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Decision makers often express their evaluations on decision problems with multi-granular linguistic terms. This fact leads to the unification of the multi-granular linguistic terms into a single linguistic set in the literature. However, this unification process increases the complexity of computation and the subjectivity in the determination of transformation functions. To overcome this deficiency, this paper aims to develop a normalized numerical scaling method for determining the semantics of multi-granular linguistic terms in the same domain. We first introduce a class of numerical scaling functions to generate several balanced or unbalanced linguistic sets. Since these scaled linguistic sets have different domains, we then develop a normalized numerical scaling method to form them into the unique interval [0,1]. As a result of this development, two classes of normalized scaling functions are derived from the priori scale information and applications of piecewise linear interpolation and piecewise arc interpolation. Finally, an example is given to illustrate how the method works. [ABSTRACT FROM AUTHOR]

A new method is proposed to solve multiple criteria group decision making (MCGDM) problems, in which both the criteria values and criteria weights take the form of linguistic information, and the information about linguistic criteria weights is partly known or completely unknown. Firstly, to get reasonable decision result, instead of assigning the same weight to the decision maker (DM) for all criteria, we propose a method to determine the weight of DM with respect to each criterion under linguistic environment by calculating the similarity degree between individual 2-tuple linguistic evaluation value and the mean given by all decision makers (DMs). Secondly, for the situations where the information about the criteria weights is partly known or completely unknown, we establish optimization models to determine the criteria weights by defining 2-tuple linguistic positive ideal solution (TL-PIS), 2-tuple linguistic right negative ideal solution (TL-RNIS) and 2-tuple linguistic left negative ideal solution (TL-LNIS) of the collective 2-tuple linguistic decision matrix. Thirdly, we propose a new method to solve MCGDM problems with partly known or completely unknown linguistic weight information. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method. [ABSTRACT FROM AUTHOR]

In order to successfully realize the stable and sustainable execution of supply chain for complex product, it is important to improve the performance evaluation mechanism for suppliers of complex product Owing to the complexity of performance evaluation for complex product suppliers and the fact that expert's grasping degree for evaluation attribute information is not adequate and different, a linguistic evaluation approach of supplier performance for complex product was proposed in this study via taking grey information into account Firstly, the evaluation information of experts was transformed into a combination of grey information and two-tuple linguistic, and the degree of greyness was applied to measure the grey part of linguistic evaluation information. Then the geometric means of grey-levels of linguistic evaluation information corresponding to each expert was computed to adjust experts' weights on each index, thus the expert s evaluating viewpoints were gathered to obtain the rating and weight for each index as a result of group evaluation. Based on that, weighted averaging operator was utilized to integrate the group evaluation information to get the comprehensive evaluation result for suppliers' performance, and the ranking of each supplier was gained through constructing quadratic function. Finally, this method was applied to evaluate the supplier performance in a large passenger aircraft project, and the information loss and distortion emerging in collecting and calculating linguistic evaluation information could be effectively avoided. Thus, the proposed approach was able to provide decision makers richer and more accurate information. [ABSTRACT FROM AUTHOR]