scholarly journals Coherent Predictive Inference under Exchangeability with Imprecise Probabilities

2015 ◽  
Vol 52 ◽  
pp. 1-95 ◽  
Author(s):  
Gert De Cooman ◽  
Jasper De Bock ◽  
Márcio Alves Diniz
Keyword(s):  
Imprecise Probabilities ◽  
Predictive Inference ◽  
Multivariate Polynomials ◽  
Conditional Probabilities ◽  
Reasoning Under Uncertainty ◽  
Inference System ◽  
Multinomial Models ◽  
Improper Prior ◽  
Inference Systems ◽  
Proper Priors

Coherent reasoning under uncertainty can be represented in a very general manner by coherent sets of desirable gambles. In a context that does not allow for indecision, this leads to an approach that is mathematically equivalent to working with coherent conditional probabilities. If we do allow for indecision, this leads to a more general foundation for coherent (imprecise-)probabilistic inference. In this framework, and for a given finite category set, coherent predictive inference under exchangeability can be represented using Bernstein coherent cones of multivariate polynomials on the simplex generated by this category set. This is a powerful generalisation of de Finetti's Representation Theorem allowing for both imprecision and indecision. We define an inference system as a map that associates a Bernstein coherent cone of polynomials with every finite category set. Many inference principles encountered in the literature can then be interpreted, and represented mathematically, as restrictions on such maps. We discuss, as particular examples, two important inference principles: representation insensitivity—a strengthened version of Walley's representation invariance—and specificity. We show that there is an infinity of inference systems that satisfy these two principles, amongst which we discuss in particular the skeptically cautious inference system, the inference systems corresponding to (a modified version of) Walley and Bernard's Imprecise Dirichlet Multinomial Models (IDMM), the skeptical IDMM inference systems, and the Haldane inference system. We also prove that the latter produces the same posterior inferences as would be obtained using Haldane's improper prior, implying that there is an infinity of proper priors that produce the same coherent posterior inferences as Haldane's improper one. Finally, we impose an additional inference principle that allows us to characterise uniquely the immediate predictions for the IDMM inference systems.

scholarly journals Coherent Predictive Inference under Exchangeability with Imprecise Probabilities (Extended Abstract)

2017 ◽  
Author(s):  
Gert de Cooman ◽  
Jasper De Bock ◽  
Márcio Alves Diniz
Keyword(s):  
Probabilistic Inference ◽  
Imprecise Probabilities ◽  
Predictive Inference ◽  
Multivariate Polynomials ◽  
Reasoning Under Uncertainty ◽  
Inference System ◽  
General Manner ◽  
Inference Systems

Coherent reasoning under uncertainty can be represented in a very general manner by coherent sets of desirable gambles. This leads to a more general foundation for coherent (imprecise-)probabilistic inference that allows for indecision. In this framework, and for a given finite category set, coherent predictive inference under exchangeability can be represented using Bernstein coherent cones of multivariate polynomials on the simplex generated by this category set. We define an inference system as a map that associates a Bernstein coherent cone of polynomials with every finite category set. Inference principles can then be represented mathematically as restrictions on such maps, which allows us to develop a notion of conservative inference under such inference principles. We discuss, as particular examples, representation insensitivity and specificity, and show that there is an infinity of inference systems that satisfy these two principles.

scholarly journals Utilization of Current Data for Geospatial Analysis of the Appropriateness of Apple Plantation Land Based on Fuzzy Inference Systems

2019 ◽  
Vol 4 (1) ◽  
pp. 64
Author(s):  
Prayudi Lestantyo
Keyword(s):  
Fuzzy Inference System ◽  
Fuzzy Inference ◽  
Geospatial Analysis ◽  
Current Data ◽  
Inference System ◽  
Apple Industry ◽  
Accuracy Test ◽  
Spatial Factor ◽  
Apple Production ◽  
Inference Systems

Apple is a high-value import fruit in Indonesia. One of the Apple production centers in Indonesia is Batu City, but the results tend to be declining in every year. To fulfill the demand of domestic apple industry, it is than a must to open new plantation land by observing the spatial factor. Expert and direct field review are needed to perform the analysis of land suitability, so that it will takes a lot of time and effort. Therefore, a smart system that can conduct geospatial analysis by using fuzzy inference system is developed. The data was obtained by using satellite imagery, data interpolation, and digitized and then analyzed into information. The analysis was performed on each pixel with six variable inputs including altitude, rainfall, humidity, air temperature, soil type and sun shine intensity. Besides that, the five-clustering output makes the results more accurate. From the results of the accuracy test, it is obtained a 92,86% accuracy, by comparing the results of the spatial analysis using fuzzy inference system with direct review on the field.

Fuzzy Logic-Based Inference Systems

2015 ◽  
pp. 209-239
Keyword(s):  
Fuzzy Logic ◽  
Knowledge Representation ◽  
Fuzzy Inference System ◽  
Fuzzy Inference ◽  
Mathematical Formulation ◽  
Cognitive Map ◽  
Fuzzy Cognitive Map ◽  
Adaptive Networks ◽  
Inference System ◽  
Inference Systems

This chapter presents the mathematical formulation of the fuzzy logic-based inference systems, used as means to infer about the response of ill-conditioned systems, based on the field knowledge representation in the fuzzy world. Particular approaches are explored, e.g., Fuzzy Inference System (FIS), Adaptive Networks-based FIS (ANFIS), Intuitionistic FIS (IFIS) and Fuzzy Cognitive Map (FCM), surfacing their potentialities in modeling applications, such as those in the field of learning, examined in the chapters of Part III that follow.

Artificial neural networks and adaptive neuro-fuzzy inference systems for parameter identification of dynamic systems

2020 ◽  
Vol 39 (5) ◽  
pp. 6145-6155
Author(s):  
Ramin Vatankhah ◽  
Mohammad Ghanatian
Keyword(s):  
Differential Equations ◽  
Dynamic Systems ◽  
Fuzzy Inference ◽  
Dynamic Equations ◽  
Control Analysis ◽  
Unknown Parameters ◽  
Inference System ◽  
Neuro Fuzzy ◽  
Artificial Neural ◽  
Inference Systems

There would always be some unknown geometric, inertial or any other kinds of parameters in governing differential equations of dynamic systems. These parameters are needed to be numerically specified in order to make these dynamic equations usable for dynamic and control analysis. In this study, two powerful techniques in the field of Artificial Intelligence (AI), namely Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) are utilized to explain how unknown parameters in differential equations of dynamic systems can be identified. The data required for training and testing the ANN and the ANFIS are obtained by solving the direct problem i.e. solving the dynamic equations with different known parameters and input stimulations. The governing ordinary differential equations of the system is numerically solved and the output values in different time steps are obtained. The output values of the system and their derivatives, the time and the inputs are given to the ANN and the ANFIS as their inputs and the unknown parameters in the dynamic equations are estimated as the outputs. Finally, the performances of the ANN and the ANFIS for identifying parameters of the system are compared based on the test data Percent Root Mean Square Error (% RMSE) values.

Demand forecasting in the beauty industry using fuzzy inference systems

2020 ◽  
Vol 15 (4) ◽  
pp. 1389-1417
Author(s):  
Ricardo Felicio Souza ◽  
Peter Wanke ◽  
Henrique Correa
Keyword(s):  
Time Series ◽  
Fuzzy Inference System ◽  
Fuzzy Inference ◽  
Theory And Practice ◽  
Forecast Errors ◽  
Fuzzy Inference Systems ◽  
Inference System ◽  
Content Type ◽  
Forecasting Methods ◽  
Inference Systems

Purpose This study aims to analyze the performance of four different fuzzy inference system-based forecasting tools using a real case company. Design/methodology/approach The forecasting tools were tested using 27 products of the nail polish line of a multinational beauty company and the performance of said tools was compared to those of the company’s previous forecasting methods that were basically qualitative (informal and intuition-based). Findings The performance of the methods analyzed was compared by using mean absolute percentage error. It was possible to determine the characteristics and conditions that make each model the best for each situation. The main takeaways were that low kurtosis, negatively skewed demand time-series and longer horizon forecasts that favor the fuzzy inference system-based models. Besides, the results suggest that the fuzzy forecasting tools should be preferred for longer horizon forecasts over informal qualitative methods. Originality/value Notwithstanding the proposed hybrid modeling approach based on fuzzy inference systems, our research offers a relevant contribution to theory and practice by shedding light on the segmentation and selection of forecasting models, both in terms of time-series characteristics and forecasting horizon. The proposed fuzzy inference systems showed to be particularly useful not only when time-series distributions present no clear central tendency (that is, they are platykurtic or dispersed around a large plateau around the median, which is the characteristic of negative kurtosis), but also when mode values are greater than median values, which in turn are greater than mean values. This large tail to the left (negative skewness) is typical of successful products whose sales are ramping up in early stages of their life cycle. For these, fuzzy inference systems may help managers screen out forecast bias and, therefore, lower forecast errors. This behavior also occurs when managers deal with forecasts of longer horizons. The results suggest that further research on fuzzy inference systems hybrid approaches for forecasting should emphasize short-term forecasting by trying to better capture the “tribal” managerial knowledge instead of focusing on less dispersed and slower moving products, where the purely qualitative forecasting methods used by managers tend to perform better in terms of their accuracy.

scholarly journals Artificial Hydrocarbon Networks Fuzzy Inference System

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Hiram Ponce ◽  
Pedro Ponce ◽  
Arturo Molina
Keyword(s):  
Fuzzy Inference ◽  
Fuzzy Inference Systems ◽  
Inference Model ◽  
Inference System ◽  
Position Controller ◽  
Inference Systems ◽  
Linguistic Units ◽  
Output Space

This paper presents a novel fuzzy inference model based on artificial hydrocarbon networks, a computational algorithm for modeling problems based on chemical hydrocarbon compounds. In particular, the proposed fuzzy-molecular inference model (FIM-model) uses molecular units of information to partition the output space in the defuzzification step. Moreover, these molecules are linguistic units that can be partially understandable due to the organized structure of the topology and metadata parameters involved in artificial hydrocarbon networks. In addition, a position controller for a direct current (DC) motor was implemented using the proposed FIM-model in type-1 and type-2 fuzzy inference systems. Experimental results demonstrate that the fuzzy-molecular inference model can be applied as an alternative of type-2 Mamdani’s fuzzy control systems because the set of molecular units can deal with dynamic uncertainties mostly present in real-world control applications.

Evaluate Fabric Wrinkle Grade Based on Subtractive Clustering Adaptive Network Fuzzy Inference Systems

2011 ◽  
Vol 332-334 ◽  
pp. 1505-1510
Author(s):  
Xiao Bo Yang
Keyword(s):  
Network Inference ◽  
Clustering Algorithm ◽  
Fuzzy Inference ◽  
Real Data ◽  
Subtractive Clustering ◽  
Fuzzy Inference Systems ◽  
Adaptive Network ◽  
Inference System ◽  
Fuzzy Neural ◽  
Inference Systems

In this paper, a new method of subtractive clustering adaptive network fuzzy inference systems is proposed to assess degree of wrinkle in the fabric. The clustering center can be gotten through subtractive clustering algorithm, which is the base to set up adaptive network inference systems. Firstly, subtractive clustering algorithm is used to confirm the structure of fuzzy neural network, then, fuzzy inference system is used to process pattern recognition. Finally, four kinds of fabric wrinkle feature parameters are used to verify the results on real fabric. The results show the applicability of the proposed method to real data.

SCALABLE ARCHITECTURE FOR HIGH-SPEED MULTIDIMENSIONAL FUZZY INFERENCE SYSTEMS

2011 ◽  
Vol 20 (03) ◽  
pp. 375-400 ◽  
Author(s):  
INÉS DEL CAMPO ◽  
JAVIER ECHANOBE ◽  
KOLDO BASTERRETXEA ◽  
GUILLERMO BOSQUE
Keyword(s):  
High Speed ◽  
High Performance ◽  
Fuzzy Inference ◽  
Reconfigurable Hardware ◽  
Rule Base ◽  
Fuzzy Inference Systems ◽  
Scalable Architecture ◽  
Inference Model ◽  
Inference System ◽  
Inference Systems

This paper presents a scalable architecture suitable for the implementation of high-speed fuzzy inference systems on reconfigurable hardware. The main features of the proposed architecture, based on the Takagi–Sugeno inference model, are scalability, high performance, and flexibility. A scalable fuzzy inference system (FIS) must be efficient and practical when applied to complex situations, such as multidimensional problems with a large number of membership functions and a large rule base. Several current application areas of fuzzy computation require such enhanced capabilities to deal with real-time problems (e.g., robotics, automotive control, etc.). Scalability and high performance of the proposed solution have been achieved by exploiting the inherent parallelism of the inference model, while flexibility has been obtained by applying hardware/software codesign techniques to reconfigurable hardware. Last generation reconfigurable technologies, particularly field programmable gate arrays (FPGAs), make it possible to implement the whole embedded FIS (e.g., processor core, memory blocks, peripherals, and specific hardware for fuzzy inference) on a single chip with the consequent savings in size, cost, and power consumption. As a prototyping example, we implemented a complex fuzzy controller for a vehicle semi-active suspension system composed of four three-input FIS on a single FPGA of the Xilinx's Virtex 5 device family.

scholarly journals Identification of ERD using Fuzzy Inference Systems for Brain-Computer Interface

2011 ◽  
Vol 6 (3) ◽  
pp. 403 ◽  
Author(s):  
Ioan Dzitac ◽  
Tiberiu Vesselényi ◽  
Radu Cătălin Ţarcă
Keyword(s):  
Fuzzy Inference ◽  
Brain Activity ◽  
Brain Computer Interface ◽  
Computer Interface ◽  
Eeg Signals ◽  
Inference System ◽  
Eeg Data ◽  
Recent Developments ◽  
Potential Activity ◽  
Inference Systems

A Brain-Computer Interface uses measurements of scalp electric potential (electroencephalography - EEG) reflecting brain activity, to communicate with external devices. Recent developments in electronics and computer sciences have enabled applications that may help users with disabilities and also to develop new types of Human Machine Interfaces. By producing modifications in their brain potential activity, the users can perform control of different devices. In order to perform actions, this EEG signals must be processed with proper algorithms. Our approach is based on a fuzzy inference system used to produce sharp control states from noisy EEG data.

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