Study on Determination Method for Parameters of Rock’s Shear Strength through Least Absolute Linear Regression Based on Symmetric Triangular Fuzzy Numbers

2012 ◽  
Vol 170-173 ◽  
pp. 804-807
Author(s):  
Bin Lin ◽  
Zhi Bo Chen ◽  
Qing Fang
Keyword(s):  
Shear Strength ◽  
Linear Regression ◽  
Fuzzy Numbers ◽  
New Method ◽  
Determination Method ◽  
Triangular Fuzzy Numbers ◽  
Engineering Computation ◽  
Practical Engineering

In view of the randomness and fuzziness of the parameters of rock’s shear strength, first, use symmetric triangular fuzzy numbers which can reflect the interval features of parameters express the parameters of rock’s shear strength. Second, put forward to a new determination method for parameters of rock’s shear strength through least absolute linear regression based on symmetric triangular fuzzy numbers according to criteria of least absolute. Finally, the analysis of practical engineering computation and comparison to other methods shows that the new method is reasonable.

MONTE CARLO METHODS IN FUZZY NON-LINEAR REGRESSION

2008 ◽  
Vol 04 (02) ◽  
pp. 123-141 ◽  
Author(s):  
AREEG ABDALLA ◽  
JAMES BUCKLEY
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Linear Regression ◽  
Fuzzy Numbers ◽  
Random Number ◽  
Random Number Generator ◽  
Search Space ◽  
Triangular Fuzzy Numbers ◽  
Non Linear ◽  
Regression Problems

We apply our new fuzzy Monte Carlo method to certain fuzzy non-linear regression problems to estimate the best solution. The best solution is a vector of triangular fuzzy numbers, for the fuzzy coefficients in the model, which minimizes an error measure. We use a quasi-random number generator to produce random sequences of these fuzzy vectors which uniformly fill the search space. We consider example problems to show that this Monte Carlo method obtains solutions comparable to those obtained by an evolutionary algorithm.

scholarly journals Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
P. Phani Bushan Rao ◽  
N. Ravi Shankar
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Satisfactory Result ◽  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Distance Method ◽  
Fuzzy Environment ◽  
Index Of Optimism

Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking fuzzy numbers based on the Circumcenter of Centroids and uses an index of optimism to reflect the decision maker's optimistic attitude and also an index of modality that represents the neutrality of the decision maker. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of fuzzy numbers.

scholarly journals New Similarity of Triangular Fuzzy Number and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xixiang Zhang ◽  
Weimin Ma ◽  
Liping Chen
Keyword(s):  
Collaborative Filtering ◽  
Fuzzy Number ◽  
Recommendation System ◽  
Fuzzy Numbers ◽  
Comprehensive Evaluation ◽  
Cloud Model ◽  
Triangular Fuzzy Number ◽  
New Method ◽  
Triangular Fuzzy Numbers

The similarity of triangular fuzzy numbers is an important metric for application of it. There exist several approaches to measure similarity of triangular fuzzy numbers. However, some of them are opt to be large. To make the similarity well distributed, a new method SIAM (Shape’s Indifferent Area and Midpoint) to measure triangular fuzzy number is put forward, which takes the shape’s indifferent area and midpoint of two triangular fuzzy numbers into consideration. Comparison with other similarity measurements shows the effectiveness of the proposed method. Then, it is applied to collaborative filtering recommendation to measure users’ similarity. A collaborative filtering case is used to illustrate users’ similarity based on cloud model and triangular fuzzy number; the result indicates that users’ similarity based on triangular fuzzy number can obtain better discrimination. Finally, a simulated collaborative filtering recommendation system is developed which uses cloud model and triangular fuzzy number to express users’ comprehensive evaluation on items, and result shows that the accuracy of collaborative filtering recommendation based on triangular fuzzy number is higher.

scholarly journals A New Method for Fuzzy Ranking Based on Possibility and Necessity Measures

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Ranking

In this paper, a new method to rank fuzzy numbers is presented. The proposed method based on Possibility and Necessity Measures is called PNM. According to possibility and necessity measures, eight indexes are calculated to extract four rules to rank fuzzy numbers. Also a method to evaluate each rule validation especially when rules’ outcomes yield conflict conclusions is presented. To test PNM performance, some controversial triangular fuzzy numbers are considered. Additionally, four extracted rules are compared with each other and fully analyzed. Furthermore, PNM is compared with other recently proposed methods. Results confirm that PNM is capable to rank a variety of fuzzy numbers and their images with any selected bandwidths, interval and any degree of closeness

scholarly journals A Direct Method to Compare Bipolar LR Fuzzy Numbers

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Reza Ghanbari ◽  
Khatere Ghorbani-Moghadam ◽  
Nezam Mahdavi-Amiri
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Direct Method ◽  
Optimization Algorithms ◽  
Real Life ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Real Life Problem ◽  
A Direct Method

We propose a new method for ordering bipolar fuzzy numbers. In this method, for comparison of bipolar LR fuzzy numbers, we use an extension of Kerre’s method being used in ordering of unipolar fuzzy numbers. We give a direct formula to compare two bipolar triangular fuzzy numbers in O(1) operations, making the process useful for many optimization algorithms. Also, we present an application of bipolar fuzzy number in a real life problem.

scholarly journals Fuzzy Risk Analysis for a Production System Based on the Nagel Point of a Triangle

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Handan Akyar
Keyword(s):  
Risk Analysis ◽  
Fuzzy Numbers ◽  
New Method ◽  
Economic Systems ◽  
Triangular Fuzzy Numbers ◽  
Ranking Methods ◽  
Analysis Problem ◽  
Centroid Point ◽  
Fuzzy Risk Analysis ◽  
Fuzzy Ranking

Ordering and ranking fuzzy numbers and their comparisons play a significant role in decision-making problems such as social and economic systems, forecasting, optimization, and risk analysis problems. In this paper, a new method for ordering triangular fuzzy numbers using the Nagel point of a triangle is presented. With the aid of the proposed method, reasonable properties of ordering fuzzy numbers are verified. Certain comparative examples are given to illustrate the advantages of the new method. Many papers have been devoted to studies on fuzzy ranking methods, but some of these studies have certain shortcomings. The proposed method overcomes the drawbacks of the existing methods in the literature. The suggested method can order triangular fuzzy numbers as well as crisp numbers and fuzzy numbers with the same centroid point. An application to the fuzzy risk analysis problem is given, based on the suggested ordering approach.

A NEW METHOD FOR RANKING TRIANGULAR FUZZY NUMBERS

2012 ◽  
Vol 20 (05) ◽  
pp. 729-740 ◽  
Author(s):  
EMRAH AKYAR ◽  
HANDAN AKYAR ◽  
SERKAN ALİ DÜZCE
Keyword(s):  
Decision Making ◽  
Risk Analysis ◽  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Application Systems ◽  
Systems Control

The ranking and comparing of fuzzy numbers have important practical uses, such as in risk analysis problems, decision-making, optimization, forecasting, socioeconomic systems, control and certain other fuzzy application systems. Several methods for ranking fuzzy numbers have been widely-discussed though most of them have shortcomings. In this paper, we present a new method for ranking triangular fuzzy numbers based on their incenter and inradius. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method.

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.

scholarly journals A Systematic Approach to OptimizinghValue for Fuzzy Linear Regression with Symmetric Triangular Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xilong Liu ◽  
Yizeng Chen
Keyword(s):  
Linear Regression ◽  
Systematic Approach ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Numerical Study ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Linear Regression ◽  
The Real ◽  
Optimal Value ◽  
Sample Data

A systematic approach is proposed to optimizehvalue for fuzzy linear regression (FLR) analysis using minimum fuzziness criteria with symmetric triangular fuzzy numbers (TFNs). Firstly, a new concept of credibility is defined to evaluate the performance of FLR models with differenthvalues when a set of sample data pairs is given. Secondly, based on the defined concept of credibility, a programming model is formulated to optimize the value ofh. Finally, both the numerical study and the real application show that the approach proposed in this paper is effective and efficient; that is, optimal value forhcan be determined definitely with respect to a set of given sample data pairs.

Sign in / Sign up

Export Citation Format

Share Document