Pairwise comparison matrices (PCMs) over an Abelian linearly ordered (alo)-group \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$\mathcal{G}=(G, \odot, \leq)$ have been introduced to generalize multiplicative, additive and fuzzy ones and remove some consistency drawbacks. Under the assumption of divisibility of \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$\mathcal{G}$, for each PCM A=(a_ij), a ⊙-mean vector \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$\underline{w}_{m}(A)$ can be associated with A and a consistency measure \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$I_{\mathcal{G}}(A)$, expressed in terms of ⊙-mean of \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$\mathcal{G}$-distances, can be provided. In this paper, we focus on the consistency index \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$I_{\mathcal{G}}(A)$. By using the notion of rational power and the related properties, we establish a link between \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$\underline{w}_{m}(A)$ and \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$I_{\mathcal{G}}(A)$. The relevance of this link is twofold because it gives more validity to \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$I_{\mathcal{G}}(A)$ and more meaning to \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$\underline{w}_{m}(A)$; in fact, it ensures that if \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$I_{\mathcal{G}}(A)$ is close to the identity element then, from a side A is close to be a consistent PCM and from the other side \documentclass{article}\usepackage{amssymb}\pagestyle{empty}$\underline{w}_{m}(A)$ is close to be a consistent vector; thus, it can be chosen as a priority vector for the alternatives.

There are several manufacturing errors of different criticality, severity, and occurrence. Correcting all of them is difficult and costly. In this paper, we propose a new hybrid approach to classifying manufacturing errors in an automotive plant and, consequently, to selecting the portfolio of processes that require more attention from the management of the company. Our approach consists of two steps. Firstly, we classify the errors in terms of priority, based on a set of criteria agreed with the management, using the multi-criteria decision-aiding method AHPSort II. The errors belonging to the highest priority class are the most urgent and critical for the company. Secondly, we define a multi-objective portfolio problem, selecting a set of the most critical processes based on the number of errors in each of these processes and on their priority. We adopted an interactive method for finding the most preferred portfolio of processes according to the stakeholder preferences. We applied this approach to a case study of the largest automotive company in Italy, Fiat Chrysler Automobiles, showing how classical quality control tools can benefit from the integration of multi-criteria decision-aiding techniques.

Open business organizations, where information flows, is shared, and exchanged, are more prepared to adapt and survive chaos, uncertainty, and entropy, so they will be more predisposed to change management. The aim of this study is to analyze research trends at the international level on business information–entropy correlation in the accounting process of organizations. Mathematical and statistical techniques were applied to 980 articles during the period 1974–2020, obtaining results on the scientific productivity of the driving agents of this topic: authors, research institutions, countries/territories, and journals. Five lines of research were identified during the period analyzed, which mainly study information theory, maximum entropy, information entropy, decision-making, and enthalpy. Future research should focus on analyzing the evolution of this topic, which forms new thematic axes related to bitcoin market efficiency, business hierarchy information, business model evaluation systems, catastrophic economic collapse, corporate diversification, CSR reports affecting accounting conservatism, economic income accounting, and information loss. Currently, the research presents an upward trend, which allows a growing interest in the subject to be deduced in the academic and scientific community worldwide.