The present review examines decision-making methods developed for dealing with uncertainties and applied to solve problems of civil engineering. Several methodological difficulties emerging from uncertainty quantification in decision-making are identified. The review is focused on formal methods of multiple criteria decision-making (MCDM). Handling of uncertainty by means of fuzzy logic and probabilistic modelling is analysed in light of MCDM. A sensitivity analysis of MCDM problems with uncertainties is discussed. An application of stochastic MCDM methods to a design of safety critical objects of civil engineering is considered. Prospects of using MCDM under uncertainty in developing areas of civil engineering are discussed in brief. These areas are design of sustainable and energy efficient buildings, building information modelling, and assurance of security and safety of built property. It is stated that before long the decision-making in civil engineering may face several methodological problems: the need to combine fuzzy and probabilistic representations of uncertainties in one decision-making matrix, the necessity to extend a global sensitivity analysis to all input elements of a MCDM problem with uncertainties, and an application of MCDM methods in the areas of civil engineering where decision-making under uncertainty is presently not common.

An application of fragility functions to the assessment of potential damage due to an accidental action is analysed. The assessment is carried out as an estimation of the probability of a foreseeable damage event (damage probability). This probability is expressed as a mean value of a fragility function developed for the damage event under study. A Bayesian prior (posterior) distribution specified for this mean value is used as an estimate of the damage probability. The prior distribution is derived by transforming prior knowledge through the fragility function and “mapping” this knowledge on the scale of probability values. The technique of Bayesian bootstrap resampling is applied to update the prior distribution. The new information used for the updating consists of a relatively small number of experimental observations of the accidental action. To facilitate the updating, these observations are transformed into a fictitious statistical sample of fragility function values. The updating is first carried out with a fragility function which expresses aleatory uncertainty only. Then it is proposed how to perform the updating with the fragility function which quantifies both aleatory and epistemic uncertainty. This is done by discretising continuous distributions of the epistemic uncertainty related to values (parameters) of the fragility function. The proposed approach allows to utilise different sources of information for the damage assessment. A potential field of application of this approach is risk studies of hazardous industrial facilities. Santrauka Analizuojamas pažeidžiamumo funkcijų taikymas vertinant potencialius statybinių konstrukcijų pažeidimus avariniais poveikiais. Vertinimas atliekamas skaičiuojant galimos konstrukcijos pažaidos tikimybę. Ši tikimybė yra išreiškiama vidutine pažeidžiamumo funkcijos reikšme. Ta funkcija yra formuojama analizuojamam pažaidos įvykiui. Apriorinis ir aposteriorinis Bajeso skirstiniai yra taikomi pažaidos tikimybės reikšmei vertinti. Apriorinis skirstinys yra gaunamas pasinaudojant turima informacija apie avarinį poveikį ir transformuojant šią informaciją per pažeidžiamumo funkciją. Aposteriorinis skirstinys yra gaunamas pasitelkiant naują, eksperimentinę informaciją apie avarinį poveikį. Aposterioriniam skirstiniui gauti taikomas kartotinio statistinio ėmimo (būtstrapo) metodas. Naują informaciją sudaro eksperimentiniai avarinio poveikio charakteristikų matavimai, kurie tiksliai atitinka konstrukcijos ekspozicijos tiriamo poveikio situaciją. Apriorinis ir aposteriorinis skirstiniai išreiškia episteminį neapibrėžtumą vertinamos pažaidos tikimybės reikšmės atžvilgiu. Šie skirstiniai yra gaunami taikant tiek pažeidžiamumo funkciją, kuri išreiškia tik stochastinį neapibrėžtumą, tiek funkciją, kurios reikšmės yra neapibrėžtos epistemine prasme. Potenciali siūlomo metodo taikymo sritis yra pavojingų pramoninių objektų rizikos vertinimas.

The protection of buildings against fire disasters may require a comparison of alternative fire safety designs. The fire safety solutions can be compared by means of a general methodology known as multi‐attribute selection or multi‐criteria decision making. The alternative fire designs can be described by a number of attributes which characterise each of the alternatives. Fire risk expressed in the general form used for the quantitative risk assessment is applied to compose the set of attributes of a multi‐attribute selection problem. It is shown how to accomplish the multi‐attribute selection in the presence of epistemic uncertainties in the elements of fire risk estimate. Epistemic probability distributions assigned to elements of fire risk are specified and propagated though models of the multi‐attribute selection by means of Monte Carlo simulation. An example presented in the paper considers the choice among alternative systems of automatic fire sprinklers. Santruka Norint užtikrinti pastatu gaisrine sauga, gali prireikti lyginti alternatyvius projektinius saugos sprendimus. Tai atlikti galima pasitelkiant daugiakriterinio vertinimo metodologija. Alternatyvieji sprendimai gali būti aprašyti keletu charakteristiku (atributu) ir lyginami vienas su kitu. Straipsnyje atributu sarašas sudaromas naudojant gaisro rizikos išraiška, sudaroma kiekybinio rizikos vertinimo principais. Parodyta, kaip atlikti daugiakriterini vertinima, kai rizikos išraiškos elementai yra neapibrežti epistemine prasme. Episteminio neapibrežtumo skirstiniai priskiriami uždavinio atributams ir propaguojami matematiniais daugiakriterinio vertinimo modeliais pasitelkiant Monte Karlo modeliavima. Pateikiamas pavyzdys, nagrinejantis automatiniu sprinkleriu sistemos parinkima iš keliu alternatyviu variantu.