scholarly journals Uncertainty quantification through a model-based fuzzy set membership function

2018 ◽  
Keyword(s):  
Uncertainty Quantification ◽  
Membership Function ◽  
Fuzzy Set ◽  
Model Based ◽  
Set Membership

Research on Extension of the Fuzzy Rough Set Theory

2012 ◽  
Vol 532-533 ◽  
pp. 1472-1476
Author(s):  
Yu Zhang
Keyword(s):  
Set Theory ◽  
Membership Function ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Incomplete Data ◽  
Rough Set Theory ◽  
Fuzzy Rough Set ◽  
Set Membership ◽  
Lower Maximum

With the probability rules and the degree of coverage of elements in the partition set, and the combination of the Fuzzy Set Theory and Rough Set Theory, a new extension of Fuzzy Rough Set theory was proposed. It is defined the maximum of Rough Set membership function, the minimum of Rough Set membership function, the average of Rough Set membership function, the upper minimum of Rough Set membership function and the lower maximum of Rough Set membership function. The properties of the extension for the Rough Set membership functions are also given. This made Fuzzy Set Theory and Rough Set Theory complemented each other and provided a new way to deal with incomplete data.

scholarly journals Reliability Analysis of Loess Cave Dwellings Based on Fuzzy Failure Criterion

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Pinggong Guo
Keyword(s):  
Membership Function ◽  
Fuzzy Set ◽  
Failure Criterion ◽  
Reduction Method ◽  
Random Variable ◽  
Strength Reduction ◽  
Strength Reduction Method ◽  
Performance Function ◽  
Average Value ◽  
Set Membership

The reliability of loess cave dwellings based on fuzzy failure criterion is researched to analyze the influence of fuzzy set, membership function, and different combinations of random variables. Due to the strength reduction method, the basic failure criterion is established, the fuzzy property of failure criterion is characterized by fuzzy set and membership function, and the performance function of loess cave dwellings is expressed by a quadratic polynomial without cross terms. Reliability is analyzed with different random variable combinations. The reliability research of loess cave dwellings in Shan Plateau, Henan province, China, shows that the loess property in this area is suitable for loess cave dwelling construction and the reliability index of loess cave dwellings is high, which will be decreased when considering the fuzzy failure criterion and will be increasing sharply when the small cave leg width is improved to average value.

scholarly journals Approximation of real data by fuzzy sets for the classification problem

2019 ◽  
pp. 22-26
Author(s):  
Kostiantyn Sukhanov
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Real Data ◽  
Training Data ◽  
Learning Object ◽  
Membership Functions ◽  
One Dimensional ◽  
Set Membership ◽  
The Membership Function

The article deals with the method of classification of real data using the apparatus of fuzzy sets and fuzzy logic as a flexible tool for learning and recognition of natural objects on the example of oil and gas prospecting sections of the Dnieper-Donetsk basin. The real data in this approach are the values for the membership function that are obtained not through subjective expert judgment but from objective measurements. It is suggested to approximate the fuzzy set membership functions by using training data to use the approximation results obtained during the learning phase at the stage of identifying unknown objects. In the first step of learning, each traditional future of a learning data is matched by a primary traditional one-dimensional set whose membership function can only take values from a binary set — 0 if the learning object does not belong to the set, and 1 if the learning object belongs to the set. In the second step, the primary set is mapped to a fuzzy set, and the parameters of the membership function of this fuzzy set are determined by approximating this function of the traditional set membership. In the third step, the set of one-dimensional fuzzy sets that correspond to a single feature of the object is mapped to a fuzzy set that corresponds to all the features of the object in the training data set. Such a set is the intersection of fuzzy sets of individual features, to which the blurring and concentration operations of fuzzy set theory are applied in the last step. Thus, the function of belonging to a fuzzy set of a class is the operation of choosing a minimum value from the functions of fuzzy sets of individual features of objects, which are reduced to a certain degree corresponding to the operation of blurring or concentration. The task of assigning the object under study to a particular class is to compare the values of the membership functions of a multidimensional fuzzy set and to select the class in which the membership function takes the highest value. Additionally, after the training stage, it is possible to determine the degree of significance of an object future, which is an indistinctness index, to remove non-essential data (object futures) from the analysis.

Representing a probabilistic linguistic term set with an interval type-2 fuzzy set and the application in green supplier selection

2021 ◽  
pp. 1-18
Author(s):  
Le Jiang ◽  
Hongbin Liu
Keyword(s):  
Decision Making ◽  
Membership Function ◽  
Fuzzy Set ◽  
Supplier Selection ◽  
Symbolic Model ◽  
Green Supplier Selection ◽  
Linguistic Term ◽  
Interval Type ◽  
Decision Making Model

The use of probabilistic linguistic term sets (PLTSs) means the process of computing with words. The existing methods computing with PLTSs mainly use symbolic model. To provide a semantic model for computing with PLTSs, we propose to represent a PLTS by using an interval type-2 fuzzy set (IT2FS). The key step is to compute the footprint of uncertainty of the IT2FS. To this aim, the upper membership function is computed by aggregating the membership functions of the linguistic terms contained in the PLTS, and the lower membership function is obtained by moving the upper membership function downward with the step being total entropy of the PLTS. The comparison rules, some operations, and an aggregation operator for PLTSs are introduced. Based on the proposed method of computing with PLTSs, a multi-criteria group decision making model is introduced. The proposed decision making model is then applied in green supplier selection problem to show its feasibility.

Set-membership methodology for model-based prognosis

2017 ◽  
Vol 66 ◽  
pp. 216-225 ◽  
Author(s):  
Basma Yousfi ◽  
Tarek Raïssi ◽  
Messaoud Amairi ◽  
Mohamed Aoun
Keyword(s):  
Model Based ◽  
Set Membership
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