A consistency-based approach to multiple attribute decision making with preference information on alternatives

Highlights

• We propose an approach to avoid the inconsistent rankings of alternatives.

• We define the geometry consistency index in the MADM problems.

• We propose the feedback adjustment to improve the defined geometry consistency index.

• We discuss the properties of the proposed approach by simulation experiments.

Abstract

The methodology to solve the multiple attribute decision making (MADM) with preference information on alternatives has been systematically investigated. However, the inconsistency issue between the two rankings respectively derived from the preference information and the decision matrix is seldom considered. In order to investigate this issue, this paper proposes a consistency-based approach to MADM with preference information on alternatives. Based on the classical idea of the geometric consistency index in the preference relation, we define a geometric consistency index in MADM. Then, we propose an algorithm to adjust the preference information and the decision matrix simultaneously to improve the geometric consistency index in MADM. Next, some simulations experiments are designed to discuss the properties of the proposed approach. Finally, through illustrative examples and a comparative analysis, we demonstrate the effectiveness of the proposed approach.

Introduction

Multiple attribute decision making (MADM) refers to the problems of ranking the alternatives associated with multiple attributes (Dyer et al., 1992, Wallenius et al., 2008). Many MADM methods have been applied in the field of industrial engineering, such as product design (Besharati, Azarm, & Kannan, 2007), facility layout design (Maniya & Bhatt, 2011), advanced manufacturing technology (Chuu, 2009), warehouse location in a supply chain (Dey, Bairagi, Sarkar, & Sanyal, 2017), and production system life cycle (Attri & Grover, 2014). The attribute weights are one of the most common foundations (Barron and Barrett, 1996, Hwang and Yoon, 1981, Zanakis et al., 1998) in MADM problems, but they are precisely unknown due to the uncertainty of the decision environment and the limitation of decision maker’s knowledge (Barron, 1992, Jessop, 2011, Stillwell et al., 1981, Weber, 1987).

Some studies on determining the attribute weights of the MADM problems have been presented (e.g., Kirkwood and Corner, 1993, Kirkwood and Sarin, 1985). In the existing studies, the preference information on alternatives is frequently used to determine the attribute weights (e.g., Fan et al., 2004, Wang, 2015). There are two categories of the preference information on alternatives: the fuzzy preference information and the multiplicative preference information (Ureña et al., 2015, Ureña et al., 2015). As for the fuzzy preference information on alternatives, Fan, Ma, and Zhang (2002) introduced an optimization model to assess the attribute weights and to select the most desirable alternative. Based on Fan et al.’s model, Wang and Parkan (2005) utilized the linear programming technique to integrate the fuzzy preference information and the decision matrix together. As for the multiplicative preference information on alternatives, Xu (2004) proposed an optimization model to solve the MADM problems. Moreover, Fan et al., 2004, Fan et al., 2006 developed a linear goal programming model and a two-objective optimization model to integrate fuzzy and multiplicative preference information on alternatives. Wang and Parkan (2006) provided a general MADM approach to integrate the two kinds of preference information and the decision matrix into one model.

Previous studies have significantly contributed to the MADM with preference information on alternatives. In the existing studies, two rankings from the preference information on alternatives and the decision matrix are derived, respectively. And the two rankings are usually different with each other, i.e., they are inconsistent, which will be shown in the numerical examples of Section 5. However, the inconsistent issues between the two rankings are seldom considered in the previous investigations. Generally, it is difficult for the decision maker to obtain a reasonable ranking of the alternatives when the two rankings are inconsistent.

To avoid the inconsistent issues mentioned above, this paper presents a consistency-based approach to the MADM with preference information on alternatives. In the proposed approach, we define a geometric consistency index in MADM based on the idea of geometric consistency measure in the preference relation. Furthermore, we propose a feedback adjustment to improve the geometric consistency index in MADM.

The rest of this paper is organized as follows: Section 2 introduces the basic knowledge regarding the MADM problems, the geometric consistency index and the MADM with preference information on alternatives. In Section 3, the consistency-based approach is proposed in detail. Next, Section 4 designs some simulation experiments to discuss the properties of the proposed approach. In Section 5, two illustrative examples and a comparative analysis are provided to demonstrate the effectiveness of the proposed approach. Finally, concluding remarks are made in Section 6.