Dependent uncertain linguistic ordered weighted geometric operator

si ≤ s j ;.For example, S can be defined as
S = {s1 = extremely poor, s2 = very poor, s3 = poor, s4 = medium, s5 = good, s6 = very good , s7 = extremely good}
b Department of Mathematics, North Sichuan Medical College, Nanchong, China (637007)
E-mail：weiguiwu@
Abstract With respect to multiple attribute group decision making problem with uncertain linguistic information, in which the attribute weights and expert weights take the form of real numbers, and the attribute preference values take the form of uncertain linguistic variables, we develop a new dependent uncertain linguistic OWG (DULOWG) operator based on DUOWG operator in uncertain linguistic setting, and study some of its desirable properties. The prominent characteristic of this dependent uncertain linguistic OWG operator is that it can relieve the influence of unfair arguments on the aggregated results. Finally, we give an example to illustrate the developed operator. Keywords: Group decision making; ordered weighted averaging (OWA) operators; ordered weighted geometric (OWG)operators; dependent uncertain linguistic ordered weighted geometric (DULOWG) operators; uncertain linguistic variables
call sa the original linguistic term, otherwise, we call sa the virtual linguistic term. In general, the
decision maker uses the original linguistic term to evaluate attributes aቤተ መጻሕፍቲ ባይዱd alternatives, and the virtual
To preserve all the given information, we extend the discrete term set S to a continuous term set
{ } S = sa s1 ≤ sa ≤ sq , a ∈[1, q] , where q is a sufficiently large positive integer. If sa ∈ S , then we
(1) The method based on extension principle, which makes operations on the fuzzy numbers that support the semantics of the linguistic terms [19]. (2) The method based on symbols, which makes computations on the indexes of the linguistic terms [20]. (3) The method based on fuzzy linguistic representation model, which composed by a linguistic term and a number [21-23]. (4) The method, which computes with words directly [24-42]. Sometimes, however, the decision makers are willing or able to provide only uncertain linguistic information because of time pressure, lack of knowledge, or data, and their limited expertise related to the problem domain. Up to now, there are a few approaches developed for dealing with group decision making with uncertain linguistic preference relations. However, these approaches are argumentindependent approaches in which the weights are associated with particular ordered positions of the aggregated uncertain linguistic arguments, and have no connection with the aggregated uncertain linguistic arguments. In this paper, we will pay attention to the argument-dependent approaches in which determine the weights based on the input uncertain linguistic arguments. The aim of this paper is to develop a new argument-dependent approach to determining uncertain linguistic ordered weighted geometric (ULOWG) weights based on the deviation measure and the normal distribution. In order to do so, this paper is set out as follows. In Section 2 we introduce some basic concepts and operational laws of uncertain linguistic variables. In Section 3 we develop a dependent uncertain linguistic ordered weighted geometric (DULOWG) operators in which the associated weights only depend on the aggregated uncertain linguistic arguments and can relieve the influence of unfair uncertain linguistic arguments on the aggregated results by assigning low weights to those “false” and “biased” ones. In
1. Introduction
Multiple attribute decision making under linguistic environment is an interesting research topic having received more and more attention from researchers during the last several years [1-42]. In the process of multiple attribute decision making, the linguistic decision information needs to be aggregated by means of some proper approaches so as to rank the given decision alternatives and then to select the most desirable one. Several methods have been proposed for dealing with linguistic information. These methods are mainly as follows:
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Section 4 we develop a practical method based on the ULWGM and the DULOWG operators for group decision making problem with uncertain linguistic information, which is straightforward and has no loss of information. In Section 5, we give an illustrative example to verify the developed approach and to demonstrate its feasibility and practicality. In Section 6 we conclude the paper and give some remarks.