In this paper we show that some applications of a fuzzy methodology in medical diagnosis were ”inspired” by probabilistic approaches. Although probability theory and fuzzy set theory describe different facets of uncertainty. In this paper we trace the transformation of statistical measures of diagnostic accuracy to fuzzy occurrence, exclusion and confirmation relations, applied in several fuzzy...

In risk analysis, the treatment of the epistemic uncertainty associated to the probability of occurrence of an event is fundamental. Traditionally, probabilistic distributions have been used to characterize the epistemic uncertainty due to imprecise knowledge of the parameters in risk models. On the other hand, it has been argued that in certain instances such uncertainty may be best accounted ...

On the example of physics, we show that the traditional one-level description is not completely adequate. For a more adequate structure, a hierarchical description of uncertainty is necessary, which supplements the more traditional first-order uncertainty with second-order, third-order and more sophisticated models. In particular, the second-order approach seems to provide a bridge between prob...

The prevalent approach to the treatment of processing time uncertainties in production scheduling problems is through the use of probabilistic models. Apart from requiring detailed information about probability distribution functions, this approach also has the drawback that the computational expense of solving these models is very high. In this work, we present a non-probabilistic treatment of...

A risk-minimizing portfolio model under uncertainty with randomness and fuzziness is discussed. By a perception-based extension of estimations for fuzzy random variables, the risk-minimizing portfolio problem is developed. In the uncertainty model, the randomness and fuzziness are evaluated respectively by the probabilistic expectation and mean values with evaluation weights and -mean functions...

Propagating possibilistic and probabilistic variables through a mapping yields a fuzzy random variable. We propose a method to attach probability intervals to events pertaining to the output variable. We show that this method is consistent with classical approaches to fuzzy random variables and that the obtained probability interval is the mean value of the fuzzy probability defined by viewing ...

In this paper, a probabilistic fuzzy approach is proposed for mobile-robot reactive navigation using range sensors. The primary motivation is an integrated reactive navigation control system with good real-time performance under uncertainty. To accomplish this aim, a probabilistic fuzzy logic system (PFLS) is introduced to range measurement and reactive navigation in local environments. PFLS is...

In this paper a fuzzy method for determining appropriate structural design is presented. Non-stochastic uncertainty is quantified using fuzzy values and fuzzy random variables. Fuzzy structural parameters are processed on the basis of a generally applicable numerical method for arbitrary nonlinear fuzzy structural analyses. Fuzzy randomness is introduced into a fuzzy probabilistic safety assess...

1. UNCERTAINTY: ONE MUST FIGHT, BUT ONE CAN’T WIN 9 1.1. To recognize a situation 9 1.2 Predicting tomorrow 11 1.3 An expert and his cognitive activity 12 1.4 Statistics and quasi-statistics 13 2. FUZZY SETS COME TO THE AID 14 2.1 The Carrier 14 2.2 Fuzzy set 15 2.3 The Function of Belonging 15 2.4 The Linguistic Variable 15 2.5 Operations on fuzzy sub-sets 16 2.6 Fuzzy numbers and operations o...

Considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. This paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology.We study interrelationships between this theory and other fuzzy theories suchas intuitionis...