Abstract
The purpose of this chapter is to briefly expose a novice reader to basic elements of the theory of fuzzy sets and fuzzy systems. Our presentation will intuitive and constructive, and limited mainly to the elements needed for pour further analysis. Our perspective will be in the “pure” fuzzy setting, and possibility theory (which is related to fuzzy sets theory) will not be discussed; the interested reader is referred to, e.g., Dubois and Prade [4]. Basically, we will outline the idea of a fuzzy set, basic properties of fuzzy sets, operations on fuzzy sets, some extensions of the basic concept of a fuzzy set, fuzzy relations and their compositions, linguistic variables, fuzzy conditional statements, and the compositional rule of inference, the extension principle, and fuzzy arithmetic (notably with based on the LR fuzzy numbers).
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Kaur, A., Kacprzyk, J., Kumar, A. (2020). A Brief Introduction to Fuzzy Sets. In: Fuzzy Transportation and Transshipment Problems. Studies in Fuzziness and Soft Computing, vol 385. Springer, Cham. https://doi.org/10.1007/978-3-030-26676-9_2
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DOI: https://doi.org/10.1007/978-3-030-26676-9_2
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