Probabilistic Fuzzy Logic Research Articles

Reliability analysis of controlled structures based on probabilistic active controller

The reliability of controlled structures has been a subject of considerable concern in recent years. The present study investigated the effects of a probabilistic fuzzy logic controller (PFLC) as an intelligent controller and a linear quadratic regulator (LQR) controller as a classic controller on the reliability of a structure. Monte Carlo reliability analysis has been used to determine the reliability of the controlled structures. A single-degree-of-freedom (SDOF) system and multiple-degree-of-freedom (MDOF) structures with different tendon arrangements were considered. The structures were subjected to random Gaussian white noise as excitation and the variables considered were random Gaussian samples with a dispersion coefficient of 10%. The probability of failure could be estimated by PFLC at up to 10-5 as the threshold level increased in MDOF structures. Moreover, the results indicate that PFLC was more accurate than the LQR controller for a lower probability of failure because the associated limit state function includes stochastic uncertainty.

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.

Integrating an expert system with BrIMS, cost estimation, and linear scheduling at conceptual design stage of bridge projects

Highway networks are a major infrastructure system, most crucially major bridges and motorways. Proper handling of highway networks plays a significant role in enhancing the functionality of a bridge network. Besides that, estimating bridge construction costs is an increasing necessity at the conceptual design stage for accurate budgeting and effective funding. The degree of subjectivity involved in decision making of bridge projects is the main factor that influences bridge cost estimation and linear scheduling at the conceptual design stage. Objectives of this study are intended to demonstrate the viability of integrating a decision support system comprising qualitative objective functions with a bridge information management system (BrIMS) in order to overcome subjectivity in decision makings. An external data interchange protocol is implemented in synchrony with interoperability standards. The deployment of the proposed system shall include an all-in-one bridge construction cost estimation tool that can provide users with recommendations for bridge design alternatives. An integration of an expert system, cost estimation, and linear scheduling is proposed by automating cost and time scheduling techniques at the conceptual design stage. Successful implementation of such a system is a technological achievement of novelty to the integration of BrIMS solutions with probabilistic fuzzy logic strategic approaches.

Evaluation of landslide susceptibility in a hill city of Sikkim Himalaya with the perspective of hybrid modelling techniques

ABSTRACTLandslides are common and frequent occurring phenomenon in hilly terrain during monsoon season. The primary objectives of the research work are to carry out a comprehensive analysis by quantifying the landslide susceptibility using an integrated approach of random forest (RF) with the probabilistic likelihood ratio (RF-PLR), fuzzy logic (FL) and index of entropy (IOE) in Gangtok city of Sikkim state, India. Landslide inventories are prepared based on LISS-IV (MX) satellite imagery, Google Earth and reported data of Geological Survey of India. Altogether 12 landslide conditioning factors viz. slope, elevation, curvature, aspect, land use/land cover, geology, lineament, rainfall, soil type, soil thickness, water regime and distance from road are considered as input data for geospatial modelling of landslide susceptibility. Finally, model-derived landslide susceptibility maps are classified into four hazard zones, i.e. low, medium, high and very high. To measure model compatibility model comparison is performed in ArcGIS environment and models performance is assessed by confusion matrix where RF-FL gives more accuracy of 69.36% than other two models with 9.68% and 19.35% of Type I and type II error, respectively. The outputs are validated using success and prediction rate method where, RF-PLR, RF-FL and RF-IOE show area under curve (AUC) of success and prediction rate as 76%, 67%, 83%, 78% and 85%, 80%, respectively. Additionally, the differences in model performances were analyzed by means of Wilcoxon signed rank test, where it was found that statistically differences in the performance was significant in case of RF-PLR vs. RF-FL and RF-PLR vs. RF-IOE.

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.

Fuzzy data exchange

Data exchange is the problem of transforming data that conforms to one source schema into data that conforms to a target schema that reflects the source data as accurately as possible and in a way that is consistent with various dependencies. In a landmark paper, Fagin et al. have proposed a declarative, purely logical approach to this task. Since then, data exchange has been intensively studied in the database research community.In this paper we extend the classical data exchange approach of Fagin et al. to fuzzy data exchange as a framework concerned with the transformation of fuzzy data. We show that the most important properties of data exchange are preserved in this new setting. Moreover, the relation of fuzzy data exchange to the classical setting, probabilistic data exchange and fuzzy logic is studied.

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.

Probabilistic Fuzzy Logic Signal and Ramp Metering at a Diamond Interchange

In this paper, a probabilistic fuzzy logic control is developed for the signalized control of a diamond interchange to improve the traffic flow on the surface streets and highways. The signal phasing, green-time extension, and ramp metering are decided in response to real-time traffic conditions. The probabilistic fuzzy logic for diamond interchange (PFLDI) includes the following three modules: probabilistic fuzzy phase timing that controls the green-time extension process of the current running phase, phase-selection logic that decides the next phase based on the presetup phase logic by the local transport authority, and probabilistic fuzzy ramp metering that determines the on-ramp-metering rate based on the traffic conditions of the arterial streets and highways. The advanced interactive microscopic simulator for urban and nonurban network software was used to model the diamond interchange and measure the effectiveness of the proposed PFLDI algorithm. The performance of the PFLDI was compared with that of an actuated diamond interchange (ADI) control based on the asservissement linéaire d'entré autoroutière (ALINEA) algorithm and a conventional fuzzy logic control for a diamond interchange (FLDI) algorithm. Simulation results show that the PFLDI lowers system total travel time and average delay, improves the downstream average speed, and lowers the downstream average delay compared with ADI and FLDI.

Fire detection and 3D surface reconstruction based on stereoscopic pictures and probabilistic fuzzy logic

In this paper, a new fire detection method is proposed, which is based on using a stereo camera to calculate the distance between the camera and the fire region and to reconstruct the 3D surface of the fire front. For the purpose of fire detection, candidate fire regions are identified using generic color models and a simple background difference model. Gaussian membership functions (GMFs) for the shape, size, and motion variation of the fire are then generated, because fire regions in successive frames change constantly. These three GMFs are then applied to fuzzy logic for real-time fire verification. After segmentation of the fire regions from left and right images, feature points are extracted using a matching algorithm and their disparities are computed for distance estimation and 3D surface reconstruction. Our proposed algorithm was successfully applied to a fire video dataset and its detection performance was shown to be better than that of other methods. In addition, the distance estimation method yielded reasonable results when the fire was a short distance from the camera and the reconstruction of the 3D surface showed a shape that was almost the same as that of the real fire.

Probabilistic Fuzzy Logic Modeling: Quantifying Uncertainty of Mineral Prospectivity Models Using Monte Carlo Simulations

Significant uncertainties are associated with the definition of both the exploration targeting criteria and computational algorithms used to generate mineral prospectivity maps. In prospectivity modeling, the input and computational uncertainties are generally made implicit, by making a series of best-guess or best-fit decisions, on the basis of incomplete and imprecise information. The individual uncertainties are then compounded and propagated into the final prospectivity map as an implicit combined uncertainty which is impossible to directly analyze and use for decision making. This paper proposes a new approach to explicitly define uncertainties of individual targeting criteria and propagate them through a computational algorithm to evaluate the combined uncertainty of a prospectivity map. Applied to fuzzy logic prospectivity models, this approach involves replacing point estimates of fuzzy membership values by statistical distributions deemed representative of likely variability of the corresponding fuzzy membership values. Uncertainty is then propagated through a fuzzy logic inference system by applying Monte Carlo simulations. A final prospectivity map is represented by a grid of statistical distributions of fuzzy prospectivity. Such modeling of uncertainty in prospectivity analyses allows better definition of exploration target quality, as understanding of uncertainty is consistently captured, propagated and visualized in a transparent manner. The explicit uncertainty information of prospectivity maps can support further risk analysis and decision making. The proposed probabilistic fuzzy logic approach can be used in any area of geosciences to model uncertainty of complex fuzzy systems.

Uncertainty Handling for Sensor Location Estimation in Wireless Sensor Networks using Probabilistic Fuzzy System

With the increasing use of location-sensitive applications, a variety of localization techniques in wireless sensor networks (WSN) have been introduced to date; each aiming to improve accuracy of location estimation. However, most of these studies do not consider the factor of uncertainty which is naturally present in the localization problem. Focusing on range-free localization, this research examines RSS-based location estimation models. Due to environmental conditions, RSS can be influenced by several stochastic factors at the receiving node. In this research, we propose an algorithm using Probabilistic Fuzzy Logic Systems (PFLS) for the first time to address randomness and uncertainty in the location estimation problem. After optimizing PFLS by Genetic Algorithm (GA), the performance of both PFLS and the GA-optimized PFLS are compared with several other competing strategies under varying noise levels. Experimental results clearly indicate the improved efficiency of the proposed algorithm, particularly at higher noise levels.

Probabilistic Fuzzy Logic based Stock Price Prediction

In a real-time application scenario, the proposed Probabilistic Fuzzy Logic (PFL) approach can be implemented in various applications such as health care, stock trading, click stream analysis, retail and supply chain management. This work analyses stock trading due to its high non-linear, uncertain and dynamic data over time. Therefore, this paper presents an innovative probabilistic approach for stock price prediction that minimizes the investors risk while investing money in the stock market. We implemented this approach in a publisher/subscriber middleware system, where the crucial Complex Event Processing (CEP) technology processes the large number of incoming stock quotes with the deployment of probabilistic framework. This methodology identifies the event patterns subscribed by the stock traders/brokers over the incoming event stock quotes of market data. This approach triggers an appropriate output event to notify the opportunities to buy and to sell share in real-time based on event patterns of price movements. Experimental evaluation is carried out based on the published data to demonstrate the effectiveness of the proposed approach.

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.

An Advanced Certain Trust Model Using Fuzzy Logic and Probabilistic Logic theory

Trustworthiness especially for service oriented system is very important topic now a day in IT field of the whole world. Certain Trust Model depends on some certain values given by experts and developers. Here, main parameters for calculating trust are certainty and average rating. In this paper we have proposed an Extension of Certain Trust Model, mainly the representation portion based on probabilistic logic and fuzzy logic. This extended model can be applied in a system like cloud computing, internet, website, e-commerce, etc. to ensure trustworthiness of these platforms. The model uses the concept of fuzzy logic to add fuzziness with certainty and average rating to calculate the trustworthiness of a system more accurately. We have proposed two new parameters - trust T and behavioral probability P, which will help both the users and the developers of the system to understand its present condition easily. The linguistic variables are defined for both T and P and then these variables are implemented in our laboratory to verify the proposed trust model. We represent the trustworthiness of test system for two cases of evidence value using Fuzzy Associative Memory (FAM). We use inference rules and defuzzification method for verifying the model.

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.

ON THE LOOMIS–SIKORSKI THEOREM FOR MV-ALGEBRAS WITH INTERNAL STATE

AbstractIn Flaminio and Montagna [‘An algebraic approach to states on MV-algebras’, in:Fuzzy Logic 2,Proc. 5th EUSFLAT Conference, Ostrava, 11–14 September 2007 (ed. V. Novák) (Universitas Ostraviensis, Ostrava, 2007), Vol. II, pp. 201–206; ‘MV-algebras with internal states and probabilistic fuzzy logic’,Internat. J. Approx. Reason.50(2009), 138–152], the authors introduced MV-algebras with an internal state, called state MV-algebras. (The letters MV stand for multi-valued.) In Di Nola and Dvurečenskij [‘State-morphism MV-algebras’,Ann. Pure Appl. Logic161(2009), 161–173], a stronger version of state MV-algebras, called state-morphism MV-algebras, was defined. In this paper, we present the Loomis–Sikorski theorem forσ-complete MV-algebras with aσ-complete state-morphism-operator, showing that every such MV-algebra is aσ-homomorphic image of a tribe of functions with an internal state induced by a function where all the MV-operations are defined by points.

Description logic programs under probabilistic uncertainty and fuzzy vagueness

This paper is directed towards an infrastructure for handling both uncertainty and vagueness in the Rules, Logic, and Proof layers of the Semantic Web. More concretely, we present probabilistic fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (with stratified default-negation), and probabilistic uncertainty in a uniform framework for the Semantic Web. We define important concepts dealing with both probabilistic uncertainty and fuzzy vagueness, such as the expected truth value of a crisp sentence and the probability of a vague sentence. Furthermore, we describe a shopping agent example, which gives evidence of the usefulness of probabilistic fuzzy description logic programs in realistic Web applications. We also provide algorithms for query processing in probabilistic fuzzy description logic programs, and we delineate a special case where query processing can be done in polynomial time in the data complexity.

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.