Affiliations: [a] Department of Civil Engineering, University of New Mexico, Albuquerque, NM, USA | [b] Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM, USA | [x] University of Magdeburg, Germany | [y] University of Liverpool, UK | [z] University of California at Berkeley, USA
Correspondence:
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Corresponding author: Dr. Mahmoud Reda Taha, Department of Civil Engineering, MSC01 1070, 1 The University of New Mexico, Albuquerque, NM 87131-001, USA. Tel.: +1 505 277 1258; Fax: +1 505 277 1988; E-mail: [email protected].
Abstract: An effectivity tree is a new concept which we introduce to show how it can be used in applications related to uncertainty quantification of the widely varying information that typical plagues many complex problems. Modeling of effectivity trees can be thought of as an inverse process to the formulation of fault trees, where failure and effectivity are defined as complements of one another. And, just like system failure, effectivity is a "fuzzy" term. Hence, failure may not always be understood as a binary term (fail or safe), and the same can be said for the term effectivity. This paper describes a new method for representing effectivities in a tree-like model, and it addresses two different ways to propagate effectivities, and their associated uncertainty, through the tree. The trees are logical representations within a system and so connections among the various "branches" of the tree are modeled using T-norms for intersections ("and" gates) and T-conorms for unions ("or" gates). The logical models of the gates are not restricted to the probabilistic norms (product and sum of effectivities), but can be generalized by other mathematical norms. The basic information used to quantify the uncertainty in effectivities can be fuzzy membership functions or possibility intervals, instead of quantities such as scalars or probability distributions. The paper illustrates the methods that can be used to propagate the uncertainties, up through the tree to the top level to evaluate the effectivity of the system. The paper concludes with a discussion that illustrates the differences between ambiguity and non-specificity assessment of effectivities, and their use in making decisions under uncertainties.
