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An approach to multiplicative linguistic group decision making based on possibility degrees
Author(s) -
Xia Meimei,
Xu Zeshui
Publication year - 2018
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12222
Subject(s) - multiplicative function , degree (music) , consistency (knowledge bases) , reciprocal , preference , mathematics , group decision making , matrix (chemical analysis) , variable (mathematics) , group (periodic table) , mathematical economics , mathematical optimization , statistics , linguistics , discrete mathematics , mathematical analysis , philosophy , physics , materials science , organic chemistry , chemistry , political science , acoustics , law , composite material
In order to compare two uncertain multiplicative linguistic variables, a possibility degree formula has been developed and its properties are also studied. Then a possibility degree matrix (also considered as a reciprocal preference relation) is constructed to compare a collection of uncertain multiplicative linguistic variables. Two models are further provided to derive the priority vector from the possibility degree matrix based on the additive consistency and multiplicative consistency. Especially, if the parameters are assigned specific values, then the models reduce to the existing ones. A group decision making method has been developed to deal with the situations where the preferences on alternatives are expressed by uncertain multiplicative linguistic variables. In this method, the possibility degree matrix is first constructed, from which the priority of alternatives is obtained using the developed models. At the end, an example is given to illustrate the proposed method.