Towards a formal taxonomy of hybrid uncertainty representations
Recent years have seen a proliferation of methods in addition to probability theory to represent information and uncertainty, including fuzzy sets and systems, fuzzy measures, rough sets, random sets, possibility distributions, imprecise probabilities, etc. We can identify these fields collectively as General Information Theory. The components of GIT represent information according to different axiomatic bases, and are thus capable of capturing different semantic aspects of uncertainty. Traditionally, these semantic criteria include such categories as fuzziness, vagueness, nonspecificity, conflict, and randomness. So it is clear that there is a pressing need for the GIT community to synthesize these methods, searching out larger formal frameworks within which to place these various components with respect to each other. Ideally, syntactic (mathematical) generalization can both aid and be aided by the semantic analysis available in terms of the conceptual categories outlined above. In this paper we present some preliminary ideas about how to formally relate various uncertainty representations together in a taxonomic lattice, capturing both syntactic and semantic generalization. Some partial and provisional results are shown. Assume a simple finite universe of discourse {Omega} = (a, b, c). We want to describe a situation in which we ask a question of the sort {open_quotes}what is the value of a variable x which takes values in {Omega}?{close_quotes}. When there is no uncertainty, we have a single alternative, say x = a. In logical terms, we would say that the proposition p: {open_quotes}the value of x is a{close_quotes} is TRUE. Our approach begins with two primitive concepts which can change our knowledge of x, each of which represents a different form of uncertainty, nonspecificity and fuxxiness.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- Department of Defense, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 475585
- Report Number(s):
- LA-UR-97-655; CONF-970377-1; ON: DE97005009; TRN: 97:003284
- Resource Relation:
- Conference: 5. international on fuzzy theory and technology, Triangle Park, NC (United States), 2-5 Mar 1997; Other Information: PBD: Feb 1997
- Country of Publication:
- United States
- Language:
- English
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