四类直觉数总结

Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making

Shu-ping Wan

College of Information Technology,Jiangxi University of Finance and Economics,Nanchang 330013,China

a r t i c l e i n f o Article history:Received 14April 2012Received in revised form 2August 2012Accepted 11September 2012Available online 21September 2012Keywords:Multi-attribute group decision making Trapezoidal intuitionistic fuzzy number Hausdorff metric Power average operator

a b s t r a c t

Trapezoidal intuitionistic fuzzy numbers (TrIFNs)is a special intuitionistic fuzzy set on a

real number set.TrIFNs are useful to deal with ill-known quantities in decision data and

decision making problems themselves.The focus of this paper is on multi-attribute group

decision making (MAGDM)problems in which the attribute values are expressed with TrIF-

Ns,which are solved by developing a new decision method based on power average oper-

ators of TrIFNs.The new operation laws for TrIFNs are given.From a viewpoint of Hausdorff

metric,the Hamming and Euclidean distances between TrIFNs are defined.Hereby the

power average operator of real numbers is extended to four kinds of power average oper-

ators of TrIFNs,involving the power average operator of TrIFNs,the weighted power aver-

age operator of TrIFNs,the power ordered weighted average operator of TrIFNs,and the

power hybrid average operator of TrIFNs.In the proposed group decision method,the indi-

vidual overall evaluation values of alternatives are generated by using the power average

operator of TrIFNs.Applying the hybrid average operator of TrIFNs,the individual overall

evaluation values of alternatives are then integrated into the collective ones,which are

used to rank the alternatives.The example analysis shows the practicality and effectiveness

of the proposed method.

Ó2012Elsevier Inc.All rights reserved.1.Introduction

Fuzzy set (FS)theory has long been introduced to handle inexact and imprecise data by Zadeh [1].The drawback of using the single membership value in FS theory is that the evidence for x 2X and the evidence against x 2X are in fact mixed to-gether (Here X is the universe of discourse).In order to tackle this problem,Atanassov [2]proposed the intuitionistic fuzzy set (IFS)using two characteristic functions expressing the degree of membership and the degree of non-membership of ele-ments of the universal set to the IFS.It can cope with the presence of vagueness and hesitancy originating from imprecise knowledge or information.

IFS has been widely applied to the multi-attribute decision making (MADM)and multi-attribute group decision making (MAGDM)[3–49].These researches can be roughly classified into four types:aggregation operators [3–22],similarity (or dis-tance)measures and entropy [23–29],extension of classic decision making methods [30–38]and new decision making methods [39–48],and judgment matrix [49,26],which are respectively reviewed as follows.

In the aspect of aggregation operators,Li [3–5]proposed the generalized OWA operators with IFSs.Zhao et al.[6]devel-oped some new generalized aggregation operators,such as generalized intuitionistic fuzzy (IF)weighted averaging operator,generalized IF ordered weighted averaging operator,generalized IF hybrid averaging operator,and applied to MADM with IF information.Xu and Yager [7],Xu [8]and Wei [9]developed some geometric aggregation operators based on IFS,such as the

0307-904X/$-see front matter Ó2012Elsevier Inc.All rights reserved./10.1016/j.apm.2012.09.017

E-mail address:shupingwan@