Abstract
The defuzzification process converts fuzzy numbers to crisp ones and is an important stage in the implementation of fuzzy systems. In many actual applications, we encounter cases, in which the observed or derived values of the variables are approximate, yet the variables themselves must satisfy a set of relationships dictated by physical principle. When the observed values do not satisfy the relationships, each value is adjusted until they satisfy the relationships among observed data indicating their mathematical dependence on one another. Hence, this study proposes a new method based on the Data Envelopment Analysis (DEA) model to defuzzify groups of fuzzy numbers. It also aims to assume that each observed value is an approximate number (or a fuzzy number) and the true value (crisp value) is found in the production possibility set of the DEA model. The proposed method partitions the fuzzy numbers and the relationships among these observed data are observed as constraints. The paper presents the model, the computational process and applications in a real problem.
Highlights
The modeling of complex systems is limited by incomplete knowledge and lack of information (Lai and Hwang, 1992)
This study mainly presents a new method to defuzzify groups of fuzzy numbers with the tool Data Envelopment Analysis (DEA)
The method proposed to defuzzify groups of fuzzy numbers operates in six stages: Stage 1: n triangular fuzzy numbers are generated based on the method proposed by Yeh and
Summary
The modeling of complex systems is limited by incomplete knowledge and lack of information (Lai and Hwang, 1992). The fuzzy set theory developed by Zadeh (1965), along with its techniques, is an interesting and promising approach to address complex, real-world issues. A fuzzy representation provides more information regarding a set than a crisp representation. This crisp representation remains necessary because it simplifies conception and clarification. The objective determination of the fuzzy structures of problematic systems is difficult. To replace a fuzzy representation of sets with a crisp representation in fuzzy system applications, the process of defuzzification is applied (Leekwijck and Kerre, 1999; Mahdiani et al, 2013)
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