This paper presents a rational approach to the representation and manipulation of imprecise degrees of belief in the framework of evidence theory. We adopt as a starting point the non probabilistic interpretation of belief functions provided by Smets' Transferable Belief Model, as well as previous generalizations of evidence theory allowing to deal with fuzzy propositions. We then introduce the...

A proper representation of the uncertainty involved in a prediction is an important prerequisite for the acceptance of machine learning and decision support technology in safety-critical application domains such as medical diagnosis. Despite the existence of various probabilistic approaches in these fields, there is arguably no method that is able to distinguish between two very different sourc...

In this work we suggest an approach to comparing fuzzy numbers motivated by a probabilistic view of the underlying uncertainty. An important aspect of the method suggested is its context dependency, the numbers being compared a€ect the process. We discuss the e€ect of decision attitude and show that this approach is particularly useful for aiding decision makers having a temperate decision atti...

In this paper, we give some new coupled common  fixed point theorems for probabilistic $varphi$-contractions  in Menger probabilistic metric spaces.  As applications of the main results, we obtain some coupled common fixed point theorems in usual metric spaces and fuzzy metric spaces. The main results of this paper improvethe corresponding results given by some authors. Finally, we give one exa...

In this paper the fuzzy structural reliability index was determined through modeling epistemic uncertainty arising from ambiguity in statistical parameters of random variables. The First Order Reliability Method (FORM) has been used and a robust genetic algorithm in the alpha level optimization method has been proposed for the determination of the fuzzy reliability index. The sensitivity level ...

Comparing the performance of a set of activities or organizations under uncertainty environment has been performed by means of Fuzzy Data Envelopment Analysis (FDEA) since the traditional DEA models require accurate and precise performance data. As regards a method for dealing with uncertainty environment, many researchers have introduced DEA models in fuzzy environment. Some of these models ar...

Multi-criteria decision analysis (MCDA) is increasingly used to support decisions in healthcare involving multiple and conflicting criteria. Although uncertainty is usually carefully addressed in health economic evaluations, whether and how the different sources of uncertainty are dealt with and with what methods in MCDA is less known. The objective of this study is to review how uncertainty ca...

Stochastic, as well fuzzy uncertainty, can be found in most real-world systems. Considering both types of uncertainties simultaneously makes optimization problems incredibly challenging. In this paper, we analyze the permutation flow shop problem (PFSP) with stochastic and processing times. The main goal is to find solution (permutation jobs) that minimizes expected makespan. However, due exist...

Abstract: Fate and transport models have extensively been used to predict distribution of toxic substances in the multi-media environment. In mining industry, predictive models are commonly used to evaluate performance of mitigation measures and estimate remediation costs during different phases of a mine lifecycle. These models are often used in deterministic form; however the probabilistic an...