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Fuzzy Integral Representation Associated With Spectral Measure
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Author(s): Mathews Mottackal George (Providence College of Engineering, India), Sunny Joseph Kalayathankal (Jyothi Engineering College, India)and Joseph Varghese Kureethara (CHRIST University, India)
Copyright: 2022
Pages: 15
Source title:
Handbook of Research on Advances and Applications of Fuzzy Sets and Logic
Source Author(s)/Editor(s): Said Broumi (Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco & Regional Center for the Professions of Education and Training (CRMEF), Casablanca-Settat, Morocco)
DOI: 10.4018/978-1-7998-7979-4.ch011
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Abstract
One of the most ubiquitous constructions in functional analysis is the spectral measure. The aim of this chapter is to develop the possibility to use the fuzzy spectral measure to define spectral representation theorems. Firstly, the authors introduce the fuzzy spectral measure and examine some of its properties. Furthermore, they elucidate fuzzy Hilbert space, the fuzzy normal, bounded, and adjoint operator on it. Finally, they establish the main result of this study which states that for a given fuzzy integral representation of C(X), there is a unique fuzzy spectral measure E on the Borel subsets of X.
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