Fuzzy measure theory is a generalization of classical measure theory. It was first introduced by Lotfi Zadeh in 1965 in his famous paper ”Fuzzy Sets”. After more than 50 years of the existence and development of classical measure theory, mathematicians felt that the additivity property is, in some applications, too restrictive. It is also unrealistic under real and physical conditions where measurement errors are unavoidable. According to Sugeno, fuzzy measures are obtained by replacing the additivity condition of classical measures with weaker conditions of monotonicity and continuity. Chapter ...

The term operational risk became widespread in the late 1990s when central bank representatives of twelve countries formed a working committee; the Basel Committee on Banking Supervision (BCBS). The BCBS defines operational risk as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This research aims to model operational risk data using the Loss Distribution Approach under BCBS requirements. Simulated data was used consisting of 3,192 operational loss events between the years 2009 and 2018. The implementation of the LDA was ...