TITLE:
Multiyear Discrete Stochastic Programming with a Fuzzy Semi-Markov Process
AUTHORS:
C. S. Kim, Richard M. Adams, Dannele E. Peck
KEYWORDS:
Drought, Discrete Stochastic Economic Modeling, Fuzzy Logic, Fuzzy Markov Process, Fuzzy Semi-Markov Process
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.6,
March
24,
2016
ABSTRACT: Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.