1. Gradualness: the idea that many categories in natural language are a matter of degree, including truth. The extension of a gradual predicate is a fuzzy set, a set where the transition between membership and non-membership is gradual rather than abrupt. This is Zadeh’s original intuition [29]. 2. Epistemic Uncertainty: the idea of partial or incomplete information. In its most primitive form,...

Interval-valued fuzzy sets were proposed thirty years ago as a natural extension of fuzzy sets. Many variants of these mathematical objects exist, under various names. One popular variant proposed by Atanassov starts by the specification of membership and non-membership functions. This paper focuses on interpretations of such extensions of fuzzy sets, whereby the two membership functions that d...

An integrated model, combining spatial wildlife population and timber harvest and growth models, was developed to explore tradeoffs between the likelihood of persistence of a wildlife species, the northern flying squirrel (Glaucomys sabrinus), and timber production on a landscape on the west side of the Oregon Cascade Range. A simplified wildlife model was developed from the fully parameterized...

Alternative rules for the aggregation of different sources of information are discussed in the ambit of random set theory, which gives a general framework in the field of the uncertainty measures, containing probabilistic measures, set-based models (interval analysis or more generally convex models), fuzzy sets and possibility theory as particular extreme cases. Analogies and extensions of the ...

The problem of converting possibility measures into probability measures has received attention in the past, but not by so many scholars. This question is philosophically interesting as part of the debate between probability and fuzzy sets. The imbedding of fuzzy sets into random set theory as done by Goodman and Nguyen (1985), Wang Peizhuang (1983), among others, has solved this question in pr...

A probability density function verifies more demanding properties than a possibility measure. Probabilistic models ensure a predictable asymptotic behaviour. This should not be taken to suggest possibility theory should not be used. In fact, a histogram is a possibility measure and it is generally a better descriptor of a small sample of data than a probability density function regardless of it...

In safety, reliability as well as risk analysis and management, information often is uncertain and imprecise. The approach to air incident analysis under uncertain and imprecise information presented in our paper is inspired by the possibility theory. Notably, in such analyses these are both: static and dynamic components that have to be included. As part of this work, static analysis of a seri...

The Shilkret integral with respect to a completely maxitive capacity is fully determined by possibility distribution. In this paper, we introduce weaker topological form of maxitivity and show that under assumption the still its distribution for functions are sufficiently regular. Motivated large deviations theory, provide Laplace principle integrals characterize certain separation convexity as...

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In data envelopment analysis (DEA), identification of the strong defining hyperplanes of the empirical production possibility set (PPS) is important, because they can be used for determining rates of change of outputs with change in inputs. Also, efficient hyperp...

In real problems, there are basically two kind of uncertainty: uncertainty due to the lack of knowledge with respect to well defined objects, but for which there are different hypothetical situations, and uncertainty due to the intrinsic vagueness of the objects. Traditionally, the first type of uncertainty has been studied with the help of Probability Theory while the second one has used Fuzzy...