Uncertainty is present in all areas of human activity, it is an inherent part of reality. This means that any attempt to describe this reality should take into account the presence of uncertainty. It is in the need to model uncertainty should be seen as the impetus for the development of fuzzy set theory and its subsequent generalizations.
Accounting for uncertainty in describing reality requires identifying the sources of that uncertainty. Two basic ones can be identified reasons for uncertainty:
For both sources of uncertainty, an object is most often described by a set containing all possible representations of it. In the first case, such a collection contains elements that make up a larger whole. In other words, each element in the set is an equal component of a precisely defined whole. In the second case, the collection describes incomplete information. This means that there are elements in the set treated as possible representations of a certain object, of which only one is correct.
The first approach corresponds to an ontic and the second to an epistemic understanding of uncertainty. This distinction is not only theoretical, as both approaches require the use of different information processing methods to capture the nature of uncertainty. This means that the way uncertain information is combined depends on the type of uncertainty.
Sets that describe uncertainty ontically (called conjunctive sets), contain elements that are equally possible. Sets describing uncertainty epistemically (called disjunctive sets) contain many alternative representations, of which only one is true, but without additional knowledge it is not possible to determine which one. The differences between the two approaches for describing uncertainty can be better understood by the following example. Consider the demand for a certain product over a one-week period. This demand can be described by an interval . If this range describes the range of demand for a given product, then we have a Ontic uncertainty. Each value in the range is a component of a larger whole, in this case the demand range. We are at the same time to determine what was the value of demand in a particular week (last week, last year). If, on the other hand, an interval describes our knowledge of the demand for a particular product in a particular week, then we are dealing with epistemic uncertainty, because the demand for a particular product in a particular week is determined precisely, while our lack of knowledge forced the determination of this demand by means of an interval. The epistemic interpretation of the compartment, as opposed to the ontic one, assumes that it does not have its reflection in reality, but represents only subjective and An incomplete state of knowledge about some precise fact (the source of uncertainty is lack of knowledge).
Fuzzy sets are a concept so general that they are can be used for modeling uncertainty in both senses cited, it just requires that the membership function be properly defined and interpreted.
This article was written thanks to the funds from the European Union’s co-financing of the Operational Program Intelligent Development 2014-2020, a project implemented under the competition of the National Center for Research and Development: under the “Fast Track” competition for micro, small and medium-sized entrepreneurs – competition for projects from less developed regions under Measure 1.1: R&D projects of enterprises Sub-measure 1.1.1 Industrial research and development work carried out by enterprises. Project title: “Developing software to improve forecast accuracy and inventory optimization from the perspective of customer and supplier collaborating in the supply chain using fuzzy deep neural networks.
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