Browsing by Author "Runkler, Thomas"

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    Interval Type-2 Defuzzification Using Uncertainty Weights
    (Springer, 2017-09-27) Coupland, Simon; Runkler, Thomas; John, Robert, 1955-; Chen, Chao
    One of the most popular interval type–2 defuzzification methods is the Karnik–Mendel (KM) algorithm. Nie and Tan (NT) have proposed an approximation of the KM method that converts the interval type–2 membership functions to a single type–1 membership function by averaging the upper and lower memberships, and then applies a type–1 centroid defuzzification. In this paper we propose a modification of the NT algorithm which takes into account the uncertainty of the (interval type–2) memberships. We call this method the uncertainty weight (UW) method. Extensive numerical experiments motivated by typical fuzzy controller scenarios compare the KM, NT, and UW methods. The experiments show that (i) in many cases NT can be considered a good approximation of KM with much lower computational complexity, but not for highly unbalanced uncertainties, and (ii) UW yields more reasonable results than KM and NT if more certain decision alternatives should obtain a larger weight than more uncertain alternatives.
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    Interval type-2 fuzzy decision making
    (Elsevier, 2016-09-23) Coupland, Simon; Runkler, Thomas; John, Robert, 1955-
    This paper concerns itself with decision making under uncertainty and the consideration of risk. Type-1 fuzzy logic by its (essentially) crisp nature is limited in modelling decision making as there is no uncertainty in the membership function. We are interested in the role that interval type-2 fuzzy sets might play in enhancing decision making. Previous work by Bellman and Zadeh considered decision making to be based on goals and constraints. They deployed type-1 fuzzy sets. This paper extends this notion to interval type-2 fuzzy sets and presents a new approach to using interval type-2 fuzzy sets in a decision making situation taking into account the risk associated with the decision making. The explicit consideration of risk levels increases the solution space of the decision process and thus enables better decisions. We explain the new approach and provide two examples to show how this new approach works.