Optimization of Gaussian fuzzy membership functions and evaluation of the monotonicity property of Fuzzy Inference Systems

2011 ◽  
Author(s):  
Kai Meng Tay ◽  
Chee Peng Lim
Keyword(s):  
Fuzzy Inference ◽  
Monotonicity Property ◽  
Fuzzy Membership ◽  
Membership Functions ◽  
Fuzzy Inference Systems ◽  
Fuzzy Membership Functions ◽  
Inference Systems

Air Quality Modeling by Fuzzy Sets and IF-Sets

2011 ◽  
pp. 118-143 ◽  
Author(s):  
Vladimír Olej ◽  
Petr Hájek
Keyword(s):  
Air Quality ◽  
Fuzzy Sets ◽  
Fuzzy Inference ◽  
Air Quality Modeling ◽  
Membership Functions ◽  
Fuzzy Inference Systems ◽  
Feature Maps ◽  
Quality Classification ◽  
Quality Modeling ◽  
Inference Systems

The chapter presents a design of parameters for air quality classification of districts into classes according to their pollution. Therefore, the chapter presents basic notions of fuzzy sets introduced by L. A. Zadeh for design hierarchical fuzzy inference systems Mamdani type and IF-sets introduced by K. T. Atanassov for design of hierarchical IF-inference systems Mamdani type. In the next part of the chapter the authors describe air quality modeling by hierarchical fuzzy inference systems, hierarchical IF-inference systems and we analyze the results. Moreover, the chapter describes air quality modeling, the design of membership functions and non-membership functions, if-then rules of individual subsystems and inference mechanism. Further, the authors present basic notions of IF-relations and their determination by Kohonen’s Self-organizing Feature Maps and K-means algorithms and process air quality classification.

scholarly journals Study of Hybrid Neurofuzzy Inference System for Forecasting Flood Event Vulnerability in Indonesia

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Sri Supatmi ◽  
Rongtao Hou ◽  
Irfan Dwiguna Sumitra
Keyword(s):  
Fuzzy Inference ◽  
Flood Event ◽  
Membership Functions ◽  
Fuzzy Inference Systems ◽  
Flood Vulnerability ◽  
Inference System ◽  
Forecasting Accuracy ◽  
Proposed Model ◽  
Inference Systems ◽  
Takagi Sugeno

An experimental investigation was conducted to explore the fundamental difference among the Mamdani fuzzy inference system (FIS), Takagi–Sugeno FIS, and the proposed flood forecasting model, known as hybrid neurofuzzy inference system (HN-FIS). The study aims finding which approach gives the best performance for forecasting flood vulnerability. Due to the importance of forecasting flood event vulnerability, the Mamdani FIS, Sugeno FIS, and proposed models are compared using trapezoidal-type membership functions (MFs). The fuzzy inference systems and proposed model were used to predict the data time series from 2008 to 2012 for 31 subdistricts in Bandung, West Java Province, Indonesia. Our research results showed that the proposed model has a flood vulnerability forecasting accuracy of more than 96% with the lowest errors compared to the existing models.

GENERALIZING T-CONORMS TO FACE SATURATION IN MAMDANI FUZZY INFERENCE SYSTEMS

2007 ◽  
Vol 15 (01) ◽  
pp. 57-73
Author(s):  
MARIO ARRIGONI NERI ◽  
ALESSANDRA CHERUBINI
Keyword(s):  
Fuzzy Inference ◽  
Fuzzy Reasoning ◽  
Monotonicity Property ◽  
Aggregation Function ◽  
Fuzzy Inference Systems ◽  
Possibility Distribution ◽  
Rational Agents ◽  
Fuzzy Aggregation ◽  
Definition Of ◽  
Inference Systems

Fuzzy aggregation is the way in which different contributions to the same fuzzy fact are merged together to obtain a possibility distribution representative of the acquired knowledge. The choice of the aggregation function is a fundamental step in the definition of inference framework. In most cases aggregation has some monotonicity property and this can lead to saturation problems in complex frameworks, particularly in stateful rational agents. In this paper, we propose an extension to the fuzzy aggregation to handle these cases and apply fuzzy reasoning to complex KBs. We especially focus on Mamdani inference framework, where aggregation is implemented by a triangular conorm.

scholarly journals Properties of interval type-2 fuzzy sets in decision support systems

2021 ◽  
pp. 75-81
Author(s):  
Alexander Zakovorotniy ◽  
Artem Kharchenko
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Inference ◽  
Systems Design ◽  
Membership Functions ◽  
Fuzzy Inference Systems ◽  
Footprint Of Uncertainty ◽  
Expert Assessments ◽  
Interval Type ◽  
Inference Systems

Definitions and methods of designing interval type-2 fuzzy sets in fuzzy inference systems for control problems of complex technical objects in conditions of uncertainty are considered. The main types of uncertainties, that arise when designing fuzzy inference systems and depend on the number of expert assessments, are described. Methods for assessing intra-uncertainty and inter-uncertainty are proposed, taking into account the different number of expert assessments at the stage of determining the types and number of membership functions. Factors influencing the parameters and properties of interval type-2 fuzzy during experimental studies are determined. Such factors include the number of experiments performed, external factors, technical parameters of the control object, and the reliability of the components of the computer system decision support system. The properties of the lower and upper membership functions of interval type-2 fuzzy sets are investigated on the example of the Gaussian membership function, which is one of the most used in the problems of fuzzy inference systems design. The main features and differences in the methods of determining the lower and upper membership functions of interval type-2 fuzzy sets for different types of uncertainties are taken into account. Methods for determining the footprint of uncertainty, as well as the dependence of its size on the number of expert assessments, are considered. The footprint of uncertainty is characterized by the lower and upper membership functions, and its size directly affects the accuracy of the obtained solutions. Methods for determining interval type-2 fuzzy sets using regulation factors of membership function parameters for intra-uncertainty and weighting factors of membership functions for inter-uncertainties have been developed. The regulation factor of the function parameters can be used to describe the lower and upper membership functions while determining the size of the footprint of uncertainty. Complex interval type-2 sets are determined to take into account inter-uncertainties in the problems of fuzzy inference systems design.

scholarly journals On the Monotonicity of Fuzzy Inference Models

2012 ◽  
Vol 16 (5) ◽  
pp. 592-602 ◽  
Author(s):  
Hirosato Seki ◽  
◽  
Kai Meng Tay ◽  
Keyword(s):  
Fuzzy Inference ◽  
Monotonicity Property ◽  
Fuzzy Inference Systems ◽  
Inference Model ◽  
Inference System ◽  
Inference Models ◽  
Input Type ◽  
Single Input ◽  
Monotonicity Conditions ◽  
Inference Systems

Monotonicity property is very important in real systems. The monotonicity may need to be satisfied in a variety of application domains, e.g., control, medical diagnosis, educational evaluation, etc. A search in the literature reveals that the importance of the monotonicity in fuzzy inference system has been highlighted. Therefore, this paper surveys the works relating the monotonicity for various fuzzy inference systems. It firstly focuses on the monotonicity of the Mamdani inference model. Themonotonicity ofMamdani model is shown by using a defuzzification method in cases of three t-norms. Secondly, the monotonicity conditions and applications of the T–S inference model are stated. Finally, the monotonicity of the single input type fuzzy inference models is surveyed.

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