<p>Double hierarchy linguistic term set is an innovative linguistic expression tool, its unique two-tiered structure that enables the description of complex linguistic terms. Despite its innovative approach, the tool encounters limitations, one is its ineffectiveness in capturing the degree of hesitation, or the degree of both hesitation and fuzziness in linguistic descriptions. Another is that the evaluations based on this tool always have varying lengths and cannot be compared effectively. Addressing these shortcomings, this study proposes the probability double hierarchy hesitant fuzzy linguistic term set, which introduce the probability information to describe the degree of hesitation, or the degree of both hesitation and fuzziness. In addition, a simple, yet effective adjustment method is proposed to handle a situation that the number of linguistic variables terms included in the evaluations always varies. Building on this novel adjustment method, measurements such as distance measure and correlation coefficient were proposed. A weight-derived method based on the correlation coefficient is also proposed to determine the weights of the criteria. Subsequently, a case of selecting the optimal multi-sensor information scheme for RV reducer was evaluated by the PDHHFLTS and sorted by the PDHHFL-MULTIMOORA method.</p>

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Probability Double Hierarchy Hesitant Fuzzy Linguistic Term Set and Its Application in MCDM Problem

  • Guofa Li,
  • Chao Liu,
  • Jialong He,
  • Yuan Zhong,
  • Tianzhe Wang

摘要

Double hierarchy linguistic term set is an innovative linguistic expression tool, its unique two-tiered structure that enables the description of complex linguistic terms. Despite its innovative approach, the tool encounters limitations, one is its ineffectiveness in capturing the degree of hesitation, or the degree of both hesitation and fuzziness in linguistic descriptions. Another is that the evaluations based on this tool always have varying lengths and cannot be compared effectively. Addressing these shortcomings, this study proposes the probability double hierarchy hesitant fuzzy linguistic term set, which introduce the probability information to describe the degree of hesitation, or the degree of both hesitation and fuzziness. In addition, a simple, yet effective adjustment method is proposed to handle a situation that the number of linguistic variables terms included in the evaluations always varies. Building on this novel adjustment method, measurements such as distance measure and correlation coefficient were proposed. A weight-derived method based on the correlation coefficient is also proposed to determine the weights of the criteria. Subsequently, a case of selecting the optimal multi-sensor information scheme for RV reducer was evaluated by the PDHHFLTS and sorted by the PDHHFL-MULTIMOORA method.