###### Abstract
However, because of the computational complexity associated with the processing of GT2 FSs, only their constrained version, the interval T2 (IT2) FSs, have been widely used. While IT2 FSs allow for fast processing, they lack the expressive power of GT2 FSs when modeling various kinds of uncertainties [25]. In this paper, the concept of a shadowed fuzzy set is introduced and some of its related operations are studied. A shadowed fuzzy set enables localization of the underlying uncertainty of fuzzy grades in type-2 fuzzy sets through exploitation of shadowed sets. It provides a capable framework that, despite preserving the uncertainties of fuzzy grades in type-2 fuzzy sets, adheres the simplicity of the concept and operations of interval type-2 fuzzy sets [26]. The use of the shadowed set theory is presented for parameter adaptation of the harmony search, which is inspired by music specifically in jazz improvisation. In this article, the goal was the optimization of an interval type-2 controller utilizing the variant of the harmony search with fuzzy adaptation. The study case with which the experimentation was carried out is a direct current motor, and its main characteristic is to maintain the stability of the motor position [27]; this paper suggests a better solution for such traffic issues via the delay-optimized Shortest Path Prediction (SPP) method. Even though shadowed type-2 (ST2) fuzzy logic works well for delay optimization with uncertain data, it causes a rise in fuzzy partitioning complexity [28]. The shadowed fuzzy set discussed in this paper provides a framework with a simplicity that is comparable with an interval type-2 fuzzy set but, on the other hand, preserves the fuzziness of the third dimension of type-2 fuzzy sets [29], and this study introduces a new concept of shadowed sets that can be regarded as a certain operational framework, simplifying processing carried out with the aid of fuzzy sets and enhancing interpretation of results obtained therein [30]. In [31; 32; 33; 34; 35], recent articles are presented where novel metaheuristics are used to solve various problems, which can be viewed as representative of the state of the art in this area. The main contribution involves conducting a comprehensive behavioral analysis, utilizing an ST2-FHS for controlling the search space exploitation carried out by the harmony search, using two alpha planes in the approximation. Additionally, the application of this approach involves finding the parameter values of the membership functions in the design of a type-2 controller. Upon reviewing the existing literature, no similar work has been found, making this contribution significant. This article is structured as follows: Section 2 provides the theory of fuzzy shadowed sets, while Section 3 presents the theoretical basis of the harmony search, as well as the description of the proposal. In Section 4, the use of shadowed fuzzy logic in the harmony search is discussed, and Section 5 contains the description and implementation of the controller. This is followed by Section 6, where simulations and an analysis of the results are outlined, and Section 7 offers the conclusions.