečan", "Anna Tirpáková"

Probability Theory for Fuzzy Quantum Spaces with Statistical Applications

eBook: US $39 Special Offer (PDF + Printed Copy): US $117
Printed Copy: US $98
Library License: US $156
ISBN: 978-1-68108-539-5 (Print)
ISBN: 978-1-68108-538-8 (Online)
Year of Publication: 2017
DOI: 10.2174/97816810853881170101
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The reference considers probability theory in two main domains: fuzzy set theory, and quantum models. Readers will learn about the Kolmogorov probability theory and its implications in these two areas.

Other topics covered include intuitionistic fuzzy sets (IF-set) limit theorems, individual ergodic theorem and relevant statistical applications (examples from correlation theory and factor analysis in Atanassov intuitionistic fuzzy sets systems, the individual ergodic theorem and the Poincaré recurrence theorem).

This book is a useful resource for mathematics students and researchers seeking information about fuzzy sets in quantum spaces.


Review 1

This book is the first monograph known to me on the fuzzy events’ probability defined as a denumerable additive measure on the fuzzy space. The well-known Kolmogorov's theory is subsequently generalized to specific cases: fuzzy random events, intuitionistic fuzzy random events and fuzzy quantum observables. The most attention was devoted to fuzzy quantum space which has been suggested by Riečan as an alternative axiomatic model of quantum mechanics. The book is a useful source of information for mathematicians and physicists seeking information about the probability defined on fuzzy quantum spaces. It is also very useful for readers looking for a competent lecture on the probability defined on any space of fuzzy events.

The second important value of this book is the fact that it was written by Professor Beloslav Riečan and his co-workers. We can say that the fuzzy quantum space theory is the work of his life. The main foundations of this theory were formulated by Professor Riečan. This theory was further developed by a large team of Slovak mathematicians led by Professor Riečan. The results obtained in this way were discussed with friends with whom Slovaks mathematicians met during the Winter School on Measure Theory organized annually by Professor Riečan in Liptovsky Jan, Slovakia. The fruitful discussion that took place there was also reflected in this book. I know this because I participated myself in these meetings. I can say that the book is also a wonderful homogeneous result of cooperation between scientists from various scientific centers. This is another reason to get to know the contents of this book.

Prof. dr. hab. Krzysztof Piasecki,
Department of Investment and Real Estate, Poznan University of Economics


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