scholarly journals Double Integral-Based Method for Ranking Intuitionistic Multiplicative Sets and Its Application in Selecting Logistics Transfer Station

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhiyong Tian ◽  
Jian Lin
Keyword(s):  
Integral Method ◽  
Score Function ◽  
Risk Preference ◽  
Order Relation ◽  
Total Order ◽  
Ranking Method ◽  
Feasible Region ◽  
Accuracy Function ◽  
Double Integral ◽  
Transfer Station

Intuitionistic multiplicative sets can be applied in many practical situations, most of which are based on ranking of intuitionistic multiplicative numbers. This study develops an integral method for ranking intuitionistic multiplicative numbers based on the new definitions of multiplicative score function and accuracy function. The ranking method considers both the risk preference and infinitely many possible values in feasible region. Some reasonable properties of multiplicative score function and accuracy function are studied, respectively. We construct a total order relation on the set of intuitionistic multiplicative numbers. The multiplicative score function and accuracy function are utilized to select the optimal logistics transfer station. A comparison example is developed to highlight the advantage of the risk preference-based ranking method.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

2021 ◽  
pp. 1-23
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Score Function ◽  
Aggregation Operators ◽  
Unit Interval ◽  
Multi Criteria Decision Making ◽  
Accuracy Function ◽  
Special Cases

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

scholarly journals Dual Generalized Nonnegative Normal Neutrosophic Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

Information ◽  
2018 ◽  
Vol 9 (8) ◽  
pp. 201 ◽  
Author(s):  
Jiongmei Mo ◽  
Han-Liang Huang
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Ranking Method ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Geometric Bonferroni Mean ◽  
Neutrosophic Number

For multiple attribute decision making, ranking and information aggregation problems are increasingly receiving attention. In a normal neutrosophic number, the ranking method does not satisfy the ranking principle. Moreover, the proposed operators do not take into account the correlation between any aggregation arguments. In order to overcome the deficiencies of the existing ranking method, based on the nonnegative normal neutrosophic number, this paper redefines the score function, the accuracy function, and partial operational laws. Considering the correlation between any aggregation arguments, the dual generalized nonnegative normal neutrosophic weighted Bonferroni mean operator and dual generalized nonnegative normal neutrosophic weighted geometric Bonferroni mean operator were investigated, and their properties are presented. Here, these two operators are applied to deal with a multiple attribute decision making problem. Example results show that the proposed method is effective and superior.

A New Method for Ranking Intuitionistic Fuzzy Numbers

2011 ◽  
Vol 2 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Cui-Ping Wei ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Ranking Method ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Additional Information ◽  
Intuitionistic Fuzzy ◽  
Possibility Degree

In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making problems.

Calculation of Meshing Efficiency of Helical Gear Based on Double Integral Method

2016 ◽  
Vol 693 ◽  
pp. 458-462
Author(s):  
D.G. Chang ◽  
F. Shu ◽  
X.B. Chen ◽  
Y.J. Zou
Keyword(s):  
Experimental Data ◽  
Coordinate System ◽  
Theoretical Basis ◽  
Integral Method ◽  
Helical Gear ◽  
Design Parameters ◽  
Double Integral ◽  
Rectangular Coordinate System ◽  
Helical Gears ◽  
Theoretical Results

The meshing efficiency of helical gear transmission is calculated by using the method of double integral. The external involute helical gear meshing is taken and the model of helical gears is simplified by the idea of differential. The instantaneous efficiency equation of a meshing point is derived, and further more the rectangular coordinate system of meshing zone of helical gears is established. The average meshing efficiency of helical gears is achieved by using double integral method. Then, the influence of design parameters is studied and the efficiency formula is verified by comparing the theoretical results with relevant experimental data, which can provide a theoretical basis for decide the design parameters.

scholarly journals Evaluation of Transfer Efficiency between Subway and Bus Based on the Interval Number Ranking Method by Employing Probability Reliability: Taking Ningbo for Example

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhenyu Chen ◽  
Zhengfeng Huang ◽  
Lingli Yang ◽  
Pengjun Zheng
Keyword(s):  
Order Relation ◽  
Interval Number ◽  
Ranking Method ◽  
Transfer Efficiency ◽  
Transfer Time ◽  
Time Data ◽  
Interval Numbers ◽  
Global Positioning ◽  
Travel Efficiency ◽  
Subway Stations

In recent years, the construction and operation of urban subways have been gradually increasing in developing countries. In the next step, more attention should be paid to the transfer efficiency between subway and bus so as to improve the travel efficiency of more urban residents. This paper uses the probability credibility interval number ranking method to evaluate the bus transfer efficiency. Firstly, this study obtains the dynamic transfer time data by matching individual smart card and subway/bus global positioning system (GPS) records, which is used to evaluate the transfer efficiency of corresponding subway stations. Then, we establish a probability density function to represent the characteristic information of transfer time. Accordingly, the probability reliability model of the order relation of interval numbers can be constructed. In the end, the method is applied to evaluate the transfer efficiency between subway and bus stations in Ningbo. Compared to the traditional interval number ranking method, the evaluation result shows that this method can get a more objective transfer efficiency order relation. The reason is that this method can not only consider the random feature of transfer time but also make use of the data distribution characteristics. This method could be applied to obtain the stations with relatively low transfer efficiency and the feedback can be used for bus line operation and station layout improvement.

scholarly journals Fractional diffusion equation described by the Atangana-Baleanu fractional derivative and its approximate solution

2021 ◽  
Vol 2 (1) ◽  
pp. 60-75
Author(s):  
Ndolane Sene
Keyword(s):  
Approximate Solution ◽  
Diffusion Equation ◽  
Fractional Derivative ◽  
Integral Method ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Double Integral ◽  
Uniqueness Of The Solution ◽  
The Impact ◽  
The Heat Balance

In this paper, we propose the approximate solution of the fractional diffusion equation described by a non-singular fractional derivative. We use the Atangana-Baleanu-Caputo fractional derivative in our studies. The integral balance methods as the heat balance integral method introduced by Goodman and the double integral method developed by Hristov have been used for getting the approximate solution. In this paper, the existence and uniqueness of the solution of the fractional diffusion equation have been provided. We analyze the impact of the fractional operator in the diffusion process. We represent graphically the approximate solution of the fractional diffusion equation.

A New Method for Ranking Intuitionistic Fuzzy Numbers

2013 ◽  
pp. 45-51
Author(s):  
Cui-Ping Wei ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Ranking Method ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Additional Information ◽  
Intuitionistic Fuzzy ◽  
Possibility Degree

In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making problems.

An Extended TODIM Method Based on Novel Score Function and Accuracy Function under Intuitionistic Fuzzy Environment

2019 ◽  
Vol 27 (06) ◽  
pp. 905-930 ◽  
Author(s):  
Dong Zhang ◽  
Xin Bao ◽  
Chong Wu
Keyword(s):  
Decision Making ◽  
Programming Model ◽  
Choquet Integral ◽  
Score Function ◽  
Accuracy Function ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Nonlinear Programming Model ◽  
Todim Method ◽  
The Difference

Recently, multi-attribute decision making (MADM) approaches concerning decision maker’s psychological behaviors have received increasing attention, but few of them have taken all the criteria interactions (positive, negative and dependent interactions) into consideration. In this paper, we combine the TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method with the 2-additive fuzzy measure and Choquet integral theory to demonstrate how criteria interactions can be determined and further extend it into intuitionistic fuzzy environment. To begin with, we propose the novel score function and accuracy function to compare the difference among intuitionistic fuzzy sets, which have been proven to be more effective and rational than the existing measure functions. Next, we construct the nonlinear programming model based on maximum-entropy principal to obtain the optimal criteria interactions. Further, 2-additive Choquet-based dominance degree is defined whereby we put forward the 2-additive Choquet integral-based TODIM method under intuitionistic fuzzy environment to handle more challenging MADM problems. Finally, we present results of a didactic example, which concerns selection of suppliers for a manufacturing company, to evaluate the validity and rationality of proposed approach.

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