Abstract
A hesitant intuitionistic fuzzy linguistic set (HIFLS) that integrates both qualitative and quantitative evaluations is an extension of the linguistic set, intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS) and hesitant intuitionistic fuzzy set (HIFS). It can describe the qualitative evaluation information given by the decision-makers (DMs) and reflect their uncertainty. In this article, we defined some new operational laws and comparative method for HIFLSs. Then, based on these operations, we propose two prioritized aggregation (PA) operators for HIFLSs: prioritized weighted averaging operator for HIFLSs (HIFLPWA) and prioritized weighted geometric operator for HIFLSs (HIFLPWG). Based on these aggregation operators, an approach for multi-attribute decision-making (MADM) is developed under the environment of HIFLSs. Finally, a practical example is given to show the practicality and effectiveness of the developed approach by comparing with the other representative methods.
Highlights
One of the most important research topics is multi-attribute decision-making (MADM) which can select the best alternative according to multiple influential attributes [1,2,3] Generally, the decision-makers (DMs) use crisp numbers to manifest their preferences about the alternative in traditional MADM problems
There is a set of alternatives denoted by {m1, m2, . . . , mk }, and the DMs gave the evaluation value of the attribute cj for alternative mi by the HIFLN c j, (i = 1, 2, . . . , k, j = 1, 2, . . . , g)
Considering the shortcomings in the existing studies, we proposed some new operational laws of HIFLNs based on the linguistic scale function (LSF) which provided a flexible way to express the qualitative evaluation information given by the DMs, and we presented a new score function, accuracy function and comparative method for the HIFLNs
Summary
One of the most important research topics is multi-attribute decision-making (MADM) which can select the best alternative according to multiple influential attributes [1,2,3] Generally, the decision-makers (DMs) use crisp numbers to manifest their preferences about the alternative in traditional MADM problems. It is insufficient to depict complete information due to lack of comprehensive and systematic knowledge. To deal with such cases, Torra [8] made an extension of the FSs and proposed the concept of hesitant fuzzy set (HFS).
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