Combination Weighting Method Based on Generalized Mahalanobis Distance and Weighting Relative Entropy

2014 ◽  
Vol 998-999 ◽  
pp. 1674-1677
Author(s):  
Feng Zhang ◽  
Zhen Hua Xie ◽  
Jiang Tao Cheng ◽  
Gao Lun Cui ◽  
Lin Li
Keyword(s):  
Relative Entropy ◽  
Mahalanobis Distance ◽  
Euclidean Distance ◽  
Weight Vector ◽  
Multiple Attribute Decision Making ◽  
Entropy Model ◽  
Weighting Method ◽  
New Approach ◽  
Multiple Attribute ◽  
Optimal Weight Vector

Aimed at combination weighting in multiple attribute decision making, a new approach for combining different weighting vectors is proposed. The proposed approach considers the randomicity of weights themselves and the consistency among weighting vectors, constructs a constrained weighted relative entropy model. Aimed at the disadvantage in the TOPSIS based on Euclidean distance, the TOPSIS based on Mahalanobis distance is adopted to solve the coefficients of optimal weight vector. Finally, an example is conducted and the results show the proposed approach is effective and is more reasonable than three other combination approaches.

A COMBINATION WEIGHTING ALGORITHM USING RELATIVE ENTROPY FOR DOCUMENT CLUSTERING

2014 ◽  
Vol 28 (03) ◽  
pp. 1453002 ◽  
Author(s):  
BO JI ◽  
YANGDONG YE ◽  
YU XIAO
Keyword(s):  
Relative Entropy ◽  
Document Clustering ◽  
Multiple Attribute Decision Making ◽  
Entropy Method ◽  
Data Object ◽  
Information Bottleneck ◽  
Subjective Weight ◽  
Multiple Attribute ◽  
Sequential Information ◽  
Relative Entropy Method

This paper proposes a combination weighting algorithm using relative entropy for document clustering. Combination weighting is widely used in multiple attribute decision making (MADM) problem. However, there exist two difficulties to hinder the applications of combination weighting on document clustering. First, combination weighting is based on the integration of subjective weighting and objective weighting. However, there are so many attributes in documents that the subjective weights which rely on manual annotation by experts are impracticable. Secondly, a document data object might contain hundreds or even thousands of features. It is an extremely time-consuming task to calculate the combination weights. To address the issues, we suggest to simplify the combination weighting by not distinguishing subjective weight and objective weight. Meanwhile, we choose relative entropy method to reduce running time. In our algorithm, we obtain a combination weight set with 14 combination forms. The experiments on real document data show that both on the AC/PR/RE measures and the mutual information (MI) measure, the proposed CWRE-sIB algorithm is superior to the original sequential information bottleneck (sIB) algorithm and a series of weighting-sIB algorithms, which are built by applying a single weighting scheme to the original sIB algorithm.

Model for Software Quality Evaluation with Fuzzy Information

2016 ◽  
Vol 13 (10) ◽  
pp. 7394-7398
Author(s):  
Yi-Ding Zhao ◽  
Zhi-Min Li ◽  
Xi-Guang Zhang
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Software Quality ◽  
Quality Evaluation ◽  
Multiple Attribute Decision Making ◽  
Triangular Fuzzy Number ◽  
Ideal Solution ◽  
Software Quality Evaluation ◽  
Relative Closeness ◽  
Multiple Attribute

To study the problem of multiple attribute decision making in which the decision making information values are triangular fuzzy number, a relative entropy decision making method for software quality evaluation is proposed. Then, according to the concept of the relative entropy, the relative closeness degree is defined to determine the ranking order of all alternatives by calculating the relative entropy to both the fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS) simultaneously. At last, a numerical example for software quality evaluation is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.

scholarly journals Relative Similarity Programming Model for Uncertain Multiple Attribute Decision-Making Objects and Its Application

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Zhili Huang ◽  
Qinglan Chen ◽  
Liu Chen ◽  
Qinyuan Liu
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Programming Model ◽  
Weight Vector ◽  
Multiple Attribute Decision Making ◽  
Triangular Fuzzy Number ◽  
Similarity Degree ◽  
Multiple Attribute ◽  
Model Algorithm ◽  
Relative Similarity

This paper is concerned with the uncertain multiattribute decision-making (UMADM) of which the attribute value is triangular fuzzy number. Firstly, the max-relative similarity degree and min-relative similarity degree of alternative decision-making objects are given based on the relative similarity degree of triangular fuzzy number, the advantage relation theories to comparative relative similarity degree of triangular fuzzy number are proposed, and some good properties, relations, and conclusions are derived. Secondly, in order to determine the attribute weight vector, a triangular fuzzy number-based decision-making object relative similarity programming model is established with the help of maximizing possibility degree algorithm rules in the cooperative game theory. Subsequently, by aggregating the comparison overall relative similarity degree values of all decision-making objects, we could pick over and sort the set of alternative objects and gather a new model algorithm for the relative similarity programming of triangular fuzzy number-based multiple attribute decision-making alternatives. Finally, an example is given to illustrate the feasibility and practicability of the model algorithm presented in this paper.

scholarly journals Decision-Maker’s Risk Preference Based Intuitionistic Fuzzy Multiattribute Decision-Making and Its Application in Robot Enterprises Investment

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Liandong Zhou ◽  
Qifeng Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Weight Vector ◽  
Multiple Attribute Decision Making ◽  
Decision Makers ◽  
Research Papers ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Fuzzy Weight

At present, the utilization of hesitation information of intuitionistic fuzzy numbers is insufficient in many methods which were proposed to solve the intuitionistic fuzzy multiple attribute decision-making problems. And also there exist some flaws in the intuitionistic fuzzy weight vector constructions in many research papers. In order to solve these insufficiencies, this paper defined three construction equations of weight vectors based on the risk preferences of decision-makers. Then we developed an intuitionistic fuzzy dependent hybrid weighted operator (IFDHW) and proposed an intuitionistic fuzzy multiattribute decision-making method. Finally, the effectiveness of this method is verified by a robot manufacturing investment example.

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