Possibilistic processes for complex systems modeling

Possibility theory is being developed as an alternative to traditional information theory. While possibility theory is logically independent of probability theory, they are related: both arise in Dempster-Shafer evidence theory as fuzzy measures defined on random sets; and their distributions are both fuzzy sets. Together these fields comprise the new field of Generalized Information Theory (scGIT). Traditionally mathematical possibilistic semantics has been based strictly on fuzzy sets and their interpretation in the context of psychological uncertainty and subjective evaluations. The purpose of this dissertation is to extend interpretations and applications of possibility theory beyond those of fuzzy sets; in particular, to develop a natural semantics of possibility for the purposes of qualitative modeling of complex physical systems. The dissertation addresses the following: Possibility Theory in scGIT. The relations between possibility theory and the other formalisms of scGIT are explicated; random set distributions and their distribution operators and structural and numerical aggregation functions are introduced to relate probability with possibility in the context of scGIT; possibility arises from consistent random sets; and methods for possibilistic normalization and possibilistic approximation of inconsistent random sets are developed. It is argued that there is no special relationship between possibility theory and fuzzy systems theory. Semantics of possibility. Drawing from semiotics and general models, criteria for the natural semantics of possibility are explored; the basis for a graduated, de re possibility is related to modal, natural language, and probabilistic views; a strong compatibility requirement for possibility and probability is advanced; possibilistic concepts are developed from mathematical, statistical and physical interpretations; and the traditional semantics of possibility from subjective evaluations, converted probabilities, and likelihoods are critiqued. Possibilistic measurement. Measurement methods for possibility values based on subset observations, and which are consistent with possibilistic semantics, are developed; possibilistic histograms which are fuzzy intervals, and their continuous approximations, are defined; set statistics are derived from indirect measurement of system components, ensembles of differently calibrated instruments, interval-based time series data from order statistics, and local extrema of time series data. Possibilistic processes. General processes are defined as semirings operating on state vectors and transition matrices, and the special case of possibilistic processes using max/t-norm semirings and possibilistically normal conditional transition matrices, are introduced, and their properties developed; possibilistic Markov processes and a possibilistic Monte Carlo method are defined. Software architecture. An architecture for a C$\sp{++}$ implementation of possibilistic and scGIT methods is proposed in the context of the Computer-Aided Systems Theory (scCAST) research program. Qualitative model-based diagnosis and trend an analysis: The use of possibility theory as a new method for qualitative modeling is explored. The potential for the application of possibilistic methods in systems for the qualitative model-based diagnosis and trend analysis of complex systems like spacecraft is described.