scholarly journals On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy Number

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 526 ◽  
Author(s):  
Krzysztof Piasecki ◽  
Anna Łyczkowska-Hanćkowiak
Keyword(s):  
Portfolio Management ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Fuzzy Topsis ◽  
Information Support ◽  
Entropy Measure ◽  
Management Evaluation ◽  
Energy Measure ◽  
Approximation Problems ◽  
Information Ambiguity

In this paper, the model of imprecise quantity information is an ordered fuzzy number. The purpose of our study is to propose some methods of approximating any ordered fuzzy number using a trapezoidal ordered fuzzy number. The information ambiguity is evaluated by means of an energy measure. The information indistinctness is evaluated by Kosko’s entropy measure. We discuss the problem of approximation of an arbitrary ordered fuzzy number by the nearest trapezoidal ordered fuzzy number. This way, we can simplify arithmetical operations on the linear space of ordered fuzzy numbers. The set of feasible trapezoidal ordered numbers is limited by the combination of the following conditions: invariance of energy measure, invariance of entropy measure, and invariance of information support. Evaluating the influence of individual limits combinations on the utility of given approximations, two combinations of those restraints, recommended for use, were chosen. It was also indicated that one of the recommended approximation problems can be used only for ordered fuzzy numbers characterized by a low level of entropy. The obtained results are currently used in such multi-criterial decision making models as financial portfolio management, evaluation of negotiations offers, the fuzzy TOPSIS model, and the fuzzy SAW model.

scholarly journals Trapezoidal Linguistic Cubic Fuzzy TOPSIS Method and Application in a Group Decision Making Program

2019 ◽  
Vol 29 (1) ◽  
pp. 1283-1300 ◽  
Author(s):  
Aliya Fahmi ◽  
Saleem Abdullah ◽  
Fazli Amin ◽  
Muhammad Aslam ◽  
Shah Hussain
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Hamming Distance ◽  
Fuzzy Topsis ◽  
Multi Criteria Decision Making ◽  
Topsis Method ◽  
Mcdm Method

Abstract The aim of this paper is to define some new operation laws for the trapezoidal linguistic cubic fuzzy number and Hamming distance. Furthermore, we define and use the trapezoidal linguistic cubic fuzzy TOPSIS method to solve the multi criteria decision making (MCDM) method. The new ranking method for trapezoidal linguistic cubic fuzzy numbers (TrLCFNs) are used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method.

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.

ANALYSIS OF FUZZY QUEUES BY USING PENTAGONAL FUZZY NUMBER

2021 ◽  
Vol 23 (04) ◽  
pp. 211-224
Author(s):  
Gurcharan Singh ◽  
◽  
Baljodh Singh ◽  
Neelam Kumari ◽  
◽  
...  
Keyword(s):  
Probability Theory ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Queuing Theory ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Linguistic Terms

This paper deals with the fact thatpentagonal fuzzy numbers are pre-owned and systematic outcomes are discussed in real-life situations. The fuzzy set supposition is combined with well-established classical queuing theory but the classical queuing theory is far away from real-life situations. In this approach, we can use both fuzzy and probability theory to make this work more realistic with the help of the α-cut technique. Symmetric pentagonal fuzzy numbers are used to elaborate on the situation of the queue in linguistic terms.

A Study On α-Cuts of Trapezoidal Fuzzy Numbers And α-Cuts of Trapezoidal Fuzzy Number Matrices

2021 ◽  
Vol 67 (7) ◽  
pp. 9-20
Author(s):  
Kohila Gowri G M ◽  
Thamil selvi P ◽  
Kavitha P
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Trapezoidal Fuzzy Numbers ◽  
Trapezoidal Fuzzy Number

scholarly journals Optimizing Cancer Clinical Trials Research Investment Decisions In The United States: A Proof Of Concept Portfolio Management Evaluation

2015 ◽  
Vol 18 (3) ◽  
pp. A8
Author(s):  
C.S. Bennette ◽  
J.A. Roth ◽  
A. Basu ◽  
J.J. Carlson ◽  
S. Ramsey ◽  
...  
Keyword(s):  
United States ◽  
Clinical Trials ◽  
Portfolio Management ◽  
Investment Decisions ◽  
The United States ◽  
Cancer Clinical Trials ◽  
Proof Of Concept ◽  
Management Evaluation ◽  
Research Investment

CHARACTERIZATIONS OF THE BOREL -FIELDS OF THE FUZZY NUMBER SPACE

2017 ◽  
Vol 58 (3-4) ◽  
pp. 265-275
Author(s):  
TAI-HE FAN ◽  
MENG-KE BIAN
Keyword(s):  
Approximation Method ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Hausdorff Metric ◽  
Measurable Space ◽  
Borel Field ◽  
Applied Fields ◽  
Supremum Metric

In this paper, we characterize Borel $\unicode[STIX]{x1D70E}$-fields of the set of all fuzzy numbers endowed with different metrics. The main result is that the Borel $\unicode[STIX]{x1D70E}$-fields with respect to all known separable metrics are identical. This Borel field is the Borel $\unicode[STIX]{x1D70E}$-field making all level cut functions of fuzzy mappings from any measurable space to the fuzzy number space measurable with respect to the Hausdorff metric on the cut sets. The relation between the Borel $\unicode[STIX]{x1D70E}$-field with respect to the supremum metric $d_{\infty }$ is also demonstrated. We prove that the Borel field is induced by a separable and complete metric. A global characterization of measurability of fuzzy-valued functions is given via the main result. Applications to fuzzy-valued integrals are given, and an approximation method is presented for integrals of fuzzy-valued functions. Finally, an example is given to illustrate the applications of these results in economics. This example shows that the results in this paper are basic to the theory of fuzzy-valued functions, such as the fuzzy version of Lebesgue-like integrals of fuzzy-valued functions, and are useful in applied fields.

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.

Ranking of Fuzzy Numbers by using Scaling Method

2019 ◽  
Vol 3 (2) ◽  
pp. 137-143
Author(s):  
Ayad Mohammed Ramadan
Keyword(s):  
Multidimensional Scaling ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Scaling Method ◽  
Ranking Of Fuzzy Numbers ◽  
First Time

In this paper, we presented for the first time a multidimensional scaling approach to find the scaling as well as the ranking of triangular fuzzy numbers. Each fuzzy number was represented by a row in a matrix, and then found the configuration points (scale points) which represent the fuzzy numbers in . Since these points are not uniquely determined, then we presented different techniques to reconfigure the points to compare them with other methods. The results showed the ability of ranking fuzzy numbers

A MODIFICATION OF THE INDEX OF LIOU AND WANG FOR RANKING FUZZY NUMBER

2007 ◽  
Vol 15 (04) ◽  
pp. 411-424 ◽  
Author(s):  
M. SOCORRO GARCIA ◽  
M. TERESA LAMATA
Keyword(s):  
Satisfactory Result ◽  
Coefficient Of Variation ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Mean Value ◽  
Weighted Mean ◽  
Numerical Examples ◽  
Centroid Point ◽  
Ranking Fuzzy Number ◽  
Index Of Optimism

Different methods have been proposed for ranking fuzzy numbers. These include methods based on distances, centroid point, coefficient of variation, and weighted mean value. However, there is still no method that can always give a satisfactory result to every situation; some are counterintuitive and not discriminating. This paper presents an approach for ranking fuzzy numbers with integral value that is an extension of the index of Liou and Wang. This method, that is independent of the type of membership function used, can rank more than two fuzzy numbers simultaneously. This ranking method use an index of optimism to reflect the decision maker's optimistic attitude, but rather it also contains an index of modality that represents the neutrality of the decision maker. The approach is illustrated with numerical examples.

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