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.

scholarly journals A Generalized Fuzzy Integer Programming Approach for Environmental Management under Uncertainty

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Y. R. Fan ◽  
G. H. Huang ◽  
K. Huang ◽  
L. Jin ◽  
M. Q. Suo
Keyword(s):  
Integer Programming ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Mixed Integer ◽  
Programming Approach ◽  
Management Problem ◽  
Membership Functions ◽  
Interactive Algorithm ◽  
Waste Flow ◽  
The Membership Function

In this study, a generalized fuzzy integer programming (GFIP) method is developed for planning waste allocation and facility expansion under uncertainty. The developed method can (i) deal with uncertainties expressed as fuzzy sets with known membership functions regardless of the shapes (linear or nonlinear) of these membership functions, (ii) allow uncertainties to be directly communicated into the optimization process and the resulting solutions, and (iii) reflect dynamics in terms of waste-flow allocation and facility-capacity expansion. A stepwise interactive algorithm (SIA) is proposed to solve the GFIP problem and generate solutions expressed as fuzzy sets. The procedures of the SIA method include (i) discretizing the membership function grade of fuzzy parameters into a set ofα-cutlevels; (ii) converting the GFIP problem into an inexact mixed-integer linear programming (IMILP) problem under eachα-cut level; (iii) solving the IMILP problem through an interactive algorithm; and (iv) approximating the membership function for decision variables through statistical regression methods. The developed GFIP method is applied to a municipal solid waste (MSW) management problem to facilitate decision making on waste flow allocation and waste-treatment facilities expansion. The results, which are expressed as discrete or continuous fuzzy sets, can help identify desired alternatives for managing MSW under uncertainty.

scholarly journals OPERATOR ⊞A and ⊠A ON INTUITIONISTIC FUZZY RING

2020 ◽  
Vol 12 (1) ◽  
pp. 35
Author(s):  
Dian Pratama
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Ring Theory ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ring ◽  
The Membership Function

Intuitionistic fuzzy sets is a sets that are characterized by membership and non-membership function which  sum is less than one. When applied to ring theory, it will called intuitionistic fuzzy rings. The fuzzy set operator is a mapping between the membership function and the interval [0,1]. In this study, we will describe properties of operator  and  in intuitionistic fuzzy rings. The characteristics that will be studied include the structure of  and  if A is an intuitive and fuzzy ring and vice versa.

scholarly journals METHOD FOR OBTAINING THE PARAMETERS OF MEMBERSHIP FUNCTIONS OF FUZZY SETS BASED ON REAL DATA FOR AUTOMATED INFORMATION PROCESSING SYSTEMS

2019 ◽  
Vol 46 (3) ◽  
pp. 79-86
Author(s):  
E. E. Bisyanov ◽  
A. A. Gutnik
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Real Data ◽  
Linguistic Variables ◽  
Membership Functions ◽  
Automated Systems ◽  
Accessory Function ◽  
Different Types ◽  
Automated Processing ◽  
The Membership Function

Objectives Development of a method for selecting the type of accessory function and obtaining its parameters to allow subjective personal influences in automated information processing to be excluded.Method. Existing methods for constructing membership functions were analysed. The research was based on the methods of fuzzy logic and data analysis.Results. A method for obtaining the parameters of membership functions of fuzzy sets using real data is suggested. It is proposed to use the data obtained from the object under study to determine the kernel of the fuzzy number, as well as derive theoretical information about the object for the carrier. Triangular, trapezoidal, bell-shaped and Gaussian membership functions are considered. The appearance of the membership function can be defined using the criterion of the relations of the kernel to the carrier of a fuzzy set. The results of calculations for obtaining the membership functions based on data on the power consumption of electric motors of different types are given.Conclusion. The developed method can be used both in decision support systems as well as in automated systems for controlling technological processes. If necessary, the values of the criterion proposed in the article can be revised to take the values included in the set of measured real data into account or to simplify the procedure of automated processing. Further research will use the described method to obtain the terms of linguistic variables. 

The role of properties of the membership function in construction of fuzzy sets ranking

2021 ◽  
Vol 0 (11-12/2020) ◽  
pp. 5-12
Author(s):  
Andrzej Ameljańczyk
Keyword(s):  
Decision Making ◽  
Decision Support ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
The Membership Function

The paper presents a several new definitions of concepts regarding the properties of fuzzy sets in the aspect of their use in decision support processes. These are concepts such as the image and counter – image of the fuzzy set, the proper fuzzy set, the fuzzy support and the ranking of fuzzy set. These concepts can be important in construction decision support algorithms. Particularly a lot of space was devoted to the study of the properties of membership function of the fuzzy set as a result of operations on fuzzy sets. Two additional postulates were formulated that should be fulfilled by the membership function product of fuzzy sets in decision making.

scholarly journals Type-II Fuzzy Decision Support System for Fertilizer

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Ather Ashraf ◽  
Muhammad Akram ◽  
Mansoor Sarwar
Keyword(s):  
Decision Support ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Inference ◽  
Type I ◽  
Type Ii ◽  
Membership Functions ◽  
Fuzzy Decision ◽  
Fuzzy Decision Support System

Type-II fuzzy sets are used to convey the uncertainties in the membership function of type-I fuzzy sets. Linguistic information in expert rules does not give any information about the geometry of the membership functions. These membership functions are mostly constructed through numerical data or range of classes. But there exists an uncertainty about the shape of the membership, that is, whether to go for a triangle membership function or a trapezoidal membership function. In this paper we use a type-II fuzzy set to overcome this uncertainty, and develop a fuzzy decision support system of fertilizers based on a type-II fuzzy set. This type-II fuzzy system takes cropping time and soil nutrients in the form of spatial surfaces as input, fuzzifies it using a type-II fuzzy membership function, and implies fuzzy rules on it in the fuzzy inference engine. The output of the fuzzy inference engine, which is in the form of interval value type-II fuzzy sets, reduced to an interval type-I fuzzy set, defuzzifies it to a crisp value and generates a spatial surface of fertilizers. This spatial surface shows the spatial trend of the required amount of fertilizer needed to cultivate a specific crop. The complexity of our algorithm isO(mnr), wheremis the height of the raster,nis the width of the raster, andris the number of expert rules.

Logistics Demand Forecasting with Asymmetry-Width Probabilistic Fuzzy Logic System

2013 ◽  
Vol 706-708 ◽  
pp. 2012-2016
Author(s):  
Zhong Wei Wang ◽  
Li Xin Lu
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Demand Forecasting ◽  
Fuzzy Logic System ◽  
The Asymmetry ◽  
Logistics Demand ◽  
Better Than ◽  
Logic System

There are a lot of approaches in logistics demand forecasting field and perform different characters. The probabilistic fuzzy set (PFS) and probabilistic fuzzy logic system is designed for handling the uncertainties in both stochastic and nonstochastic nature. In this paper, an asymmetric probabilistic fuzzy set is proposed by randomly varying the width of asymmetric Gaussian membership function. And the related PFLS is constructed to be applied to a logistics demand forecasting. The performance discloses that the asymmetry-width probabilistic fuzzy set performs better than precious symmetric one. It is because the asymmetric probabilistic fuzzy sets variability and malleability is higher than this of the symmetric probabilistic fuzzy set.

scholarly journals Learning Membership Functions in a Function-Based Object Recognition System

1995 ◽  
Vol 3 ◽  
pp. 187-222 ◽  
Author(s):  
K. Woods ◽  
D. Cook ◽  
L. Hall ◽  
K. Bowyer ◽  
L. Stark
Keyword(s):  
Object Recognition ◽  
Membership Function ◽  
Learning Algorithm ◽  
Physical Property ◽  
Recognition System ◽  
Tree Structure ◽  
Membership Functions ◽  
Recognition Systems ◽  
Membership Value ◽  
The Membership Function

Functionality-based recognition systems recognize objects at the category level by reasoning about how well the objects support the expected function. Such systems naturally associate a ``measure of goodness'' or ``membership value'' with a recognized object. This measure of goodness is the result of combining individual measures, or membership values, from potentially many primitive evaluations of different properties of the object's shape. A membership function is used to compute the membership value when evaluating a primitive of a particular physical property of an object. In previous versions of a recognition system known as Gruff, the membership function for each of the primitive evaluations was hand-crafted by the system designer. In this paper, we provide a learning component for the Gruff system, called Omlet, that automatically learns membership functions given a set of example objects labeled with their desired category measure. The learning algorithm is generally applicable to any problem in which low-level membership values are combined through an and-or tree structure to give a final overall membership value.

scholarly journals Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 1

2021 ◽  
Vol 27 (1) ◽  
pp. 53-59
Author(s):  
Mladen V. Vassilev-Missana
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Sets Theory ◽  
Membership Functions ◽  
Real Numbers ◽  
Intuitionistic Fuzzy ◽  
Sets Theory

The inequality \mu^{\frac{1}{\nu}} + \nu^{\frac{1}{\mu}} \leq 1 is introduced and proved, where \mu and \nu are real numbers, for which \mu, \nu \in [0, 1] and \mu + \nu \leq 1. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E. Also, a generalization of the above inequality for arbitrary n \geq 2 is proposed and proved.

Complex bipolar fuzzy sets: An application in a transport’s company

2020 ◽  
pp. 1-17
Author(s):  
Muhammad Gulistan ◽  
Naveed Yaqoob ◽  
Ahmed Elmoasry ◽  
Jawdat Alebraheem
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Cartesian Product ◽  
Real Numbers ◽  
Wide Range ◽  
Fuzzy Aggregation ◽  
Bipolar Fuzzy Sets ◽  
Range Of Values

Zadeh’s fuzzy sets are very useful tool to handle imprecision and uncertainty, but they are unable to characterize the negative characteristics in a certain problem. This problem was solved by Zhang et al. as they introduced the concept of bipolar fuzzy sets. Thus, fuzzy set generalizes the classical set and bipolar fuzzy set generalize the fuzzy set. These theories are based on the set of real numbers. On the other hand, the set of complex numbers is the generalization of the set of real numbers so, complex fuzzy sets generalize the fuzzy sets, with wide range of values to handle the imprecision and uncertainty. So, in this article, we study complex bipolar fuzzy sets which is the generalization of bipolar fuzzy set and complex fuzzy set with wide range of values by adding positive membership function and negative membership function to unit circle in the complex plane, where one can handle vagueness in a much better way as compared to bipolar fuzzy sets. Thus this paper leads us towards a new direction of research, which has many applications in different directions. We develop the notions of union, intersection, complement, Cartesian product and De-Morgan’s Laws of complex bipolar fuzzy sets. Furthermore, we develop the complex bipolar fuzzy relations, fundamental operations on complex bipolar fuzzy matrices and some operators of complex bipolar fuzzy matrices. We also discuss the distance measure on complex bipolar fuzzy sets and complex bipolar fuzzy aggregation operators. Finally, we apply the developed approach to a numerical problem with the algorithm.

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