FUZZY QUANTIFICATION THEORY TYPE I

Fuzzy type theory with partial functions

This paper is a study of fuzzy type theory (FTT) with partial functions. Out of several possibilities we decided tointroduce a special value ”∗” that represents ”undefined”. In the interpretation of FTT, this value lays outside of thecorresponding domain. In the syntax it can be naturally represented by the description operator acting on the empty(fuzzy) set, because choosing an element from it...

On fuzzy type theory

Fuzzy Probability Theory I: Discrete Case

This chapter introduces the underlying theory of Fuzzy Probability and Statistics related to the differences and similarities between discrete probability and possibility spaces. Fuzzy Probability Theory for Discrete Case starts with the fundamental tools to implement an immigration of crisp probability theory into fuzzy probability theory. Fuzzy random variables are the initial steps to develo...

Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory

Article history: Received 17 April 2015 Received in revised form 18 June 2015 Accepted 6 July 2015 Available online 22 July 2015

Quantification of Temporal Fault Trees Based on Fuzzy Set Theory

Fault tree analysis (FTA) has been modified in different ways to make it capable of performing quantitative and qualitative safety analysis with temporal gates, thereby overcoming its limitation in capturing sequential failure behaviour. However, for many systems, it is often very difficult to have exact failure rates of components due to increased complexity of systems, scarcity of necessary s...