Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making

Abstract

With respect to multiple attribute group decision making problems with linguistic information, some new decision analysis methods are proposed. Firstly, we develop three new aggregation operators: generalized 2-tuple weighted average (G-2TWA) operator, generalized 2-tuple ordered weighted average (G-2TOWA) operator and induced generalized 2-tuple ordered weighted average (IG-2TOWA) operator. Then, a method based on the IG-2TOWA and G-2TWA operators for multiple attribute group decision making is presented. In this approach, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.

Introduction

Multiple attribute decision making (MADM) is a usual task in human activities (Merigó, 2010, Merigó and Casanovas, 2009, Merigó and Casanovas, 2010, Merigó et al., 2010, Merigó and Gil-Lafuente, 2010, Wei, 2008, Wei, 2009a, Wei, 2009b, Wei, 2010a, Wei, 2010b, Wei, 2010c, Wei, 2010d, Wei, Lin, Zhao et al., 2010, Wei, Zhao, Lin, 2010, Wei, Zhao, Wang et al., 2010, Xu, 2009, Wang et al., 2007). It consists of finding the most desirable alternative(s) from a given alternative set. However, under many conditions, for the real multiple attribute decision making problems, the decision information about alternatives is usually uncertain or fuzzy due to the increasing complexity of the socio-economic environment and the vagueness of inherent subjective nature of human thinking, thus, numerical values are inadequate or insufficient to model real-life decision problems. Indeed, human judgments including preference information may be stated in linguistic terms. Several methods have been proposed for dealing with linguistic information.

• The approximative computational model based on the Extension Principle (Degani & Bortolan, 1988). This model transforms linguistic assessment information into fuzzy numbers and uses fuzzy arithmetic to make computations over these fuzzy numbers. The use of fuzzy arithmetic increases the vagueness. The results obtained by the fuzzy arithmetic are fuzzy numbers that usually do not match any linguistic term in the initial term set.

• The ordinal linguistic computational model (Delgado, Verdegay, & Vila, 1993). This model is also called symbolic model which makes direct computations on labels using the ordinal structure of the linguistic term sets. But symbolic method easily results in a loss of information caused by the use of the round operator.

• The 2-tuple linguistic computational model (Herrera and Martínez, 2000a, Herrera and Martínez, 2000b, Herrera and Martínez, 2001, Herrera et al., 2005). This model uses the 2-tuple linguistic representation and computational model to make linguistic computations.

Thus, multiple attribute decision making problems under 2-linguistic environment is an interesting research topic having received more and more attention from researchers during the last several years. Herrera and Martínez (1991) show 2-tuple linguistic information processing manner can effectively avoid the loss and distortion of information. It has a distinct advantage over other linguistic processing methods in accuracy and reliability. Herrera and Martínez (2000a) developed 2-tuple arithmetic average (TAA) operator, 2-tuple weighted average (TWA) operator, 2-tuple ordered weighted average (TOWA) operator and extended 2-tuple weighted average (ET-WA) operator. Jiang and Fan (2003) proposed the 2-tuple ordered weighted geometric (TOWG) operator. Wang and Fan (2003) proposed a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for solving multiple attribute group decision making problems with linguistic assessment information. Herrera-Viedma, Martinez, Mata, and Chiclana (2005) presented a model of consensus support system to assist the experts in all phases of the consensus reaching process of group decision making problems with multi-granular linguistic preference relations. Herrera et al. (2005) presented a group decision making process for managing non-homogeneous information. The non-homogeneous information can be represented as values belonging to domains with different nature as linguistic, numerical and interval valued or can be values assessed in label sets with different granularity, multi-granular linguistic information. Liao, Li, and Lu (2007) presented a model for selecting an ERP system based on linguistic information processing. Herrera, Herrera-Viedma, and Martínez (2008) proposed a fuzzy linguistic methodology to deal with unbalanced linguistic term sets. Jiang, Fan, and Ma (2008) developed a method for group decision making with multi-granularity linguistic assessment information. Tai and Chen (2009) developed a evaluation model for intellectual capital based on computing with linguistic variable. Wang (2009) presented a 2-tuple fuzzy linguistic computing approach to deal with heterogeneous information and information loss problems during the processes of subjective evaluation integration which is based on the group decision-making scenario to assist business managers to measure the performance of New Product Development (NPD) manipulates the heterogeneous integration processes and avoids the information loss effectively. Zhang and Chu (2009) developed fuzzy group decision making for multi-format and multi-granularity linguistic judgments in quality function deployment. Fan, Feng, Sun, and Ou (2009) evaluated knowledge management capability of organizations by using a fuzzy linguistic method. Fan and Liu (2010) developed a method for group decision making based on multi-granularity uncertain linguistic information. Wei (2010a) extended Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to 2-tuple linguistic multiple attribute group decision making with incomplete weight information. Wei (2010b) proposed some extended geometric aggregating operators with 2-tuple linguistic information. Chang and Wen (2010) developed a approach for Design Failure Mode and Effect Analysis (DFMEA) combining 2-tuple and the OWA operator.

The traditional generalized aggregating operators and induced generalized aggregating operators are generally suitable for aggregating the information taking the form of numerical values, and yet they will fail in dealing with linguistic information. The aim of this paper is to extend the traditional generalized aggregating operators to linguistic environment and develop three new generalized aggregation operators: generalized 2-tuple weighted average (G-2TWA) operator, generalized 2-tuple ordered weighted average (G-2TOWA) operator and induced generalized 2-tuple ordered weighted average (IG-2TOWA) operator. Furthermore, a method based on the IG-2TOWA and G-2TWA operators for multiple attribute group decision making is presented. In this approach, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. In doing so, the remainder of this paper is set out as follows. In the next section, we introduce some basic concepts and operational laws of 2-tuple linguistic variables. In Section 3 we develop some generalized weighted average operator with linguistic assessment information. In Section 4 we develop some generalized ordered weighted average operator with linguistic assessment information. In Section 5 we develop some induced generalized ordered weighted average operator with linguistic assessment information. In Section 6 we apply the IG-2TOWA and G-2TWA operator to multiple attribute group decision making with linguistic assessment information. In Section 7, we give an illustrative example about risk analysis to verify the developed approach and to demonstrate its feasibility and practicality. In Section 8 we conclude the paper and give some remarks.