Computational method for monotonic hesitant fuzzy linguistic terms by fitting Weibull distribution function concerns explicit and implicit appraisal information

Abstract

Natural monotonic linguistic language is widely used to express experts’ uncertain subjective appraisal opinion, such as “More than”, “At least”, “Less than” and “At most”, which reveals explicit information about performance range and implicit information about his hiding preference on a linguistic scale. A novel computational method for monotonic hesitant fuzzy linguistic terms is developed to transfer experts’ uncertain appraisal information to decision-making data, which can systematically consider and mine expert’s obvious explicit and hidden implicit appraisal information. Specially, the comprehensive meanings of monotone decreasing and increasing hesitant fuzzy linguistic terms are investigated, in which both explicit and implicit appraisal information are explored to reveal its actual meaning. Additionally, Weibull distribution functions with three parameters are fitted considering the comprehensive meaning of monotone increasing appraisals, which is determined by a multi-objective programming model following ABC classification method. Symmetry principle is employed to confirm the expression of monotone decreasing appraisals, which are transferring from monotone increasing appraisals with same length of domain field. Moreover, feasibility analysis is explored to show the influence of parameters on decision-making precision. Finally, a numerical study is conducted to show the feasibility and advantage of the new method, which can effectively improve the precision of computational transfer by comparing to previous method.