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.

In recent years, the application of hedge algebras in the field of control has been studied. The results show that this approach has many advantages. In additions, industrial robots are being well-developed and extensively used, especially in the industrial revolution 4.0. Accurate control of industrial robots is a class of problems that many scientists are interested in. In this paper, we design a controller based on hedge algebra for serial robots. The control rule is given by linguistic rule base system. The goal is to accurately control the moving robot arm which adheres given trajectories. Optimization of fuzzy parameters for the controller is done by genetic algorithms. The system has been simulated on the Matlab-Simulink software. The simulation results show that the orbital deviation is very small. Moreover, the controller worked well with correct control quality. This result once presents the simplicity and efficiency of the hedge algebras approach to control.

Recently, numerous scholars have suggested fuzzy time series (FTS) models to forecast many different fields. One of the vital issues for high accurate forecasting in FTS model is method of partitioning in Universe of discourse (UoD). In this research, we propose a novel FTS model, which is established by using hedge algebra (HA) and particle swarm optimization (PSO) for forecasting the different problems. In this model, HA is considered an algebraic structure for partitioning the UoD into unequal-size intervals based on optimal parameters which is determined by PSO. After making the intervals with unequallength, the data values of times series on each interval are symbolized by fuzzy sets and then, these fuzzy sets are utilized to make fuzzy relation groups. Lastly, we keep using the PSO to adjust the size of each interval with view to reaching the better accurate prediction rate. The effectiveness of the proposed method is demonstrated on two datasets which are often applied in many studies in literature as enrolments data of the University of Alabama and Car road accident data in Belgium. The obtained results show that the proposed model produces higher accuracy forecasting when compared with the some of the recent FTS prediction models for all orders of model.

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