Linguistic q-rung orthopair fuzzy sets and their interactional partitioned Heronian mean aggregation operators
Linguistic q-rung orthopair fuzzy sets and their interactional partitioned Heronian mean aggregation operators
复制标题
语言 q-rung 正交模糊集及其交互划分 Heronian 均值聚合算子
DOI：
10.1002/int.22136
复制
发表时间：
2020-02-01
影响因子：
7
通讯作者：
Chen, Lifei
中科院分区：
文献类型：
--
作者：
Lin, Mingwei;Li, Xinmei;Chen, Lifei
语言直觉模糊集（LIFS）和语言勾股模糊集（LPFSs）是两种语言正射模糊集，它们的隶属度是从预定义的语言项集（LTS）中选取的语言项对。一个语言术语表示隶属度（MD），而另一个则表示非隶属度（NMD）。在每个LIFS中，MD和NMD的下标之和小于LTS的基数。在LPFS中，MD和NMD的下标的平方和小于LTS的基数的平方。本文提出了这两种语言正射模糊集的一般形式，称之为语言q-横档正射模糊集。在此基础上，提出了语言q阶正射模糊加权平均（LqROFWA）算子和语言q阶正射模糊加权几何（LqROFWG）算子，用于集结语言q阶正射模糊数（LqROFN）.在此基础上，给出了考虑不同LqROFN的MD和NMD相互作用的新的互操作律。分块几何Heronian均值（PGHM）算子可以有效地解决同一类中属性之间存在关联，而不同类中属性之间不存在关联的决策问题。基于这些新的运算律和PGHM算子，提出了语言q阶正射模糊插值PGHM（LqROFIPGHM）算子和语言q阶正射模糊插值加权PGHM（LqROFIWPGHM）算子，并讨论了它们的性质.基于LqROFIWPGHM算子，给出了一种有效的多属性群决策模型，用于处理语言q-横档正射模糊信息.最后，通过一些算例验证了插值运算律和LqROFIWPGHM算子的优越性.
The linguistic intuitionistic fuzzy sets (LIFSs) and linguistic Pythagorean fuzzy sets (LPFSs) are two linguistic orthopair fuzzy sets whose membership grades are pairs of linguistic terms from the predefined linguistic term sets (LTSs). One linguistic term indicates the membership degree (MD), while the other one gives the nonmembership degree (NMD). In each LIFS, the sum of the subscripts of MD and NMD is less than the cardinality of LTS. In the LPFSs, the sum of the squares of the subscripts of MD and NMD is less than the square of the cardinality of LTS. In this paper, we propose a general form of these two linguistic orthopair fuzzy sets, which can be named linguistic q‐rung orthopair fuzzy sets. We devise the operational laws, based on which, the linguistic q‐rung orthopair fuzzy weighted averaging (LqROFWA) operator and linguistic q‐rung orthopair fuzzy weighted geometric (LqROFWG) operator are developed to aggregate the linguistic q‐rung orthopair fuzzy numbers (LqROFNs). Then, the novel interactional operational laws that consider the interactions between the MD and NMD from different LqROFNs are given. The partitioned geometric Heronian mean (PGHM) operator can effectively solve the decision‐making problems in which the attributes grouped into the same clusters have interrelationships and the attributes belonging to different clusters have no interrelationship. Based on these novel operational laws and PGHM operator, the linguistic q‐rung orthopair fuzzy interactional PGHM (LqROFIPGHM) operator and linguistic q‐rung orthopair fuzzy interactional weighted PGHM (LqROFIWPGHM) operator are proposed and their properties are discussed. Based on the LqROFIWPGHM operator, an efficient multiattribute group decision‐making model is given to deal with the linguistic q‐rung orthopair fuzzy information. Finally, the superiorities of the interactional operational laws and LqROFIWPGHM operator are tested using some illustrative examples.