2型犹豫q阶三角不确定语言Schweizer-Sklar-Muirhead算子

Type-2 hesitant q-rung triangular uncertain linguistic Schweizer-Sklar-Muirhead operators

摘要

为了描述多属性决策问题中决策者们多层的犹豫性,本文结合犹豫模糊集、q阶三角犹豫模糊集和q阶犹豫模糊不确定语言集,提出2型犹豫q阶三角不确定语言集,定义了基于Schweizer-Sklar范数的模糊元的运算,证明运算的性质。为了有效处理评估属性之间相互关联的现实决策问题,将Muirhead平均算子推广至2型犹豫q阶三角不确定语言集,提出2型犹豫q阶三角不确定语言Schweizer-Sklar-Muirhead平均算子和加权Muirhead平均算子,并给出这些算子的计算公式和性质。最后,给出基于2型犹豫q阶三角不确定语言Muirhead平均算子的多属性决策方法,并进行算例分析。

Abstract

In order to describe the multi-layer hesitation of decision-makers in multi-attribute decision-making problems, the type-2 hesitant q-rung triangular uncertain linguistic set is defined by combining hesitant fuzzy set, q-rung triangular hesitant fuzzy set and q-rung hesitant fuzzy uncertain linguistic set. Based on the Schweizer-Sklar norm, the operation laws and properties of the type-2 hesitant q-rung triangular uncertain linguistic fuzzy elements are discussed. In addition, in order to better handle the practical problem with interrelated evaluation attributes, the Muirhead mean operator is extended to the type-2 hesitant q-rung triangular uncertain linguistic set, and the type-2 hesitant q-rung triangular uncertain linguistic Schweizer-Sklar-Muirhead mean operator and its weighted form are proposed. Moreover, the calculation formulae of the operators are given and their properties are discussed. Finally, a multi-attribute decision-making problem model based on the type-2 q-rung hesitant triangular fuzzy uncertain linguistic weighted Muirhead mean operator is established and further analyzed by a numerical example.

关键词

犹豫模糊集 / 2型犹豫q阶三角不确定语言集 / Muirhead平均算子 / 多属性决策

Key words

hesitant fuzzy set / type-2 hesitant q-rung triangular uncertain linguistic set / Muirhead mean operator / multi-attribute decision making

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基金资助

国家自然科学基金资助项目(12171386)