Multiple criteria group decision making based on group satisfaction

Highlights

• A new group decision making method based on group satisfaction (GS) is proposed.

• Alternative assessment and ranking differences are measured to construct GS.

• Assessment difference constructed from nth moment is proven to be a distance measure.

• The proposed method is used to solve the problem of selecting management software.

• Comparison between GS and group consensus is made using the problem and simulation.

Abstract

To generate solutions to multiple criteria group decision-making (MCGDM) problems that are satisfactory to the decision makers, this paper proposes a new method. To examine whether a group solution is satisfactory to the decision makers, group satisfaction is constructed from alternative assessment and ranking differences between the decision makers and the group. The difference between a decision maker's assessment and a group's assessment is designed based on differences in assessment grades, whose normalization is theoretically proven to construct alternative assessment differences. Inspired by Spearman's rank correlation coefficient, the expected utilities of decision makers’ and the group's assessments are used to construct alternative ranking differences. An abstract two-variable function with specific properties is designed to relate alternative assessment difference to alternative ranking difference to form group satisfaction. From the constructed group satisfaction, the process of generating group-satisfactory solutions to MCGDM problems is presented. The problem of selecting engineering project management software is analyzed by using the proposed method to demonstrate its applicability. To highlight the importance of group satisfaction in MCGDM, relationships and differences between group satisfaction and group consensus are analyzed through the problem and simulation experiments.

Introduction

In the Internet era, people and things are closely connected through emerging information technologies such as the Internet of things, big data, and machine learning. In people's activities that are closely associated with things, large volumes of data are generated, which is attributed to the application of these information technologies. The obtained data are beneficial for improving both the precision and efficiency of decisions made in different fields so that people can make more reasonable decisions than before. For example, in the manufacturing sector, the incorporation of machine learning into failure map pattern monitoring, failure cause identification, and failure recurrence monitoring can help engineers significantly increase yields [26], and in the medical sector, large volumes of medical data collected with advanced tools such as digital microscopy tests, ultrasound tests, and high-resolution magnetic resonance imaging can help doctors improve their diagnostic accuracy and efficiency [15], [35]. Meanwhile, large volumes of collected data make it difficult for individual engineers or doctors to effectively and efficiently address real problems due to their limited expertise and experience. In addressing this difficulty, group expertise and experience are usually preferred.

To facilitate the application of group expertise and experience in real situations, many different group decision-making (GDM) methods have been proposed. These methods have different focuses such as the aggregation of different decision makers’ preferences [1], [18] or the convergence of group consensus [9], [31], [40], [43]. The purpose of reaching group consensus is to find a solution that is preferred or accepted by most or all decision makers [5], [40]. To accelerate the convergence of group consensus, feedback mechanisms are usually designed to identify decision makers’ assessments that negatively contribute to group consensus and help decision makers reconsider their assessments [5], [9]. To focus on the efficient acceleration of convergence to group consensus, some recent studies have aimed to minimize costs related to the adjustment of decision makers’ assessments [4], [32], [33], [39]. A group is usually considered to be satisfied with a solution generated when the predefined level of group consensus is reached [28]. This seems to show that a high level of group consensus indicates strong group satisfaction with the GDM.

In practice, group satisfaction is measured as the degree to which each decision maker is satisfied with a group's solution to a GDM problem [10], [11], [23], [29]. Each decision maker's level of satisfaction can be evaluated using certain methods such as Siskos et al.’s multicriteria method [30], which was originally developed to assess customer (or user) satisfaction. This idea may be feasible in constructing group satisfaction. However, it exacerbates burdens placed on decision makers who engage in GDM. In fact, group satisfaction can be understood as the extent to which a group's solution can reflect the inputs of each decision maker [8], [12]. The more a solution reflects the inputs of decision makers, the higher the level of group satisfaction is. In conforming to this understanding, many efforts have been made to measure and increase group satisfaction.

Some studies have focused on GDM with a requirement for group satisfaction. In Mikhailov [24], a group prioritization method based on the analytic hierarchy process (AHP) is developed to maximize each decision maker's overall satisfaction with the group priority vector. This is implemented by minimizing the difference between the priority ratios of each decision maker and the group priority vector. In Huang et al. [11], a group AHP method is proposed to consider group satisfaction from the two perspectives: the difference between the alternative priorities of each decision maker and those of the group and the difference between the alternative rankings of each decision maker and those of the group.

There have been other attempts to analyze multiple criteria group decision-making (MCGDM) problems with requirements for group satisfaction. In Goletsis et al. [7], an MCGDM method is proposed to construct group satisfaction from the satisfaction of each decision maker and improve it. The decision maker's level of satisfaction is derived from the difference between each decision maker's rankings of alternatives and the group's rankings of alternatives, which is measured with Spearman's rank correlation coefficient (SRCC) [17]. In Shen et al. [29], an MCGDM method is developed to measure group satisfaction from the difference between each decision maker's rankings of alternatives and the group's rankings of alternatives, in which an automatic adjustment strategy is designed to enhance group satisfaction. Another MCGDM method based on multi-attribute utility theory is proposed by Huang et al. [10] to measure group satisfaction based on the difference between the alternative utility values of each decision maker and those of the group and the difference between the alternative rankings of each decision maker and those of the group.

Due to the complexity of real situations, MCGDM may be more meaningful and applicable than GDM in real cases. In the context of MCGDM, we believe that the comprehensive consideration of alternative assessment differences and alternative ranking differences between decision makers and a group can reflect the inputs of decision makers more pertinently than the sole consideration of the alternative ranking differences. It can work in all cases where alternative ranking differences are applicable, especially in the situations where there are large alternative assessment differences and small alternative ranking differences, or small alternative assessment differences and large alternative ranking differences. These analyses show that Huang et al.’s [10] method may be more applicable than other methods for GDM with group satisfaction in real situations. However, Huang et al.’s study has three limitations: (1) uncertain assessments, such as belief distributions (BDs) (see Section 2), are not addressed; (2) alternative assessment differences and ranking differences are combined in a fixed way, in which decision makers’ preferences for the contributions of the two types of differences to group satisfaction are not considered; and (3) group satisfaction is not intended for improvement to reach the required level to generate a group-satisfactory solution. The first limitation may make Huang et al.’s study inapplicable in the context of uncertainties that may be induced by large volumes of data and information or lack of knowledge and experience. The second and third limitations negatively influence the generation of a group-satisfactory solution. In addition to these three limitations, the relationships and differences between group satisfaction and group consensus are not analyzed in Huang et al.’s study. This is also an interesting issue.

To address the above three limitations and the issue, this paper presents a new method based on the evidential reasoning (ER) approach, in which uncertain assessments are modeled using BDs for decision making [19], [20], [21], [36], [37]. By considering the rationality of the comprehensive consideration of alternative assessment differences and alternative ranking differences for reflecting the inputs of decision makers, as demonstrated above, group satisfaction is constructed from alternative BD and ranking differences with the aid of Hurwicz's rule [2], [14], [16]. Utilities of assessment grades, which reflect differences between grades, are used to construct alternative BD differences that are proven to be normalized. Utilities of assessment grades and alternative BDs are combined to construct alternative ranking differences inspired by the SRCC. The process of the proposed method is then presented based on the constructed group satisfaction. To analyze the relationships and differences between group satisfaction and group consensus, group consensus is constructed based on alternative BD differences according to principles described by Fu and Yang [5].

The contributions of this paper include: (1) a new method is developed based on BDs to address uncertain MCGDM problems with the requirement of group satisfaction; (2) group satisfaction is flexibly constructed from alternative BD and ranking differences with the aid of an abstract two-variable function, in which decision makers’ preferences are considered; (3) an iterative process is designed based on several rounds of group analysis and discussion to reach the predefined level of group satisfaction; and (4) the relationships and differences between group satisfaction and group consensus are analyzed using a real case and simulation experiments.

The rest of this paper is organized as follows. Section 2 introduces the modeling of MCGDM problems with BDs. Section 3 presents the proposed method. Section 4 describes the construction of group consensus. In Section 5, the problem of selecting engineering project management software [5] is reinvestigated to demonstrate the proposed method, in which group consensus and group satisfaction are compared. In Section 6, the relationships and differences between group consensus and group satisfaction are analyzed with simulation experiments. The constructed group satisfaction is compared with existing group satisfaction in Section 7. The paper's conclusions are presented in Section 8.