scholarly journals A Distance Model of Intuitionistic Fuzzy Cross Entropy to Solve Preference Problem on Alternatives

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Mei Li ◽  
Chong Wu
Keyword(s):  
Decision Making ◽  
Correlation Analysis ◽  
Distance Measure ◽  
Multiple Attribute Decision Making ◽  
Cross Entropy ◽  
Grey Correlation ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Grey Correlation Analysis

In the field of decision-making, for the multiple attribute decision-making problem with the partially unknown attribute weights, the evaluation information in the form of the intuitionistic fuzzy numbers, and the preference on alternatives, this paper proposes a comprehensive decision model based on the intuitionistic fuzzy cross entropy distance and the grey correlation analysis. The creative model can make up the deficiency that the traditional intuitionistic fuzzy distance measure is easy to cause the confusion of information and can improve the accuracy of distance measure; meanwhile, the grey correlation analysis method, suitable for the small sample and the poor information decision-making, is applied in the evaluation. This paper constructs a mathematical optimization model of maximizing the synthesis grey correlation coefficient between decision-making evaluation values and decision-makers’ subjective preference values, calculates the attribute weights with the known partial weight information, and then sorts the alternatives by the grey correlation coefficient values. Taking venture capital firm as an example, through the calculation and the variable disturbance, we can see that the methodology used in this paper has good stability and rationality. This research makes the decision-making process more scientific and further improves the theory of intuitionistic fuzzy multiple attribute decision-making.

scholarly journals A New Multi-Attribute Emergency Decision-Making Algorithm Based on Intuitionistic Fuzzy Cross-Entropy and Comprehensive Grey Correlation Analysis

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 768
Author(s):  
Ping Li ◽  
Ying Ji ◽  
Zhong Wu ◽  
Shao-Jian Qu
Keyword(s):  
Decision Making ◽  
Correlation Analysis ◽  
Cross Entropy ◽  
Analysis Algorithm ◽  
Grey Correlation ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Grey Correlation Analysis ◽  
Emergency Decision Making ◽  
Emergency Decision

Intuitionistic fuzzy distance measurement is an effective method to study multi-attribute emergency decision-making (MAEDM) problems. Unfortunately, the traditional intuitionistic fuzzy distance measurement method cannot accurately reflect the difference between membership and non-membership data, where it is easy to cause information confusion. Therefore, from the intuitionistic fuzzy number (IFN), this paper constructs a decision-making model based on intuitionistic fuzzy cross-entropy and a comprehensive grey correlation analysis algorithm. For the MAEDM problems of completely unknown and partially known attribute weights, this method establishes a grey correlation analysis algorithm based on the objective evaluation value and subjective preference value of decision makers (DMs), which makes up for the shortcomings of traditional model information loss and greatly improves the accuracy of MAEDM. Finally, taking the Wenchuan Earthquake on May 12th 2008 as a case study, this paper constructs and solves the ranking problem of shelters. Through the sensitivity comparison analysis, when the grey resolution coefficient increases from 0.4 to 1.0, the ranking result of building shelters remains stable. Compared to the traditional intuitionistic fuzzy distance, this method is shown to be more reliable.

scholarly journals Algorithms Based on COPRAS and Aggregation Operators with New Information Measures for Possibility Intuitionistic Fuzzy Soft Decision-Making

2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Harish Garg ◽  
Rishu Arora
Keyword(s):  
Decision Making ◽  
Distance Measure ◽  
Score Function ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Soft Decision ◽  
Information Measures ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

The objective of this paper is to present novel algorithms for solving the multiple attribute decision-making problems under the possibility intuitionistic fuzzy soft set (PIFSS) information. The prominent characteristics of the PIFSS are that it considers the membership and nonmembership degrees of each object during evaluation and their corresponding possibility degree. Keeping these features, this paper presents some new operation laws, score function, and comparison laws between the pairs of the PIFSSs. Further, we define COmplex PRoportional ASsessment (COPRAS) and weighted averaging and geometric aggregation operators to aggregate the PIFSS information into a single one. Later, we develop two algorithms based on COPRAS and aggregation operators to solve decision-making problems. In these approaches, the experts and the weights of the parameters are determined with the help of entropy and the distance measure to remove the ambiguity in the information. Finally, a numerical example is given to demonstrate the presented approaches.

Cross-Entropy of Dual Hesitant Fuzzy Sets for Multiple Attribute Decision-Making

2016 ◽  
Vol 8 (3) ◽  
pp. 20-30 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multiple Attribute Decision Making ◽  
Cross Entropy ◽  
Entropy Measure ◽  
Fuzzy Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
The Cross

This paper proposes a cross-entropy measure between dual hesitant fuzzy sets (DHFSs) as an extension of the cross-entropy measures of intuitionistic fuzzy sets. Then the cross-entropy measure between DHFSs is applied to multiple attribute decision making under dual hesitant fuzzy environments. Through the weighted cross-entropy measure between each alternative and the ideal alternative, we can obtain the ranking order of all alternatives and the best one. The decision-making method based on the cross-entropy measure of DHFSs can deal with dual hesitant fuzzy multiple attribute decision making problems and can automatically take into account much more information than existing hesitant (or intuitionistic) fuzzy decision-making methods and the differences of the evaluation data given by different experts or decision makers. Finally, a practical example about investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

scholarly journals Extended TODIM Method for MADM Problem under Trapezoidal Intuitionistic Fuzzy Environment

2019 ◽  
Vol 14 (2) ◽  
pp. 220-232 ◽  
Author(s):  
Haiping Ren ◽  
Manfeng Liu ◽  
Hui Zhou
Keyword(s):  
Decision Making ◽  
Distance Measure ◽  
Multiple Attribute Decision Making ◽  
Decision Making Process ◽  
Final Decision ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Psychological Behavior ◽  
Multiple Attribute ◽  
Todim Method

In actual decision making process, the final decision result is often affected by decision maker’s psychological behavior, however, for the multiple attribute decision making (MADM) problem in which attributes values are expressed with trapezoidal intuitionistic fuzzy numbers (TIFNs), there is few literature considering the decision maker's behavior factors in decision making process. For this case, this paper first proposes a new distance measure of TIFNs and a new ranking method which considers decision maker’s attitude behavior, and then develops an extended TODIM decision making method. Finally an example is given to illustrate the validity and practicability of the proposed method.

MODELS FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH INTUITIONISTIC FUZZY INFORMATION

2007 ◽  
Vol 15 (03) ◽  
pp. 285-297 ◽  
Author(s):  
Z. S. XU
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Information ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by Atanassov [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems 20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy Sets", Information and Control 8 (1965) 338–353] to deal with fuzziness and uncertainty. In this paper, we investigate the multiple attribute decision making (MADM) problems, in which the information about attribute weights is incomplete, and the attribute values are expressed in intuitionistic fuzzy numbers (IFNs). We first define the concept of intuitionistic fuzzy ideal solution (IFIS), and then, based on the IFIS and the distance measure, we establish some optimization models to derive the attribute weights. Furthermore, based on the developed models, we develop some procedures for the rankings of alternatives under different situations, and extend the developed models and procedures to handle the MADM problems with interval-valued intuitionistic fuzzy information. Finally, we give some illustrative examples to verify the effectiveness and practicability of the developed models and procedures.

An Integrated Approach to Index Weight Based on Improved D-S Evidence Theory and Application of the Product Solution Evaluation

2013 ◽  
Vol 834-836 ◽  
pp. 1654-1658
Author(s):  
Er Tian Hua ◽  
Wei Han ◽  
Da Qiang Chen ◽  
Jian Zhang
Keyword(s):  
Correlation Analysis ◽  
Evidence Theory ◽  
Integrated Approach ◽  
Multiple Attribute Decision Making ◽  
Combination Rules ◽  
Weighting Method ◽  
Grey Correlation ◽  
Multiple Attribute ◽  
Grey Correlation Analysis ◽  
Product Solution

To overcome the defect of the traditional method to determine attribute weight in the multiple attribute decision making problems, this paper proposed a kind of data fusion method based on The D-S Evidence Theory improved by The Grey Correlation Analysis. The method, firstly, calculated the basic probability assignment functions discount factor based on The Grey Correlation Analysis, then let the subjective weight and objective weight together based on D-S combination rules in order to avoid the deficiency of the single weighting method. Using the fusion of evaluation indexs subjective and objective weight of mobile phone product solution as an example, the results show that the proposed method is effective.

scholarly journals An Entropy-Based Knowledge Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application to Multiple Attribute Decision Making

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 981 ◽  
Author(s):  
Gang Wang ◽  
Jie Zhang ◽  
Yafei Song ◽  
Qiang Li
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Degree ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Knowledge Measure ◽  
Multiple Attribute ◽  
New Knowledge ◽  
Atanassov’S Intuitionistic Fuzzy Sets

As the complementary concept of intuitionistic fuzzy entropy, the knowledge measure of Atanassov’s intuitionistic fuzzy sets (AIFSs) has attracted more attention and is still an open topic. The amount of knowledge is important to evaluate intuitionistic fuzzy information. An entropy-based knowledge measure for AIFSs is defined in this paper to quantify the knowledge amount conveyed by AIFSs. An intuitive analysis on the properties of the knowledge amount in AIFSs is put forward to facilitate the introduction of axiomatic definition of the knowledge measure. Then we propose a new knowledge measure based on the entropy-based divergence measure with respect for the difference between the membership degree, the non-membership degree, and the hesitancy degree. The properties of the new knowledge measure are investigated in a mathematical viewpoint. Several examples are applied to illustrate the performance of the new knowledge measure. Comparison with several existing entropy and knowledge measures indicates that the proposed knowledge has a greater ability in discriminating different AIFSs and it is robust in quantifying the knowledge amount of different AIFSs. Lastly, the new knowledge measure is applied to the problem of multiple attribute decision making (MADM) in an intuitionistic fuzzy environment. Two models are presented to determine attribute weights in the cases that information on attribute weights is partially known and completely unknown. After obtaining attribute weights, we develop a new method to solve intuitionistic fuzzy MADM problems. An example is employed to show the effectiveness of the new MADM method.

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