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

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.

A noval ranking approach based on incircle of triangular intuitionistic fuzzy numbers

2020 ◽  
Vol 39 (5) ◽  
pp. 6271-6278
Author(s):  
Gultekin Atalik ◽  
Sevil Senturk
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Fuzzy Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Linear Programming Problems ◽  
Relationship Of ◽  
Ranking Of Fuzzy Numbers

Since proposed by Zadeh in 1965, ordinary fuzzy sets help us to model uncertainty and developed many types such as type 2 fuzzy, intuitionistic fuzzy, hesitant fuzzy etc. Intuitionistic fuzzy sets include both membership and non-membership functions for their each element. Ranking of a number is to identify a relationship of scalar quantity between these numbers. Ranking of fuzzy numbers play an important role in modeling problems such as fuzzy decision making, fuzzy linear programming problems. In this study, a new ranking method for triangular intuitionistic fuzzy numbers is proposed. The method based on the incircle of the membership function and non-membership function of TIFN uses lexicographical order to rank intuitionistic fuzzy numbers. Two examples are provided to illustrate the applicability of the method. Also, a comparative study is performed to demonstrate the validity of the proposed method. The results indicate that proposed method is consistent with other methods in the literature. Also, the method overcomes the problems such as numbers being very small or close to each other.

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.

scholarly journals ON THE RATIO OF FUZZY NUMBERS – EXACT MEMBERSHIP FUNCTION COMPUTATION AND APPLICATIONS TO DECISION MAKING

2015 ◽  
Vol 21 (5) ◽  
pp. 815-832 ◽  
Author(s):  
Bogdana STANOJEVIĆ ◽  
Ioan DZIŢAC ◽  
Simona DZIŢAC
Keyword(s):  
Decision Making ◽  
Programming Problem ◽  
Membership Function ◽  
Fractional Programming ◽  
Fuzzy Numbers ◽  
Linear Constraints ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Fuzzy Linear Fractional Programming ◽  
Linear Fractional Programming Problem

In the present paper, we propose a new approach to solving the full fuzzy linear fractional programming problem. By this approach, we provide a tool for making good decisions in certain problems in which the goals may be modelled by linear fractional functions under linear constraints; and when only vague data are available. In order to evaluate the membership function of the fractional objective, we use the α-cut interval of a special class of fuzzy numbers, namely the fuzzy numbers obtained as sums of products of triangular fuzzy numbers with positive support. We derive the α-cut interval of the ratio of such fuzzy numbers, compute the exact membership function of the ratio, and introduce a way to evaluate the error that arises when the result is approximated by a triangular fuzzy number. We analyse the effect of this approximation on solving a full fuzzy linear fractional programming problem. We illustrate our approach by solving a special example – a decision-making problem in production planning.

RANKING-INTUITIONISTIC FUZZY NUMBERS

2004 ◽  
Vol 12 (03) ◽  
pp. 377-386 ◽  
Author(s):  
H. B. MITCHELL
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Sets ◽  
Test Cases ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Statistical Viewpoint

Intuitionistic fuzzy sets are a generalization of ordinary fuzzy sets which are characterized by a membership function and a non-membership function. In this paper we consider the problem of ranking a set of intuitionistic fuzzy numbers. We adopt a statistical viewpoint and interpret each intuitionistic fuzzy number as an ensemble of ordinary fuzzy numbers. This enables us to define a fuzzy rank and a characteristic vagueness factor for each intuitionistic fuzzy number. We show the reasonablesness of the results obtained by examining several test cases.

scholarly journals Fractional two-stage transshipment problem under uncertainty: application of the extension principle approach

2021 ◽  
Author(s):  
Harish Garg ◽  
Ali Mahmoodirad ◽  
Sadegh Niroomand
Keyword(s):  
Objective Function ◽  
Membership Function ◽  
Solution Method ◽  
Fuzzy Numbers ◽  
Objective Function Value ◽  
Transformation Method ◽  
Extension Principle ◽  
Two Stage ◽  
Objective Value

AbstractIn this paper, a fuzzy fractional two-stage transshipment problem where all the parameters are represented by fuzzy numbers is studied. The problem uses the ratio of costs divided by benefits as the objective function. A solution method which employs the extension principle is used to find the fuzzy objective value of the problem. For this purpose, the fuzzy fractional two-stage transshipment problem is decomposed into two sub-problems where each of them is tackled individually using various $$\alpha$$ α levels to obtain the fuzzy objective function value and its associated membership function. To deal with the nonlinearity of the objective function the Charnes–Cooper transformation method is embedded to the proposed approach. The superior efficiency of the presented formulation and the proposed solution method is examined over a numerical example as well as a case study comparing to the literature.

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