scholarly journals A Novel MADM Approach Based on Fuzzy Cross Entropy with Interval-Valued Intuitionistic Fuzzy Sets

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xin Tong ◽  
Liying Yu
Keyword(s):  
Fuzzy Sets ◽  
Programming Model ◽  
Intuitionistic Fuzzy Sets ◽  
Cross Entropy ◽  
Ideal Solution ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Relative Closeness ◽  
Multiple Attribute ◽  
Interval Valued

The paper presents a novel multiple attribute decision-making (MADM) approach for the problem with completely unknown attribute weights in the framework of interval-valued intuitionistic fuzzy sets (IVIFS). First, the fuzzy cross entropy and discrimination degree of IVIFS are defied. Subsequently, based on the discrimination degree of IVIFS, a nonlinear programming model to minimize the total deviation of discrimination degrees between alternatives and the positive ideal solution PIS as well as the negative ideal solution (NIS) is constructed to obtain the attribute weights and, then, the weighted discrimination degree. Finally, all the alternatives are ranked according to the relative closeness coefficients using the extended TOPSIS method, and the most desirable alternative is chosen. The proposed approach extends the research method of MADM based on the IVIF cross entropy. Finally, we illustrate the feasibility and validity of the proposed method by two examples.

scholarly journals AN INCLUSION COMPARISON APPROACH FOR MULTIPLE CRITERIA DECISION ANALYSIS BASED ON INTERVAL-VALUED INTUITIONISTIC FUZZY SETS

2015 ◽  
Vol 22 (3) ◽  
pp. 357-392 ◽  
Author(s):  
Ting-Yu CHEN
Keyword(s):  
Decision Analysis ◽  
Fuzzy Sets ◽  
Programming Model ◽  
Intuitionistic Fuzzy Sets ◽  
Multiple Criteria ◽  
Multiple Criteria Decision Analysis ◽  
Intuitionistic Fuzzy ◽  
Nonlinear Programming Model ◽  
Ranking Order ◽  
Interval Valued

The theory of interval-valued intuitionistic fuzzy sets provides an intuitive and feasible way of addressing uncertain and ambiguous properties. Many useful models and methods have been developed for multiple criteria decision analysis within the interval-valued intuitionistic fuzzy environment. In contrast to the elaborate existing methods, this paper establishes a simple and effective method for managing the sophisticated data expressed by interval-valued intuitionistic fuzzy sets. An inclusion comparison possibility defined on interval-valued intuitionistic fuzzy sets is proposed, and some important properties are investigated. Then, an inclusion-based index that considers positive and negative ideals is offered. Considering the maximal comprehensive inclusion-based indices, this paper constructs a linear programming model (for consistent information) and an integrated, nonlinear programming model (for inconsistent information) to estimate the criterion weights and the optimal ranking order of the alternatives under an incomplete preference structure. The feasibility of the proposed method is illustrated by a practical example of selecting a suitable bridge construction method, and a comparative analysis with other relevant methods is conducted to validate the effectiveness and applicability of the proposed methodology.

Entropy Analysis on Intuitionistic Fuzzy Sets and Interval-Valued Intuitionistic Fuzzy Sets and its Applications in Mode Assessment on Open Communities

2018 ◽  
Vol 22 (1) ◽  
pp. 147-155 ◽  
Author(s):  
Hang Tian ◽  
Jiaru Li ◽  
Fangwei Zhang ◽  
Yujuan Xu ◽  
Caihong Cui ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Entropy Measures ◽  
Interval Valued

This paper identifies four variables to reveal the internal mechanisms of the entropy measures on intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs). First, four variables are used to propose a pair of generalized entropy measures on IFSs and IVIFSs. Second, three specific entropy measures are put forward to illustrate the effectiveness of the generalized entropy measure functions. Third, a novel multiple attribute decision-making approach under an intuitionistic fuzzy environment is proposed. The superiority of the decision-making approach is that the weight values of the attributes are obtained by their related entropy measures. Finally, the performance of the proposed entropy regulations on IFSs and IVIFSs is illustrated through a mode assessment example on open communities.

Interval-Valued Intuitionistic Fuzzy Multi-Attribute Decision Making Based on Satisfactory Degree

2017 ◽  
pp. 49-71 ◽  
Author(s):  
Gao-Feng Yu ◽  
Deng-Feng Li ◽  
Jin-Ming Qiu
Keyword(s):  
Nonlinear Programming ◽  
Programming Model ◽  
Intuitionistic Fuzzy Sets ◽  
Ideal Solution ◽  
Satisfactory Degree ◽  
Intuitionistic Fuzzy ◽  
Nonlinear Programming Model ◽  
Multi Attribute Decision Making ◽  
Negative Ideal Solution ◽  
Interval Valued

The aim of this paper is to propose a satisfactory degree method by using nonlinear programming for solving multi-attribute decision making (MADM) problems in which ratings of alternatives on attributes is expressed via interval-valued intuitionistic fuzzy (IVIF) sets and preference information on attributes is incomplete. Concretely, a nonlinear programming model is firstly explored to determine the satisfactory degree which is the ratio of the square of the weight Euclidean distance between an alternative and the IVIF negative ideal solution (IVIFNIS) to the sum of the square of the weight Euclidean distance between the IVIF negative ideal solution (IVIFNIS) and the IVIF positive ideal solution (IVIFPIS). Another nonlinear programming model is also developed to obtain satisfactory intuitionistic fuzzy sets, and then the general satisfactory degrees of the satisfactory intuitionistic fuzzy sets are used to generate the ranking order of the alternatives. Finally, a real example is employed to verify the applicability of the proposed approach and illustrate its practicality and effectiveness.

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