the traditional event tree analysis uses a single probability to represent each top event. however, it is unrealistic to evaluate the occurrence of each event by using a crisp value without considering the inherent uncertainty and imprecision a state has. the fuzzy set theory is universally applied to deal with this kind of phenomena. the main purpose of this study is to construct an easy metho...

Uncertainty is inevitable in any reliability analysis of complex engineering systems due to uncertainties present in models, parameters of the model, phenomena and assumptions. Uncertainties at the component level are propagated to quantify uncertainty at the system level reliability. It is very important to identify all the uncertainties and treat them effectively to make reliability studies m...

The traditional event tree analysis uses a single probability to represent each top event. However, it is unrealistic to evaluate the occurrence of each event by using a crisp value without considering the inherent uncertainty and imprecision a state has. The fuzzy set theory is universally applied to deal with this kind of phenomena. The main purpose of this study is to construct an easy metho...

Information theory was introduced by Shannon in 1948 and it includes the study of uncertainty measures. Analogous to information theory which is founded on probability theory, notion of fuzzy sets was established by Zadeh in 1965 which is a mechanism to manage uncertainty. The pedestal for present study is information theory with intuitionistic fuzzy sets. Atanassov (1986) devised Intuitionisti...

Uncertainty in parameters is present in many risk assessment problems and leads to uncertainty in model predictions. In this work, we introduce a global sensitivity indicator which looks at the influence of input uncertainty on the entire output distribution without reference to a specific moment of the output (moment independence) and which can be defined also in the presence of correlations a...

The main aim of this paper is to connect R-Fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the si...

Several types of entropy of fuzzy variables or fuzzy sets have been given in the literature in order to measure the degree of uncertainty. In order to measure the degree of uncertainty of fuzzy vectors, a new definition of entropy of fuzzy vectors is proposed. Some properties are then investigated and the relations between the entropy of fuzzy variables and fuzzy vectors are discussed.

We introduce the fuzzy measure as a unifying structure for modeling knowledge about an uncertain variable. We show that a large class of well established types of uncertainty representation can be modeled in this framework. A measure of entropy associated with a fuzzy measure is introduced and its manifestation for different fuzzy measures is described. The problem of uncertain decision making ...

The aim of the presented approach is to combine two views on robustness within a comprehensive design approach. These two main views are on the one hand the resistance to extraordinary (unforeseen) events, and on the other hand the consideration of uncertainty in structural parameters in order to monitor and reduce the variation of structural responses. To capture this, an enhanced robustness m...