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Introduction
Published in Abhijit Pandit, Mathematical Modeling using Fuzzy Logic, 2021
A membership function is substantially a curve that defines how each point in the input space is mapped to a membership value (or stratum of membership) between 0 and 1. As an example, consider height as a fuzzy set. Let the universe of discourse be heights from 40 to 90 inches. In a crisp set, all people with a height of 72 inches or more are considered tall, and all people with a height of <72 inches are considered not tall. The curve defines the transition from not tall and shows the stratum of membership for a given height. We can proffer this concept to multiple sets. If we consider a universal set from 40 to 90 inches, then we can use three term values to describe height, namely, short, average, and tall. In practice, the terms short, average, and tall are not used in a strict sense. Instead, they imply a smooth transition.
Fuzzy Linear Programming
Published in Anindya Ghosh, Prithwiraj Mal, Abhijit Majumdar, Advanced Optimization and Decision-Making Techniques in Textile Manufacturing, 2019
Anindya Ghosh, Prithwiraj Mal, Abhijit Majumdar
The LP problem method is unarguably the most simple and commonly used classical optimization technique that has been used to solve many engineering optimization problems when both the objective and constraints functions are linear. However, most of the practical problems in engineering manufacturing are linguistic in nature; hence, they are not specified in precise or crisp terms. Such problems are dealt with in the FLP method. In this chapter, the fundamentals of crisp sets and fuzzy sets are explained. The membership function is defined, which is associated with the fuzzy set. Different fuzzy operations are explained. Then the FLP problem-solving algorithm is demonstrated step by step. Two examples of the FLP problem are cited and discussed step by step. MATLAB® coding for these examples is given. Last, the applications of FLP in the textile industry are highlighted.
Genetic Design of Fuzzy Controllers
Published in Sankar K. Pal, Paul P. Wang, Genetic Algorithms for Pattern Recognition, 2017
Cooper Mark G., Vidal Jacques J.
One of the earliest applications of genetic algorithms to the design of fuzzy systems was developed by Karr [3], again to solve the cart-pole problem. The production of the fuzzy controller begins with the definition of the fuzzy sets used to describe each input variable. Each of the four input variables are characterized by three fuzzy sets—NEGATIVE, ZERO, and POSITIVE — yielding 81 possible combinations. The fuzzy system designer then assigns one of seven choices for the output to each input combination. The resulting fuzzy system represents the expert’s “best guess”. The membership function extrema are then encoded into a bit string, and a genetic algorithm is applied to shift the membership functions so as to find locations which improve performance. The evolved system consistently outperforms the original, being capable of recovering from initial positions that fail under the original rule base.
A fuzzy rule-based system for terrain classification in highway design
Published in Transportation Planning and Technology, 2023
Erick Fiorote Leite da Silva, Gabriel Lanzaro, Michelle Andrade
This study has several limitations. The classifier considers two variables only, and the inclusion of additional variables (e.g. numbers of valleys and peaks, the quantity of rivers, drainage basin characteristics) should be investigated in future studies. Also, this study considered three output categories because it was developed for Brazilian highways, where three terrain scenarios are considered. Other locations (e.g. India, Spain, Nepal) use four categories, and the classifier can be expanded to account for these conditions. Additionally, current Brazilian design practice contains only three terrain categories, but this number of categories might be revisited in the future to reflect more accurately local conditions and potentially improve highway design overall. More specifically, additional categories, including an intermediate category between level and rolling, can be proposed. Furthermore, the study considered Gaussian membership functions, and different functional forms can be implemented. In addition, genetic algorithms can be applied to optimize the membership function parameters and the rules, which can improve the classifier’s performance.
GIS-based assessment of pedestrian-vehicle accidents in terms of safety with four different ML models
Published in Journal of Transportation Safety & Security, 2022
Burak Yiğit Katanalp, Ezgi Eren
With the 68.57% accuracy, overall performance of the innovative RFDM outperforms other ML models used in this study. On the other hand, CFDM performed second-best among the models used in this study. Based on this, it is possible to say that innovative hybrid FL models, which significantly reduce "expert judgment," were more successful than traditional ML models in the evaluation of pedestrian-vehicle crashes. However there are still some concerns about the performance of the CFDM. For example, to improve pedestrian safety on urban roads, it is especially important to accurately identify locations with high crash counts. CFDM performed worse than other models in the classification of locations with high crash counts. However, worse performance in the classification of locations with high crash counts can compromise the overall performance of the CFDM. To deal with this, techniques such as particle swarm optimization, bee colony optimization, and genetic algorithm can be applied to optimize the membership function ranges in the hybrid CFDM as suggested in previous works (Kaya & Alhajj, 2006; Nikolić, Šelmić, Macura, & Ćalić, 2020; Precup, Sabau, & Petriu, 2015).
A comprehensive stability evaluation method of multiple salt caverns underground gas storage with interlayers
Published in Petroleum Science and Technology, 2022
Jinghong Peng, Jun Zhou, Guangchuan Liang, Cao Peng, Shijie Fang
The fuzzy membership function method is to use the membership function to perform a fuzzy comprehensive evaluation on the index (Zhang et al. 2009). Membership function is a mathematical tool used to characterize fuzzy sets. The membership function of the element will be a value between 0 and 1, which indicates the "true degree" of the element belonging to a fuzzy set. The steps of the fuzzy membership function method are as follows: Determine the index lower limit a and upper limit b. For the reverse index, the optimal value is the lower limit a; for the positive index, the optimal value is the upper limit b.Determine the index membership function. This paper chooses to use the assignment method to determine the membership function of each index. The general form of the membership function is shown in Eq. (14). Calculate the index score. In order to facilitate mathematical calculation and analysis, the index membership function value is usually multiplied by 100 to get the index score, it can be calculated by Eq. (15).