Hesitant Fuzzy Multiple Criteria Decision Making Methods with Incomplete Weight Information

2016 ◽  
pp. 169-219
Author(s):  
Huchang Liao ◽  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Incomplete Weight ◽  
Incomplete Weight Information

scholarly journals Extension of Axiomatic Design Method for Fuzzy Linguistic Multiple Criteria Group Decision Making with Incomplete Weight Information

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Ming Li
Keyword(s):  
Decision Making ◽  
Information Content ◽  
Group Decision Making ◽  
Group Decision ◽  
Axiomatic Design ◽  
Weight Vector ◽  
Multiple Criteria ◽  
Incomplete Weight ◽  
Incomplete Weight Information ◽  
Fuzzy Linguistic

Axiomatic design (AD) provides a framework to describe design objects and a set of axioms to evaluate relations between intended functions and means by which they are achieved. It has been extended to evaluate alternatives in engineering under fuzzy environment. With respect to multiple criteria group decision making (MCDM) with incomplete weight information under fuzzy linguistic environment, a new method is proposed. In the method, the fuzzy axiomatic design based on triangle representation model is used to aggregate the linguistic evaluating information. In order to get the weight vector of the criteria, we establish a nonlinear optimization model based on the basic ideal of fuzzy axiomatic design (FAD), by which the criteria weights can be determined. It is based on the concept that the optimal alternative should have the least weighted information content. Then, the weighted information content is derived by summing weighted information content for each criterion. The alternative that has the least total weighted information content is the best. Finally, a numerical example is used to illustrate the availability of the proposed method.

scholarly journals A New Grey Approach for Using SWARA and PIPRECIA Methods in a Group Decision-Making Environment

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1554
Author(s):  
Dragiša Stanujkić ◽  
Darjan Karabašević ◽  
Gabrijela Popović ◽  
Predrag S. Stanimirović ◽  
Muzafer Saračević ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Multiple Criteria Decision Making ◽  
Grey System Theory ◽  
Multiple Criteria ◽  
Decision Making Process ◽  
Grey System ◽  
Criteria Weights

The environment in which the decision-making process takes place is often characterized by uncertainty and vagueness and, because of that, sometimes it is very hard to express the criteria weights with crisp numbers. Therefore, the application of the Grey System Theory, i.e., grey numbers, in this case, is very convenient when it comes to determination of the criteria weights with partially known information. Besides, the criteria weights have a significant role in the multiple criteria decision-making process. Many ordinary multiple criteria decision-making methods are adapted for using grey numbers, and this is the case in this article as well. A new grey extension of the certain multiple criteria decision-making methods for the determination of the criteria weights is proposed. Therefore, the article aims to propose a new extension of the Step-wise Weight Assessment Ratio Analysis (SWARA) and PIvot Pairwise Relative Criteria Importance Assessment (PIPRECIA) methods adapted for group decision-making. In the proposed approach, attitudes of decision-makers are transformed into grey group attitudes, which allows taking advantage of the benefit that grey numbers provide over crisp numbers. The main advantage of the proposed approach in relation to the use of crisp numbers is the ability to conduct different analyses, i.e., considering different scenarios, such as pessimistic, optimistic, and so on. By varying the value of the whitening coefficient, different weights of the criteria can be obtained, and it should be emphasized that this approach gives the same weights as in the case of crisp numbers when the whitening coefficient has a value of 0.5. In addition, in this approach, the grey number was formed based on the median value of collected responses because it better maintains the deviation from the normal distribution of the collected responses. The application of the proposed approach was considered through two numerical illustrations, based on which appropriate conclusions were drawn.

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