Fuzzy Sets, Mathematical Modeling and Indeterminacy
On January 3, 2019, Željko V. Račić has published an Open Access article entitled “Fuzzification: Decision Making in Terms of Uncertainty” in ECONOMICS: Innovative and Economic Research Journal.
A Blog Post by Pablo Markin.
In his article, Željko Račić has defined fuzzy sets “as sets where the boundary of the set is unclear and depends on subjective estimation or individual preference” (87). According to Račić, “[o]ne of the imperfections of the fuzzy sets is subjectivism when defining the boundaries of fuzzy sets and functions of belonging, which can significantly influence the final decision” (87). The importance of fuzzy set analysis derives from its capability to serve as “a suitable mathematical apparatus for modeling different processes dominated by uncertainty, subjectivity, indeterminacy” (87).
As this author notes, “[u]nlike the classical theory of sets, which very precisely defines a boundary that separates elements belonging to a set from elements that do not belong to it, the theory of fuzzy sets does not define the boundary of separation sufficiently” (88). As Račić adds, “[f]uzzy logic, as the basis of the fuzzy system, allows [for] decision making based on incomplete information and models based on […] linguistic variables” (91).
The paper of Račić suggests that “fuzzy set theory allows the analysis of insufficiently precise, accurate, complete phenomena that cannot be modeled solely by theory of probability or interval mathematics” (93). In the framework of this theoretical approach, “[i]nstead of “solid” and precise values, “soft,” blurred values are accepted and processed” (93).
By Pablo Markin
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