Abstract
Taking into account that interval-valued fuzzy numbers can provide more flexibility to represent the imprecise information and interval-valued trapezoidal fuzzy numbers are widely used in practice, this paper devotes to seek an approximation operator that produces an interval-valued trapezoidal fuzzy number which is the nearest one to the given interval-valued fuzzy number, and the approximation operator preserves the core of the original interval-valued fuzzy number with respect to the weighted distance. As an application, we use the interval-valued trapezoidal approximation to handle fuzzy risk analysis problems, which overcome the drawback of existing fuzzy risk analysis methods.
Highlights
The theory of fuzzy set, proposed by Zadeh [1], has received a great deal of attention due to its capability of handling uncertainty
The interval-valued trapezoidal approximation must preserve some parameters of the given interval-valued fuzzy number, such as α-level set invariance, translation invariance, scale invariance, identity, nearness criterion, ranking invariance, and continuity
Since interval-valued trapezoidal approximation could be performed in many ways, we propose a number of criteria which the approximation operator should possess at least one
Summary
The theory of fuzzy set, proposed by Zadeh [1], has received a great deal of attention due to its capability of handling uncertainty. Interval-valued trapezoidal fuzzy numbers are widely used in decision making, risk analysis, sensitivity analysis, and other fields [5,6,7]. We are interested in approximating interval-valued fuzzy numbers by means of intervalvalued trapezoidal fuzzy numbers to simplify calculations. The interval-valued trapezoidal approximation must preserve some parameters of the given interval-valued fuzzy number, such as α-level set invariance, translation invariance, scale invariance, identity, nearness criterion, ranking invariance, and continuity. Considering that the core (α-level set, where α = 1) of an interval-valued fuzzy number is an important parameter in practical problems, we use the Karush-KuhnTucher Theorem to investigate the interval-valued trapezoidal approximation of an interval-valued fuzzy number, which preserves its core.
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