scholarly journals Risky Multi-Attribute Decision-Making Method Based on the Interval Number of Normal Distribution

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 264
Author(s):  
Sha Fu ◽  
Xi-Long Qu ◽  
Ye-Zhi Xiao ◽  
Hang-Jun Zhou ◽  
Guo-Bing Fan
Keyword(s):  
Decision Making ◽  
Normal Distribution ◽  
Interval Number ◽  
Information Environment ◽  
Decision Makers ◽  
Standard Normal Distribution ◽  
Risky Decision ◽  
Possibility Degree ◽  
Standard Normal ◽  
Multi Attribute Decision Making

Focusing on risky decision-making problems taking the interval number of normal distribution as the information environment, this paper proposes a decision-making method based on the interval number of normal distribution. Firstly, the normalized matrix based on the decision maker’s attitude is obtained through analysis and calculation. Secondly, according to the existing properties of standard normal distribution, the risk preference factors of the decision makers are considered to confirm the possibility degree of each scheme. The possibility degree is then used for establishing a possibility degree matrix and, consequently, sequencing of all schemes is conducted according to existing theories of possibility degree meaning and the value size of possibility degree. Finally, the feasibility and validity of this method is verified through calculation example analysis.

Interval grey numbers based multi-attribute decision making method for supplier selection

Kybernetes ◽  
2014 ◽  
Vol 43 (7) ◽  
pp. 1064-1078 ◽  
Author(s):  
Naiming Xie ◽  
Jianghui Xin
Keyword(s):  
Decision Making ◽  
Supplier Selection ◽  
Decision Makers ◽  
Selection Problem ◽  
Content Type ◽  
Numerical Example ◽  
Possibility Degree ◽  
Multi Attribute Decision Making ◽  
Grey Number ◽  
Supplier Selection Problem

Purpose – The purpose of this paper is to study a novel grey possibility degree approach, which is combined with multi-attribute decision making (MADM) and applied MADM model for solving supplier selection problem under uncertainty information. Design/methodology/approach – The supplier selection problem is a typical MADM problem, in which information of a series of indexes should be aggregated. However, it is relatively easy for decision makers to define information in uncertainty, sometimes as a grey number, rather than a precise number. By transforming linguistic scale of rating supplier selection attributes into interval grey numbers, a novel grey MADM method is developed. Steps of proposed model were provided, and a novel grey possibility degree approach was proposed. Finally, a numerical example of supplier selection is utilized to demonstrate the proposed approach. Findings – The results show that the proposed approach could solve the uncertainty decision-making problem. A numerical example of supplier selection is utilized to demonstrate the proposed approach. The results show that the proposed method is useful to aggregate decision makers’ information so as to select the potential supplier. Practical implications – The approach constructed in the paper can be used to solving uncertainty decision-making problems that the certain value of the decision information could not collect while the interval value set could be defined. Obviously it can be utilized for other MADM problem. Originality/value – The paper succeeded in redefining interval grey number, constructing a novel interval grey number based MADM approach and providing the solution of the proposed approach. It is very useful to solving system forecasting problem and it contributed undoubtedly to improve grey decision-making models.

scholarly journals Generalized Fuzzy Soft Power Bonferroni Mean Operators and Their Application in Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 810
Author(s):  
Zitai Xu ◽  
Chunfang Chen ◽  
Yutao Yang
Keyword(s):  
Decision Making ◽  
Soft Power ◽  
Original Data ◽  
Decision Makers ◽  
Decision Making Process ◽  
Software Selection ◽  
Decision Method ◽  
Bonferroni Mean ◽  
Special Cases ◽  
Multi Attribute Decision Making

In decision-making process, decision-makers may make different decisions because of their different experiences and knowledge. The abnormal preference value given by the biased decision-maker (the value that is too large or too small in the original data) may affect the decision result. To make the decision fair and objective, this paper combines the advantages of the power average (PA) operator and the Bonferroni mean (BM) operator to define the generalized fuzzy soft power Bonferroni mean (GFSPBM) operator and the generalized fuzzy soft weighted power Bonferroni mean (GFSWPBM) operator. The new operator not only considers the overall balance between data and information but also considers the possible interrelationships between attributes. The excellent properties and special cases of these ensemble operators are studied. On this basis, the idea of the bidirectional projection method based on the GFSWPBM operator is introduced, and a multi-attribute decision-making method, with a correlation between attributes, is proposed. The decision method proposed in this paper is applied to a software selection problem and compared to the existing methods to verify the effectiveness and feasibility of the proposed method.

scholarly journals A New Linear Regression Kalman Filter with Symmetric Samples

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2139
Author(s):  
Xiuqiong Chen ◽  
Jiayi Kang ◽  
Mina Teicher ◽  
Stephen S.-T. Yau
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Particle Filter ◽  
Normal Distribution ◽  
Extended Kalman Filter ◽  
Nonlinear Filtering ◽  
Unscented Kalman Filter ◽  
Standard Normal Distribution ◽  
Leibler Divergence ◽  
Standard Normal

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.

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