This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seem
A Rough Fuzzy Set is defined as a set that combines fuzzy logic with rough set theory to handle uncertainty in information by capturing vagueness and indiscernibility through lower and upper approximations. AI generated definition based on: Recent Trends in Computational Intelligence Enabled Research, ...
This idea leads to an introduction of another higher order fuzzy set called intuitionistic fuzzy set introduced by Atanassov's in 1983 [1]. It takes into account the membership degree as well as the non-membership degree. In an ordinary fuzzy set, the non-membership degree is the complement...
a theory which relates to classes of objects without crisp, clearly defined boundaries. In such cases, membership in a set is a matter of degree. In this perspective, fuzzy logic in its narrow sense is a branch of FL. Even in its more narrow definition, fuzzy logic differs both in concep...
Instead, discrete crisp numbers are typically used in representing the symbolic output values. Accordingly, the rule base generation process is different by firstly dividing the labelled data set into multiple sub-data sets each sharing the same label. Then, a clustering algorithm is applied to ...
Renewable energy integration introduces grid instability due to variable and intermittent sources like solar and wind, impacting reliability. This paper provides a thorough discussion of recent advancements and emerging trends in grid-integrated wind ene
In general, the fuzzy logic provides an inference structure that enables appropriate human reasoning capabilities. On the contrary, the traditional binary set theory describes crisp events, events that either do or do not occur. It uses probability theory to explain if an event will occur, ...
system improves its performance by increasing its dynamic behavior. The total load demand of DISCO1 and DISCO2 is set as 0.01 pu. A DPM is used to make agreements between DISCOs and GENCOs. Since there is a controller for each area in the system under consideration, the tie-line power ...
All properties of the crisp set are also applicable for fuzzy sets except for the excluded-middle laws. In fuzzy set theory, the union of a fuzzy set with its complement does not yield the universe and the intersection of a fuzzy set and its complement is not the null set. This differenc...
The algorithm is similar to crisp clustering, such as k-means clustering, in several aspects but incorporates fuzzy set concepts of partial memberships by allowing data points to belong to more than one cluster. This can be observed in the form of overlapping clusters. Additionally many crisp ...