scholarly journals A New Method for Defuzzification and Ranking of Fuzzy Numbers Based on the Statistical Beta Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
A. Rahmani ◽  
F. Hosseinzadeh Lotfi ◽  
M. Rostamy-Malkhalifeh ◽  
T. Allahviranloo
Keyword(s):  
Beta Distribution ◽  
Granular Computing ◽  
Fuzzy Numbers ◽  
Mean Value ◽  
Human Reasoning ◽  
Fuzzy Information ◽  
Numerical Examples ◽  
Novel Method ◽  
The Mean ◽  
Ranking Of Fuzzy Numbers

Granular computing is an emerging computing theory and paradigm that deals with the processing of information granules, which are defined as a number of information entities grouped together due to their similarity, physical adjacency, or indistinguishability. In most aspects of human reasoning, these granules have an uncertain formation, so the concept of granularity of fuzzy information could be of special interest for the applications where fuzzy sets must be converted to crisp sets to avoid uncertainty. This paper proposes a novel method of defuzzification based on the mean value of statistical Beta distribution and an algorithm for ranking fuzzy numbers based on the crisp number ranking system on R. The proposed method is quite easy to use, but the main reason for following this approach is the equality of left spread, right spread, and mode of Beta distribution with their corresponding values in fuzzy numbers within(0,1)interval, in addition to the fact that the resulting method can satisfy all reasonable properties of fuzzy quantity ordering defined by Wang et al. The algorithm is illustrated through several numerical examples and it is then compared with some of the other methods provided by literature.

Stochastic Analysis of Temperature Distribution in a Solid With Random Heat Conductivity

1988 ◽  
Vol 110 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Da Yu Tzou
Keyword(s):  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Heat Conductivity ◽  
Stochastic Analysis ◽  
Solid Medium ◽  
Mean Value ◽  
Random Response ◽  
Thermal Failure ◽  
Numerical Examples ◽  
The Mean

Stochastic temperature distribution in a solid medium with random heat conductivity is investigated by the method of perturbation. The intrinsic randomness of the thermal conductivity k(x) is considered to be a distribution function with random amplitude in the solid, and several typical stochastic processes are considered in the numerical examples. The formulation used in the present analysis describes a situation that the statistical orders of the random response of the system are the same as those of the intrinsic random excitations, which is characteristic for the problem with extrinsic randomness. The maximum standard deviation of the temperature distribution from the mean value in the solid medium reveals the amount of unexpected energy experienced by the solid continuum, which should be carefully inspected in the thermal-failure design of structures with intrinsic randomness.

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.

Ranking Fuzzy Numbers Based on the Mean and Fuzzy Degree of Fuzzy Number

2012 ◽  
Vol 220-223 ◽  
pp. 2102-2108
Author(s):  
Gui Xiang Wang ◽  
Guang Tao Zhou
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Numerical Examples ◽  
Novel Approach ◽  
The Mean ◽  
Fuzzy Degree ◽  
Comparative Results ◽  
Ranking Index

In this paper, a novel approach to ranking fuzzy numbers based on the mean and the fuzzy degree of fuzzy number is proposed. In the approach, a new ranking index that is comprehensive consideration of the mean and the fuzzy degree of fuzzy number is constructed, and then the properties of the ranking index are given. Moreover, to compare the proposed approach with the existing approaches, numerical examples are given. The comparative results illustrate that the approach proposed in this paper is better and has simpler calculations.

Orbit Response Recognition During Touchdowns by Instantaneous Frequency in Active Magnetic Bearings

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Mindong Lyu ◽  
Tao Liu ◽  
Zixi Wang ◽  
Shaoze Yan ◽  
Xiaohong Jia ◽  
...  
Keyword(s):  
Instantaneous Frequency ◽  
Sampling Period ◽  
Threshold Value ◽  
Mean Value ◽  
Magnetic Bearings ◽  
Active Magnetic Bearings ◽  
Local Variance ◽  
Displacement Signal ◽  
Novel Method ◽  
The Mean

During touchdowns of active magnetic bearings (AMB), the violent collision between rotors and touchdown bearings (TDB) can cause damages to both parts. Orbit response recognition provides a way for the AMB controller to automatically switch the control algorithm to actively suppress the rotor–TDB vibration and promptly relevitate the rotor during touchdowns. A novel method based on Hilbert transform (HT) is proposed to recognize the orbit responses (pendulum vibration, combined rub and bouncing, and full rub) in touchdowns. In this method, the rotor suspension status is monitored by the AMB controller in real-time. When touchdown is detected, the rotor displacement signal during the sampling period is intercepted, and the instantaneous frequency (IF) is calculated by HT. Then, the local variance of IF during the sampling period is calculated, and it is compared with the threshold value. Combined rub and bouncing can be identified for it has the largest local variance. Finally, the mean value of IF during the sampling period is calculated and is compared with the other threshold value. Pendulum vibration can be identified for it has a lower and fixed mean value, while full rub has a larger value. The principle of the recognition method is demonstrated by the simulated results of a thermo-dynamic model. The results reveal that the method is feasible in recognizing the orbit responses and can be implemented in the AMB controller to help switch the control algorithms automatically in case of touchdowns.

SOME CONTINUOUS AGGREGATION OPERATORS WITH INTERVAL-VALUED INTUITIONISTIC FUZZY INFORMATION AND THEIR APPLICATION TO DECISION MAKING

2012 ◽  
Vol 20 (02) ◽  
pp. 185-209 ◽  
Author(s):  
JIAN LIN ◽  
QIANG ZHANG
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Interval Valued

In this paper, some new operators for aggregating interval-valued intuitionistic fuzzy information are proposed to deal with multiple attribute decision making problems. Firstly, the C-IFOWA operator and C-IFOWG operator are developed to aggregate all the values in the interval-valued intuitionistic fuzzy numbers. Some of their desirable properties are also studied. Secondly, in order to aggregate a set of interval-valued intuitionistic fuzzy numbers, some new aggregation operators are proposed based on the C-IFOWA operator and C-IFOWG operator. Thirdly, two methods for multiple attribute decision making, in which the attribute values are given in the forms of interval-valued intuitionistic fuzzy numbers are presented. Finally, two numerical examples are provided to illustrate the practicality and validity of the proposed methods.

Use of Grey Numbers for Evaluating a System's Performance Under Fuzzy Conditions

2021 ◽  
pp. 315-331
Author(s):  
Michael Voskoglou
Keyword(s):  
Fuzzy Numbers ◽  
Mean Value ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Quality Performance ◽  
Computational Burden ◽  
The Mean ◽  
Analogous Method

In the present research, a method using Grey Numbers as tools is developed for assessing a system's mean performance, which is useful when utilizing qualitative grades and not numerical scores for this purpose. Although this new method is proved to be equivalent with an analogous method using Triangular Fuzzy Numbers as tools developed in an earlier work, it reduces the required computational burden, since it requires the calculation of two components only (instead of three in the case of the Triangular Fuzzy Numbers) for obtaining the mean value of the Grey Numbers involved. Examples are also presented on student and athlete assessment illustrating the new method and showing that the system's quality performance, calculated by the traditional GPA index, may lead to different assessment conclusions.

A new multi-criteria decision-making method utilizing power heronian operators with picture hesitant fuzzy information

2021 ◽  
pp. 1-22
Author(s):  
Baolin Li ◽  
Lihua Yang ◽  
Jie Qian
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Multi Criteria Decision Making ◽  
Comparison Analysis ◽  
Fuzzy Information ◽  
Hesitant Fuzzy Sets ◽  
Novel Method ◽  
Picture Fuzzy Sets

In practice, picture hesitant fuzzy sets (PHFSs) combining the picture fuzzy sets (PFSs) and hesitant fuzzy sets (HFSs) are suitable to represent more complex multi-criteria decision-making (MCDM) information. The power heronian (PH) operators, which have the merits of power average (PA) and heronian mean (HM) operators, are extended to the environment of PHFSs in this article. First, some algebraic operations of picture hesitant fuzzy numbers (PHFNs), comparative functions and distance measure are introduced. Second, two novel operators, called as picture hesitant fuzzy weighted power heronian (PHFWPH) operator and picture hesitant fuzzy weighted geometric power heronian (PHFWGPH) operator, are defined. Meanwhile, some desirable characteristics and special instances of two operators are investigated as well. Third, a novel MCDM approach applying the proposed PH operators to handle PHFNs is explored. Lastly, to indicate the effectiveness of this novel method, an example regarding MCDM problem is conducted, as well as sensitivity and comparison analysis.

scholarly journals A Novel Method of Ranking Intuitionistic Fuzzy Numbers using Value and θ Multiple of Ambiguity at Flexibility Parameters

2021 ◽  
Author(s):  
Rituparna Chutia
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Number ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Novel Method ◽  
Flexibility Parameters

Abstract In this paper a novel method of ordering intuitionistic fuzzy numbers, based on the notions of ‘value’ and θ-multiple of ‘ambiguity’ of an intuitionistic fuzzy number, is developed. Further, the flexibility parameters, of decision-making at (α, β)-levels, are used in the method. These parameters allow the decision-maker to take decisions at various (α, β)-levels of decision-making. Many a times, all the reasonable properties of ranking intuitionistic fuzzy numbers were never checked in the existing studies. However, in this study an utmost attempt is being made to study the reasonable properties thoroughly. Further, the existing methods are mostly based on intuition and the geometry of the intuitionistic fuzzy numbers. However, the proposed method completely complies with the reasonable properties of ranking intuitionistic fuzzy numbers as well as the coherent intuition and the geometry of the intuitionistic fuzzy numbers. Further, newer properties are also being developed in this study. These prove the novelty of the proposed method. Further, a few numerical examples are discussed that demonstrates the proposed method.

Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 164-165
Author(s):  
Noriyuki Kuwano ◽  
Masaru Itakura ◽  
Kensuke Oki
Keyword(s):  
Electron Microscopy ◽  
Mean Value ◽  
Heavy Elements ◽  
Arc Furnace ◽  
X Ray ◽  
Long Period ◽  
Ultra High Purity ◽  
Heat Treated ◽  
Atomic Scattering ◽  
The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

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