Probabilistic Fuzzy Logic System Research Articles

A two-stage Bayesian learning-based probabilistic fuzzy interpreter for uncertainty modeling

In practical applications, there are usually complex stochastic and vague uncertainties caused by inherent randomness and unknown dynamics. How to model uncertainty and interpret the modeling result is of significance for practical applications. To address these issues, a new probabilistic fuzzy logic system (PFLS) is proposed based on two-stage Bayesian learning. On the basis of the structure of traditional FLS, the proposed PFLS can be used as probabilistic fuzzy interpreter for complex uncertainty modeling. Specifically, in the training stage, expectation–maximization-based Gaussian mixture model is used to classify given data and learn the corresponding probability distributions, which are further used to generate samples to compensate for the limited given data. Based on Bayesian learning, fuzzy rules are learned by maximizing joint probability distributions of given data and rules. In the later inference stage, Bayesian learning-based probabilistic fuzzy inference is developed to make the activated fuzzy rules best match the input and output data pairs. Through integration with the two-stage Bayesian learning, PFLS can properly handle both vague and stochastic uncertainties, and interpret modeling results with fuzzy rules under maximum likelihood. Experiments based on temperature predictions in complex industrial processes demonstrate the effectiveness of the proposed method.

Probabilistic Active Control of Structures using a Probabilistic Fuzzy Logic Controller

Because uncertainty is inherent in engineering structures, it is essential to improve the procedures of structural control. The present study investigated applying a probabilistic fuzzy logic system (PFLS) in active tendons for the covariance response control of buildings. In contrast to an ordinary fuzzy logic system, PFLS integrates probabilistic theory into a fuzzy logic system that can handle the linguistic and stochastic uncertainties existing in the process. To investigate the proficiency of the suggested controller, a single degree of freedom (SDOF) system and a three-story multiple degree of freedom (MDOF) system with different arrangements of tendons on the stories were considered. The structures were subjected to a random dynamic load modeled using Gaussian white noise, and the modeling parameters the damping, stiffness, and mass were considered to be random Gaussian samples with a dispersion coefficient of 10%. The results calculated by the suggested intelligent control scheme were evaluated with those of an uncontrolled structural model and model with a linear quadratic regulator (LQR) controller. The numerical finding revealed that the probabilistic fuzzy logic controller (PFLC) was very efficient in decreasing the structural covariance responses relative to the LQR controller. Moreover, the most and least reduction values of displacement responses for MDOF structures were about 36% and 12.5%, respectively, compared to the LQR controller. It is also showed that the PFLC is more accurate because it includes stochastic uncertainty.

Probabilistic fuzzy logic controller for uncertain nonlinear systems

This paper proposes a probabilistic fuzzy proportional - integral (PFPI) controller for controlling uncertain nonlinear systems. Firstly, the probabilistic fuzzy logic system (PFLS) improves the capability of the ordinary fuzzy logic system (FLS) to overcome various uncertainties in the controlled dynamical systems by integrating the probability method into the fuzzy logic system. Moreover, the input/output relationship for the proposed PFPI controller is derived. The resulting structure is equivalent to nonlinear PI controller and the equivalent gains for the proposed PFPI controller are a nonlinear function of input variables. These gains are changed as the input variables changed. The sufficient conditions for the proposed PFPI controller, which achieve the bounded-input bounded-output (BIBO) stability are obtained based on the small gain theorem. Finally, the obtained results indicate that the PFPI controller is able to reduce the effect of the system uncertainties compared with the fuzzy PI (FPI) controller.

Intelligent tracking control of a PMLSM using self‐evolving probabilistic fuzzy neural network

This study presents a self-evolving probabilistic fuzzy (PF) neural network with asymmetric membership function (SPFNN-AMF) controller for the position servo control of a permanent magnet linear synchronous motor (PMLSM) servo drive system. In the beginning, the dynamic model for the PMLSM is analysed on the basis of field-oriented control. Subsequently, an SPFNN-AMF control system, which integrates the advantages of self-evolving NN, PF logic system, and AMF, is proposed to handle vagueness, randomness, and time-varying uncertainties of the PMLSM servo drive system during the control process. For the SPFNN-AMF, the proposed learning algorithm consists of the structure learning and parameter learning in which the former is used to grow and prune the fuzzy rules automatically, whereas the latter is utilised to train the network parameters dynamically. Finally, detailed experimental results of two position commands tracking at different operation conditions demonstrate the validity and robustness of the proposed SPFNN-AMF for controlling the PMLSM servo drive system.

Negotiation Based on Fuzzy Logic and Knowledge Engineering: Some Case Studies

One of the most recent mathematical models for negotiation is the Compensatory Negotiation Solution by Knowledge Engineering (CNSKE). In this model a logic system called Compensatory Fuzzy Logic was used, which is more adequate to solve problems of decision making than the classical one probabilistic fuzzy logic system. The idempotency axiom of this system and the continuity of the operators allow the truth-values of the membership function to have a cardinal and not exclusively ordinal semantic meaning. On the other hand, continuity also makes ‘sensible’ the truth-values of the predicates. The aim of this paper is to illustrate the advantages of the CNSKE over other approaches in Game Theory. To show these advantages, some case studies are analyzed, consisting on the solution of three problems in which CNSKE is applied in economic and politic cases of negotiation, and compared with other alternative approaches.

Intelligent modelling of continuous stirred tank reactor process

In this paper, we discuss the theory and design of the probabilistic fuzzy inference system, one that model and minimise the effects of rule uncertainties, i.e., existing randomness in many real world systems. This approach ascends from the combination of the concepts of degree of truth and probability of truth in a unique framework. This combination is carried out both in fuzzy sets and fuzzy rules, which leads to probabilistic fuzzy sets and probabilistic fuzzy rules. Using these probabilistic elements, an innovative probabilistic fuzzy logic system is obtained as a fuzzy probabilistic model of a complex non-deterministic system. We designed probabilistic fuzzy inference system for modelling the CSTR process, which shows dynamic nonlinearity and demonstrated its upgraded performance over the conventional fuzzy inference system.

Logistics Demand Forecasting with Asymmetry-Width Probabilistic Fuzzy Logic System

There are a lot of approaches in logistics demand forecasting field and perform different characters. The probabilistic fuzzy set (PFS) and probabilistic fuzzy logic system is designed for handling the uncertainties in both stochastic and nonstochastic nature. In this paper, an asymmetric probabilistic fuzzy set is proposed by randomly varying the width of asymmetric Gaussian membership function. And the related PFLS is constructed to be applied to a logistics demand forecasting. The performance discloses that the asymmetry-width probabilistic fuzzy set performs better than precious symmetric one. It is because the asymmetric probabilistic fuzzy sets variability and malleability is higher than this of the symmetric probabilistic fuzzy set.

Probabilistic Fuzzy Control of Mobile Robots for Range Sensor Based Reactive Navigation

In this paper, a probabilistic fuzzy approach is proposed for mobile-robot reactive navigation using range sensors. The primary motivation is an integrated reactive navigation control system with good real-time performance under uncertainty. To accomplish this aim, a probabilistic fuzzy logic system (PFLS) is introduced to range measurement and reactive navigation in local environments. PFLS is first adopted to handle the fuzzy and stochastic uncertainties in range sensors and to provide more precise distance information in unknown environments. Consequently these sensor data are sent to a probabilistic fuzzy rule-based inference system with reactive behaviors for local navigation. The feasibility and effectiveness of the proposed approach are verified by simulation and the experiments on a real mobile robot.

A probabilistic fuzzy logic system for modeling and control

In this paper, a probabilistic fuzzy logic system (PFLS) is proposed for the modeling and control problems. Similar to the ordinary fuzzy logic system (FLS), the PFLS consists of the fuzzification, inference engine and defuzzification operation to process the fuzzy information. Different to the FLS, it uses the probabilistic modeling method to improve the stochastic modeling capability. By using a three-dimensional membership function (MF), the PFLS is able to handle the effect of random noise and stochastic uncertainties existing in the process. A unique defuzzification method is proposed to simplify the complex operation. Finally, the proposed PFLS is applied to a function approximation problem and a robotic system. It shows a better performance than an ordinary FLS in stochastic circumstance.