scholarly journals Construction of the membership function of normal fuzzy numbers

2013 ◽  
Vol 1 (2) ◽  
pp. 82-86 ◽  
Author(s):  
Anamika Dutta ◽  
Dhruba Das ◽  
Hemanta Baruah
Keyword(s):  
Membership Function ◽  
Fuzzy Numbers ◽  
The Membership Function

scholarly journals A study on product-sum of triangular fuzzy numbers

2021 ◽  
Vol 5 (2) ◽  
pp. 63-67
Author(s):  
Mohamed Ali A ◽  
Rajkumar N
Keyword(s):  
Membership Function ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Triangular Form ◽  
Finite Sum ◽  
The Membership Function

We  study  the  problem:   if  a˜i,   i  ∈  N   are  fuzzy  numbers  of  triangular  form,  then  what is the membership function of the infinite (or finite) sum -˜a1   +  a˜2   +  · · ·   (defined  via  the sub-product-norm convolution)

The Weighted Fuzzy Barycenter

2013 ◽  
Vol 4 (4) ◽  
pp. 48-67 ◽  
Author(s):  
Julio Rojas-Mora ◽  
Didier Josselin ◽  
Jagannath Aryal ◽  
Adrien Mangiavillano ◽  
Philippe Ellerkamp
Keyword(s):  
Membership Function ◽  
Forest Fire ◽  
Visual Inspection ◽  
Fuzzy Numbers ◽  
Fire Intensity ◽  
Spatial Clusters ◽  
Data Set ◽  
Weighting Schemes ◽  
Fuzzy Solution ◽  
The Membership Function

In this paper, the authors present a methodology to solve the weighted barycenter problem when the data is inherently fuzzy. This method, from data clustered by expert visual inspection of maps, calculates bi-dimensional fuzzy numbers from the spatial clusters, which in turn are used to obtain the weighted fuzzy barycenter of a particular area. The authors apply the methodology, to a particularly apt data set of forest fire breakouts in the PACA region of southeastern France, gathered from 1986 to 2008, and sliced into five periods over which the fuzzy weighted barycenter for each one is obtained. Two weighting schemes based on fire intensity and fire density in a cluster were used. The center provided with this fuzzy method provides leeway to planners, which can see how the membership function of the fuzzy solution can be used as a measurement of “appropriateness” of the final location.

A METHOD FOR FINDING CRITICAL PATH WITH SYMMETRIC OCTAGONAL INTUITIONISTIC FUZZY NUMBERS

2020 ◽  
Vol 9 (11) ◽  
pp. 9273-9286
Author(s):  
N. Rameshan ◽  
D.S. Dinagar
Keyword(s):  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Membership Functions ◽  
Intuitionistic Fuzzy Number ◽  
Lower And Upper Bounds ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Membership Function

The concept of this paper represents finding fuzzy critical path using octagonal fuzzy number. In project scheduling, a new method has been approached to identify the critical path by using Symmetric Octagonal Intuitionistic Fuzzy Number (SYMOCINTFN). For getting a better solution, we use the fuzzy octagonal number rather than other fuzzy numbers. The membership functions of the earliest and latest times of events are by calculating lower and upper bounds of the earliest and latest times considering octagonal fuzzy duration. The resulting conditions omit the negative and infeasible solution. The membership function takes up an essential role in finding a new solution. Based on membership function, fuzzy number can be identified in different categories such as Triangular, Trapezoidal, pentagonal, hexagonal, octagonal, decagonal, hexa decagonal fuzzy numbers etc.

Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators

2020 ◽  
Vol 39 (3) ◽  
pp. 4427-4441
Author(s):  
Bin Xu
Keyword(s):  
Network Security ◽  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Computer Network ◽  
Information Aggregation ◽  
Security Evaluation ◽  
Uncertain Information ◽  
Intuitionistic Fuzzy ◽  
Computer Network Security

The concept of fuzzy number intuitionistic fuzzy sets (FNIFSs) is designed to effectively depict uncertain information in decision making problems which fundamental characteristic of the FNIFS is that the values of its membership function and non-membership function are depicted with triangular fuzzy numbers (TFNs). The dual Hamy mean (DHM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this paper, we used the dual Hamy mean (DHM) operator and dual weighted Hamy mean (WDHM) operator with fuzzy number intuitionistic fuzzy numbers (FNIFNs) to propose the fuzzy number intuitionistic fuzzy dual Hamy mean (FNIFDHM) operator and fuzzy number intuitionistic fuzzy weighted dual Hamy mean (FNIFWDHM) operator. Then the MADM methods are proposed along with these operators. In the end, we utilize an applicable example for computer network security evaluation to prove the proposed methods.

Possibility-Based Design Optimization Method for Design Problems With Both Statistical and Fuzzy Input Data

2005 ◽  
Vol 128 (4) ◽  
pp. 928-935 ◽  
Author(s):  
Liu Du ◽  
K. K. Choi ◽  
Byeng D. Youn ◽  
David Gorsich
Keyword(s):  
Design Optimization ◽  
Optimum Design ◽  
Membership Function ◽  
Input Data ◽  
Performance Measure ◽  
Sufficient Data ◽  
Design Problems ◽  
Fuzzy Variables ◽  
Fuzzy Input ◽  
The Membership Function

The reliability based design optimization (RBDO) method is prevailing in stochastic structural design optimization by assuming the amount of input data is sufficient enough to create accurate input statistical distribution. If the sufficient input data cannot be generated due to limitations in technical and/or facility resources, the possibility-based design optimization (PBDO) method can be used to obtain reliable designs by utilizing membership functions for epistemic uncertainties. For RBDO, the performance measure approach (PMA) is well established and accepted by many investigators. It is found that the same PMA is a very much desirable approach also for the PBDO problems. In many industry design problems, we have to deal with uncertainties with sufficient data and uncertainties with insufficient data simultaneously. For these design problems, it is not desirable to use RBDO since it could lead to an unreliable optimum design. This paper proposes to use PBDO for design optimization for such problems. In order to treat uncertainties as fuzzy variables, several methods for membership function generation are proposed. As less detailed information is available for the input data, the membership function that provides more conservative optimum design should be selected. For uncertainties with sufficient data, the membership function that yields the least conservative optimum design is proposed by using the possibility-probability consistency theory and the least conservative condition. The proposed approach for design problems with mixed type input uncertainties is applied to some example problems to demonstrate feasibility of the approach. It is shown that the proposed approach provides conservative optimum design.

scholarly journals New Ranking Method For Fuzzy Numbers By Their Expansion Center

2014 ◽  
Vol 4 (3) ◽  
pp. 181-187 ◽  
Author(s):  
Zhenyuan Wang ◽  
Li Zhang-Westmant
Keyword(s):  
Decision Making ◽  
Data Analysis ◽  
Real Axis ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Ranking Method ◽  
Important Criterion ◽  
Real Numbers ◽  
Numerical Index ◽  
The Membership Function

Abstract Based on the area between the curve of the membership function of a fuzzy number and the horizontal real axis, a characteristic as a new numerical index, called the expansion center, for fuzzy numbers is proposed. An intuitive and reasonable ranking method for fuzzy numbers based on this characteristic is also established. The new ranking method is applicable for decision making and data analysis in fuzz environments. An important criterion of the goodness for ranking fuzzy numbers, the geometric intuitivity, is also introduced. It guarantees coinciding with the natural ordering of the real numbers.

scholarly journals Controllable Effective Threshold Based Fusion Coverage Algorithm in Mobile Sensor Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yong Lu ◽  
Na Sun
Keyword(s):  
Sensor Networks ◽  
Membership Function ◽  
Network Lifetime ◽  
Physical Parameters ◽  
Network Coverage ◽  
Target Node ◽  
Effective Threshold ◽  
Coverage Quality ◽  
Monitoring Area ◽  
The Membership Function

The coverage quality and network lifetime are two key parameters in the research of sensor networks. The coverage quality shows direct influences on the network lifetime. Meanwhile, it is influenced by many other factors such as physical parameters and environmental parameters. To reveal the connection between the coverage quality and the parameters of target node concerned, a fusion coverage algorithm with controllable effective threshold is proposed based on the sensing probability model. We give the model for the membership function of coverage intensity as well as the prediction model for the fusion operator. The range for the effective threshold is presented according to the membership function model. Meanwhile, the maximum of the effective coverage intensity for the target nodes within the monitoring area is derived. The derivation of the maximal fusion coverage intensity is elaborated utilizing a processing function on the distances from the target node to the ones in the sensor node set. Furthermore, we investigate different network properties within the monitoring area such as network coverage quality, the dynamic change of parameters, and the network lifetime, based on the probability theory and the geometric theory. Finally, we present numerical simulations to verify the performances of our algorithm. It is shown under different settings that, compared with the demand coverage quality, the proposed algorithm could improve the network coverage quality by 15.66% on average. The simulation experiment results show that our proposed algorithm has an average improvement by 10.12% and 13.23% in terms of the performances on network coverage quality and network lifetime, respectively. The research results are enlightening to the edge coverage and nonlinear coverage problems within the monitoring area.

scholarly journals The Complementary Membership Function of n-Trapezoidal Shape Fuzzy Numbers

2019 ◽  
Vol 561 ◽  
pp. 012043
Author(s):  
Selvam Pandian ◽  
Rajkumar Arthur ◽  
Sudha Easwari Janakaran
Keyword(s):  
Membership Function ◽  
Fuzzy Numbers ◽  
Trapezoidal Shape

scholarly journals Measuring Loss-Based Process Capability IndexLeand Its GenerationLe′′with Fuzzy Numbers

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mohammad Abdolshah
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Numbers ◽  
Process Capability ◽  
Process Capability Index ◽  
Process Capability Indices ◽  
Capability Index ◽  
Fuzzy Process ◽  
Capability Indices ◽  
Fuzzy Process Capability ◽  
The Membership Function

Loss-based process capability indices are appropriate and realistic tools in order to measure the process capability. Among them, indexLeand its generationLe′′are well-known loss-based process capability indices, whose concepts are based on the worth (the opposite concept of loss). Sometimes, in order to calculateLeandLe′′there are some uncertainties in observations, so fuzzy logic can be employed to manage the uncertainties. This paper investigates fuzzification of process capability indexL~eand its generationL~e′′. In order to find the membership function of process capability indicesL~eandL~e′′, theα-cuts of fuzzy observation were employed. Then with an example of fuzzy process capability index,L~eandL~e′′were calculated and compared. Results showed that fuzzyL~e′′was more sensitive compared withL~eand was increased while the target departs (asymmetric tolerance). This example also showed that, with departure from the target, variation of fuzzyL~e′′and consequently its fuzziness were increased.

FUZZY CLUSTERING OF FEATURE VECTORS WITH SOME ORDINAL VALUED ATTRIBUTES USING GRADIENT DESCENT FOR LEARNING

2008 ◽  
Vol 16 (02) ◽  
pp. 195-218
Author(s):  
ROELOF K. BROUWER
Keyword(s):  
Objective Function ◽  
Membership Function ◽  
Fuzzy Clustering ◽  
Gradient Descent ◽  
Ratio Scale ◽  
Interval Scale ◽  
Real Numbers ◽  
Fuzzy C Means Clustering ◽  
Feature Values ◽  
The Membership Function

There are well established methods for fuzzy clustering especially for the cases where the feature values are numerical of ratio or interval scale. Not so well established are methods to be applied when the feature values are ordinal or nominal. In that case there is no one best method it seems. This paper discusses a method where unknown numeric variables are assigned to the ordinal values. Part of minimizing an objective function for the clustering is to find numeric values for these variables. Thus real numbers of interval scale and even ratio scale for that matter are assigned to the original ordinal values. The method uses the same objective function as used in fuzzy c-means clustering but both the membership function and the ordinal to real mapping are determined by gradient descent. Since the ordinal to real mapping is not known it cannot be verified for its legitimacy. However the ordinal to real mapping that is found is best in terms of the clustering produced. Simulations show the method to be quite effective.

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