Abstract
For solving the discrete linguistic stochastic multiple criteria decision making problems with incomplete information, a new decision making method based on the differences between the superiorities and the inferiorities is proposed. According to the two basic parameters which are the possible outcome and the state probability, the superior decision matrix and the inferior decision matrix of the alternative set under each criterion are first worked out. Then, by the differences between the elements on the appropriate locations of these matrices, the corresponding dominant decision matrices are formed. Subsequently, with the help of the weight vector of the criterion set, the weighted integrated dominant decision matrix of the alternative set is built. Consequently, the weighted integrated dominant indices' sum of each alternative is calculated. Thus, the rank of the alternatives comes out. Finally, a numerical example is given. The result shows the superiority of the method.
Highlights
Due to the complexity of the things, the uncertainty of the environment, and the limitation of the ability, people usually have difficulty in describing the cognitive objects in the precise numerical values
A MCDM problem is defined on a set of the alternatives from which a decision maker has to select the optimal alternative according to some criteria
The possibility degree of a5 ≻ a3 is only 0.5003 in the possibility degree matrix. All this shows that the first method has the excellent performances
Summary
Due to the complexity of the things, the uncertainty of the environment, and the limitation of the ability, people usually have difficulty in describing the cognitive objects in the precise numerical values. Wang and Feng [48] considered the fuzziness and the randomness of the criterion values represented by the linguistic evaluation terms and attempted to use a cloud model to solve the multiple criteria and group decision making problems. They did not analyze a numerical example to verify the validity and the feasibility of the method. The expected value, the variance, the probability distribution function, and the probability density function derive from the consideration Based on this idea, the paper discusses a discrete LSMCDM problem with state probabilities and criterion weights represented by interval numbers. The discussion about the proposed method is conducted in the last section
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