A Normalized Numerical Scaling Method for the Unbalanced Multi-Granular Linguistic Sets

作者：Wang Baoli; Liang Jiye^*; Qian Yuhua

来源：International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2015, 23(2): 221-243.

DOI：10.1142/S0218488515500099

• Unbalanced
• multi-granular linguistic sets
• normalized scaling function
• piecewise interpolation
• 2-tuple linguistic

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.

• 出版日期2015-4
• 单位山西大学; 运城学院; 太原师范学院