Choice Of Membership Functions Research Articles

Prediction Analysis of Surface Roughness of Aluminum Al6061 in End Milling CNC Machine Using Soft Computing Techniques

Computer numerically controlled (CNC) milling has been one of the most commonly used manufacturing processes for the performance of multiple operations, from tiny integrated circuits to heavy-duty mining machine gearboxes. It is a well-known machining process that offers close tolerances and repeated operations. However, the choice of machining parameters to achieve a desired part’s surface roughness (SR) remains a challenge. In the present study, artificial neural network (ANN) and adaptive network-based fuzzy inference system (ANFIS) approaches have been used to predict and monitor the surface roughness of aluminum Al6061 machined blocks. Furthermore, both models have been hybridized with genetic algorithm (GA) and particle swarm optimization (PSO) to investigate the potential enhancement in the prediction performance of the hybrid approach. The results show that factors such as the population size, the acceleration values, the choice of membership functions, and the number of neurons and layers significantly influence the prediction performance of the proposed models. Through a parametric analysis, this study demonstrates how the configuration of the models could affect the prediction performance. While exhibiting the impact of models’ hyperparameter combination on the prediction ability, this study provides insight into the development of suitable prediction models and the potential of soft computing techniques to predict the surface roughness of aluminum Al6061 blocks on CNC machines.

MODELING OF INTELLECTUAL CONTROL SYSTEMS WITH APPLICATION OF MODIFIED FUZZY COLORED PETRI NETS

A modification of the Petri nets is proposed  a Fuzzy Colored Petri Net (FCPN), leading to the integration of Fuzzy Petri Nets (FPN) and Colored Petri Nets (CPN). Separately, the shortcomings of FPN and CPN and the advantages the developed FCPN for modeling intelligent control systems are identified and justified. In the developed modified FCPN the membership functions of the terms of a linguistic variable are applied to markers of the CPN as color and fuzzy existence conditions are assigned to arcs depending on the values of the linguistic variable. As a result, FCPN with enhanced capabilities was obtained, which eliminates the shortcomings of CPN and FPN. The FCPN and a simulation approach are defined, which includes a reasoning algorithm, as well as a detailed procedure for modeling and analysis of nonlinear discrete objects. The structure is organized in the CPN Tools system with the synchronization of the CPN ML (Markup Language) language with the MatLab package. The choice of membership function and fuzzification of term values is performed in the Fuzzy Toolbox application of the MatLab system. The proposed approach is illustrated by simple example, including the control of water pumps, to maintain the required water level in the pumping well. A model is developed for the automation of adaptive fuzzy control of water pumps based on modified FCPN. Based on the criteria for the operation of water pumps according to the water levels in the pumping well, many positions and transitions of the FCPN are formed. Describing the necessary behavior of the system by the relations between the positions and transitions of the FCPN using the logic “If ... Then ...” an adaptation algorithm is developed. Based on the algorithm, the matrices of input and output incidents are determined. The graph model of the FCPN is developed. Visualization of the model is implemented in the CPN Tools system. The computer simulations and net analysis experiments demonstrate the convenience of the developed approach when modeling the intelligent control of dynamic systems.

Model Based Predictive Control of Multivariable Hammerstein Processes with Fuzzy Logic Hypercube Interpolated Models.

This paper introduces the Fuzzy Logic Hypercube Interpolator (FLHI) and demonstrates applications in control of multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) processes with Hammerstein nonlinearities. FLHI consists of a Takagi-Sugeno fuzzy inference system where membership functions act as kernel functions of an interpolator. Conjunction of membership functions in an unitary hypercube space enables multivariable interpolation of N-dimensions. Membership functions act as interpolation kernels, such that choice of membership functions determines interpolation characteristics, allowing FLHI to behave as a nearest-neighbor, linear, cubic, spline or Lanczos interpolator, to name a few. The proposed interpolator is presented as a solution to the modeling problem of static nonlinearities since it is capable of modeling both a function and its inverse function. Three study cases from literature are presented, a single-input single-output (SISO) system, a MISO and a MIMO system. Good results are obtained regarding performance metrics such as set-point tracking, control variation and robustness. Results demonstrate applicability of the proposed method in modeling Hammerstein nonlinearities and their inverse functions for implementation of an output compensator with Model Based Predictive Control (MBPC), in particular Dynamic Matrix Control (DMC).

Unidimensional and multidimensional fuzzy poverty measures: New approach

the analysis of deprivation is usually seen as a unidimensional condition. However, recently it is considered to be a multidimensional one. A useful tool for such analysis is to view deprivation as a degree providing a quantitative expression to its intensity for individuals. Such fuzzy conceptualisation has been widely adopted in poverty and deprivation research. This paper aims to further develop and refine this strand of research. First, we re-examine two aspects introduced by the use of fuzzy measures, as opposed to conventional poor/non-poor dichotomous measures, namely the choice of membership functions and the rules to manipulate, resulting fuzzy sets. Secondly, we propose fuzzy monetary and non-monetary measures with the membership functions of poor and non-poor. An application based on individual well-being data from Tunisian households in 1990 is presented to illustrate use of one of the proposed concept.

A MEASURE OF AVERAGE SENSITIVITY FOR FUZZY LOGICS

Experts usually express their uncertainty by words of natural languages (like "perhaps", "for sure", etc). In the majority of expert systems and intelligent control systems, uncertainty of experts' statements is represented by a number from the interval [0, 1]. There are many different procedures that translate the words that experts use into numbers from [0, 1]. For one and the same word, different procedures can lead to different numbers. Some &– and ∨–operations are very sensitive to this difference in the sense that small changes in t(A) and t(B) can lead to absolutely different estimates for t(A&B) and t(A ∨ B). In view of that, it is reasonable to restrict ourselves to the operations that are the least sensitive to such changes. In this paper, we prove that ab and a + b − ab are "in the average" the least sensitive &– and ∨–operations. This result is in good accordance with the experimental data according to which in. many cases, these operations provide the best description of how experts actually think. We also show how this idea can be applied to other logical connectives (e.g., "not"), and to the choice of membership functions.

A land evaluation project in Greece using GIS and based on Boolean and fuzzy set methodologies

Abstract In Mediterranean regions there is little experience in using GIS as an aid to land evaluation. This paper reports a project in Greece which investigated the usefulness of such technology, Particular emphasis was also given to comparing the results of land evaluation using Boolean and fuzzy set methodologies. The need was to produce the results as quickly and efficiently as possible to aid agricultural planning. By using a GIS, a series of single factor and land evaluation maps was produced for a range of crops; a land suitability map for receipt of sewage was also derived. A comparison of results from using Boolean and fuzzy set methodologies highlighted the advantages of the latter, although critical decisions are required on choice of membership functions and weights which have a major effect on the results.