Interpolation Based on Semantic Distance Weighting in Hedge Algebra and Its Application

Abstract

When solving the approximation problems proposed by a Linguistic Rule Base System (LRBS), the choice of reasoning method has a great influence on the result. The chosen reasoning method should ensure the correctness of the variable relationship between the outputs versus the inputs. According to the Hedge Algebra's approach, we can convert the LRBS to a real "hyper surface" in semantic space, called the Quantified Semantic Rule Base System (QRBS), and use an interpolative method for reasoning. In this paper, we propose the use of the interpolation to ensure the correctness mentioned above. It is interpolation based on the semantic distance weighting of the input semantic values versus the semantic value of the elements appearing in the rule. In the input semantic value vector, for each component we define its distance weight to the semantic value of the corresponding language class that appears in the rule. This distance-weighted value is used to join the output value. With this proposal, we have designed and simulated the controller that control rules are given by LRBS for the resistance furnace. The results show that the controller works well under the control requirements.

Information and Mathematical Structures Contained in the Natural Language Word Domains and Their Applications

“…The results and analysis obtained above, and the results achieved in [15,16,17,18,19,20,21,22,23,25,26,27,28,29,30], most published in international journals ISI indexed, justify the meaning of discovering L-variables' word domain semantic structures and their quantification in problem-solving control.…”

“…The HA-methodology was applied first in the study [15], which proposes an HA-based method to design an optimized controller to solve an inverted pendulum control problem. It motivated many studies to develop HA-based controllers for controlling active vibration control of uncertain structures against earthquake [17,18,19,20,21,22,23], a self-excited induction generator [24], a grid synchronization [25], and the speed in a Stand-Alone WECS [26,27], and in solving control problems in the industry [28,29,30]. In the framework of this section, we summarize only some of these studies…”

“…The study [15] to solve an inverted pendulum problem is the first one to show the applicability of HAs in fuzzy control. Then, there are many works applying the HA-methodology to solve many different problems in this field, such as a swing-up control problem [16], vibration control problems of high-rise buildings subjected to seismic loads [17,18,19,20,21,22,23], and fuzzy control problems in the industry [28,29,30].…”

“…These achieved theoretical results sufficiently form a necessary formalized basis for solving application problems in different fields. One can find its applications in cybernetics [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], in classification and regression [31,32,33], decision making [38,39], multi-channel image processing [37], robotics [45,46,47,48,49], networking [43,44], fuzzy linguistic time series [40,41,42], linguistic data summaries [35,36], databases and object-oriented databases based on hedge algebraic semantic [58,59,60], and it is not the end.…”

Designing Hedge Algebraic Controller and Optimizing by Genetic Algorithm for Serial Robots Adhering Trajectories

“…Interpolation based on the Semantic Distance Weighting method (ISDMd) is selected as in [28]. This is a linear interpolation method that allows interpolation in n-dimensional space.…”