A mixed 0-1 programming approach for multiple attribute strategic weight manipulation based on uncertainty theory

In practical multiple attribute decision making (MADM) problems, the interest groups or individuals intentionally set attribute weights to achieve their own benefits. In this case, the rankings of different alternatives are changed strategically, which is called the strategic weight manipulation in MADM. Sometimes, the attribute values are given with imprecise forms. Several theories and methods have been developed to deal with uncertainty, such as probability theory, interval values, intuitionistic fuzzy sets, hesitant fuzzy sets, etc. In this paper, we study the strategic weight manipulation based on the belief degree of uncertainty theory, with uncertain attribute values obeying linear uncertain distributions. It allows the attribute values to be considered as a whole in the operation process. A series of mixed 0-1 programming models are constructed to set a strategic weight vector for a desired ranking of a particular alternative. Finally, an example based on the assessment of the performance of COVID-19 vaccines illustrates the validity of the proposed models. Comparison analysis shows that, compared to the deterministic case, it is easier to manipulate attribute weights when the attribute values obey the linear uncertain distribution. And a further comparative analysis highlights the performance of different aggregation operators in defending against the strategic manipulation, and highlights the impacts on ranking range under different belief degrees.

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New Distance Measures for Dual Hesitant Fuzzy Sets and Their Application to Multiple Attribute Decision Making

Symmetry ◽

10.3390/sym12020191 ◽

2020 ◽

Vol 12 (2) ◽

pp. 191

Author(s):

Wang ◽

Li ◽

Zhang ◽

Han

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Fuzzy Set ◽

Intuitionistic Fuzzy Set ◽

Multiple Attribute Decision Making ◽

Distance Measures ◽

Hesitant Fuzzy Set ◽

Hesitant Fuzzy Sets ◽

Attribute Weights ◽

Multiple Attribute

Multiple attribute decision making (MADM) is full of uncertainty and vagueness due to intrinsic complexity, limited experience and individual cognition. Representative decision theories include fuzzy set (FS), intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) and so on. Compared with IFS and HFS, DHFS has more advantages in dealing with uncertainties in real MADM problems and possesses good symmetry. The membership degrees and non-membership degrees in DHFS are simultaneously permitted to represent decision makers’ preferences by a given set having diverse possibilities. In this paper, new distance measures for dual hesitant fuzzy sets (DHFSs) are developed in terms of the mean, variance and number of elements in the dual hesitant fuzzy elements (DHFEs), which overcomes some deficiencies of the existing distance measures for DHFSs. The proposed distance measures are effectively applicable to solve MADM problems where the attribute weights are completely unknown. With the help of the new distance measures, the attribute weights are objectively determined, and the closeness coefficients of each alternative can be objectively obtained to generate optimal solution. Finally, an evaluation problem of airline service quality is conducted by using the distance-based MADM method to demonstrate its validity and applicability.

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MODELS FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH INTUITIONISTIC FUZZY INFORMATION

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488507004686 ◽

2007 ◽

Vol 15 (03) ◽

pp. 285-297 ◽

Cited By ~ 142

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.

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Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting

Journal of Intelligent Systems ◽

10.1515/jisys-2018-0099 ◽

2018 ◽

Vol 29 (1) ◽

pp. 858-876 ◽

Cited By ~ 8

Author(s):

Muhammad Sajjad Ali Khan ◽

Saleem Abdullah ◽

Peide Lui

Keyword(s):

Decision Making ◽

Choquet Integral ◽

Weight Vector ◽

Multiple Attribute Decision Making ◽

Gray Relational Analysis ◽

Ideal Solution ◽

Attribute Weights ◽

Multiple Attribute ◽

Negative Ideal Solution ◽

Magdm Problems

Abstract In this study, we developed an approach to investigate multiple attribute group decision-making (MAGDM) problems, in which the attribute values take the form of Pythagorean fuzzy numbers whose information about attribute weights is incompletely known. First, the Pythagorean fuzzy Choquet integral geometric operator is utilized to aggregate the given decision information to obtain the overall preference value of each alternative by experts. In order to obtain the weight vector of the criteria, an optimization model based on the basic ideal of the traditional gray relational analysis method is established, and the calculation steps for solving Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of gray relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of gray relation to both the positive-ideal solution and negative-ideal solution simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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Assessment of E-learning System in Higher Education Based on Hesitant Fuzzy Information with Incomplete Attribute Weights

International Journal of Emerging Technologies in Learning (iJET) ◽

10.3991/ijet.v10i8.5217 ◽

2015 ◽

Vol 10 (8) ◽

pp. 34 ◽

Cited By ~ 2

Author(s):

Hong Ye

Keyword(s):

Higher Education ◽

Decision Making ◽

Weight Vector ◽

Multiple Attribute Decision Making ◽

Learning System ◽

Hesitant Fuzzy Set ◽

Attribute Weights ◽

Multiple Attribute ◽

E Learning ◽

Weight Method

With the development of information technology, colleges and universities around the world are constructing E-learning system to meet their students' and faculty's needs. E-learning can effectively help students to learn varieties of knowledge and even skills they want to obtain. Therefore, the efficiency of E-learning system is important to popularize and develop it. Then, in this paper, we investigate to propose a method to evaluate E-learning system in higher education based on some criteria. Hereinto, this assessment problem can be considered as a multiple attribute decision making (MADM) problem. Thus, TOPSIS method, as a popular multiple attribute decision making method, is introduced in this paper to solve this assessment problem. In MADM problem, how to acquire preference of the decision maker is critical. In order to solve this issue, hesitant fuzzy set is developed in this paper. Weight vector, as a balance to weight the importance of different attributes, is hard to obtain. Then, a new fuzzy weight method is proposed to determine attribute weights. Finally, a case study is demonstrated to verify the applicability of this method.

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