Based On LWOWA Operator And Computing With Words To Solve The Problem Of Group Decision Making

Group decision making based on computing with words has played an important part in modern fuzzy decision making and modern decision making reasearch. The theory and method of group decision based on computing with words were broadly applied to the areas of plan implement, city construction, economic administration, financial investment, project evaluation, military, etc. Recent years, more and more scholars have been attracted to pay attention to the research of group decision making and they have acquired plenty of achievement. Because of the complexity, uncertainty and fuzzyness of most objective matter, in the course of decision making, it is difficult for decision makers to make use of number value to express preference information. However, if they take advantage of nature language as their evaluation, then, the process of decision making will be convenient. So the research of group decision making based on computing with words is indispensable. Group decision making based on computing with words, namely, all of experts or decision makers evaluate all alternatives by means of nature language. These years, there is an increasing number scholars devoted themselves to research about group decision making based on computing with words.Based on given research fruits, we propose a new method to slove group decision making based on computing with words, and main contents is contained as following:(1) We introduce the research background, significance and give a review of research situation at home and abroad in detail. There are four aspects of research situation. The one aspect is based on extension principle, the other is based on all kinds of aggregated operator. And others are 2-tuple linguistic representation and the consensus in group decision making. Besides, we summarise three given aggregated operators and three methods which solve group decision making problems based on computing with words. The aggregated operators are weighted mean operator (WM operator), ordered weighted averaging operator (OWA operator) and weighted ordered weighted averaging operator (WOWA operator). The three methods are the method based on extension principle, the method of satisfactory-oriented rules and the method of based on 2-tuple linguistic representation model.(2) The given methods can solve the problems of group decision making, but there are two limitations. The one limitation is that three methods ignored the information of linguistic terms that have been chosen to evaluate all alternatives. The other limitation is that disregard of the weights of experts. To solve these problems, we propose the notion of the weight of linguistic term and useful linguistic term set. Besides, based on the WOWA operator provided by Torra and 2-tuple linguistic representation model given by Herrera, We propose a new operator-linguistic weighted ordered weighted averaging operator, (LWOWA operator), and we give the definitions and properties of the LWOWA operator. Furthermore, we prove a 2-tuple linguistic representation of LWOWA operator can respectively reduce to a 2-tuple linguistic representation of OWA operator, a 2-tuple linguistic representation of WM operator and a 2-tuple linguistic representation of arithmetic mean operator in different conditions. Anyway, the proposition of LWOWA operator not only avoid miss information but also get evaluated information effectively, which can reflect the all-around evaluated information. (3) To demonstrate the method of LWOWA operator, we give an example and compare the new approach to given methods. We also discuss the example of group decision making with different weights of all experts.(4) Summarize the research process and point out some limitations of this paper.