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This article investigates multiplicative consistency ascertaining, inconsistency repairing, and weights derivation for hesitant multiplicative preference relations (HMPRs). First, the completely multiplicative consistency and weakly multiplicative consistency of HMPRs are defined. Based on them, 0–1 mixed programming models and simple algebraic operations are proposed to ascertain the multiplicative consistency of HMPRs. Then, some goal programming models are developed to generate the weights from consistent HMPRs and to revise inconsistent HMPRs. An integrated procedure to manage the multiplicative consistencies of HMPRs is designed. The proposed methods are also extended to accommodate incomplete HMPRs, and to estimate missing values. Finally, some numerical examples, a comparative analysis with existent approaches, and a simulation analysis are included to illustrate the practicality and effectiveness of the developed models. [ABSTRACT FROM AUTHOR]

The Dempster–Shafer (D-S) evidence theory has been widely used in many fields from probabilistic inference, information fusion to decision analysis due to its superiority to formulate uncertain and incomplete information under a weaker condition than the Bayesian probability theory. To support the elicitation of basic probability assignment (BPA), numerous uncertainty measures have been proposed in the recent decades, which take into account nonspecificity and structural conflict (SC) in either the entropy-alike or nonentropy form. This article is focused primarily on developing a generalized belief entropy to measure and quantify the uncertainty of BPA in a consistent and comprehensive way. The definition of the proposed belief entropy involves three components. Specifically, the first component is Shannon’s definition of entropy of probability functions which can be interpreted as the measure of discord of the mass function among various focal elements. The second component is the measure of total nonspecificity which is the generalization of Dubois–Prade’s definition of nonspecificity measure. Furthermore, the critical component introduced in this article is the utilization of the SC coefficient within an evidence, which fully considers the intersection between each pair of focal elements of the BPA. The characteristics and properties of the new generalized belief entropy are analyzed systematically with theoretical proofs. Finally, the proposed belief entropy is embedded to a three-tuple approach to deal with a practical multiple attribute decision-making (MADM) problem to demonstrate its validity and strengths of measuring nonspecificity and SC in uncertain decision making. [ABSTRACT FROM AUTHOR]

This article proposes a framework of personalized feedback mechanism to help multiple inconsistent experts to reach consensus in group decision making by allowing to select different feedback parameters according to individual consensus degree. The general harmony degree (GHD) is defined to determine the before/after feedback difference between the original and revised opinions. It is proved that the GHD index is monotonically decreasing with respect to the feedback parameter, which means that higher parameter values will result in higher changes of opinions. An optimization model is built with the GHD as the objective function and the consensus thresholds as constraints, with the solution being personalized feedback advices to the inconsistent experts that keep a balance between consensus (group aim) and independence (individual aim). This approach is, therefore, more reasonable than the unpersonalized feedback mechanisms in which the inconsistent experts are forced to adopt feedback generated with only consensus target without considering the extent of the changes acceptable by individual experts. Furthermore, the following interesting theoretical results are also proved: 1) the personalized feedback mechanism guarantees that the increase of consensus level after feedback advices are implemented; 2) the GHD by the personalized feedback mechanism is higher than that of the unpersonalized one; and 3) the personalized feedback mechanism generalizes the unpersonalized one as it is proved the latter is a particular type of the former. Finally, a numerical example is provided to model the feedback process and to corroborates these results when comparing both feedback mechanism approaches. [ABSTRACT FROM AUTHOR]

Different feedback mechanisms have been reported in consensus reaching models to provide advices for preference adjustment to assist decision makers to improve their consensus levels. However, most feedback mechanisms do not consider the willingness of decision makers to accept these advices. In the opinion dynamics discipline, the bounded confidence model justifies well that in the process of interaction a decision maker only considers the preferences that do not exceed a certain confidence level compared to his own preference. Inspired by this idea, this article proposes a new consensus reaching model with personalized feedback mechanism to help decision makers with bounded confidences in achieving consensus. Specifically, the personalized feedback mechanism produces more acceptable advices in the two cases where bounded confidences are known or unknown, and the unknown ones are estimated by a learning algorithm. Finally, numerical example and simulation analysis are presented to explore the effectiveness of the proposed model in reaching consensus. [ABSTRACT FROM AUTHOR]

Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised: 1) to find the multiplicative inconsistent elements and 2) to detect the ordinally inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Finally, some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article provides a brief tour through the main fuzzy and linguistic decision-making trends, studies, methodologies, and models developed in the last 50 years. Fuzzy and linguistic decision-making approaches allow to address complex real-world decision problems where humans exhibit vagueness, imprecision, and/or use natural language to assess decision alternatives, criteria, etc. The aim of this article is threefold. First, the main fuzzy set theory and computing with words-based representation paradigms of decision information, with their different levels of expressive richness and complexity, are reviewed. Second, three core decision-making frameworks are examined: 1) multicriteria decision making; 2) group consensus-driven decision making; and 3) multiperson multicriteria decision making. Third, the article discusses new complex decision-making frameworks that have emerged in recent years, where decisions are guided by the “wisdom of the crowd”: their associated challenges are highlighted and considerations on much needed key guidelines for future research in the field are provided. [ABSTRACT FROM AUTHOR]

To commemorate the 50th anniversary of the IEEE Transactions on Systems, Man, and Cybernetics: Systems, this article examines and reports on its past to current topical coverage of systems science and engineering toward exploring the evolving focus of the research community. Results of a systematic bibliometric analysis are presented with associated conclusions, implications, and summary of topical areas. In addition, respective views regarding the current state of the field and where it is headed are offered by recent leaders of the IEEE Systems, Man, and Cybernetics Society, including its continued relevance and role in the advancement of systems technology. [ABSTRACT FROM AUTHOR]

In multiple attribute decision making (MADM), strategic weight manipulation is understood as a deliberate manipulation of attribute weight setting to achieve a desired ranking of alternatives. In this paper, we study the strategic weight manipulation in a group decision making (GDM) context with interval attribute weight information. In GDM, the revision of the decision makers’ original attribute weight information implies a cost. Driven by a desire to minimize the cost, we propose the minimum cost strategic weight manipulation model, which is achieved via optimization approach, with the mixed 0–1 linear programming model being proved appropriate in this context. Meanwhile, some desired properties to manipulate a strategic attribute weight based on the ranking range under interval attribute weight information are proposed. Finally, numerical analysis and simulation experiments are provided with a twofold aim: 1) to verify the validity of the proposed models and 2) to show the effects of interval attribute weights information and the unit cost, respectively, on the cost to manipulate strategic weights in the MADM in a group decision context. [ABSTRACT FROM AUTHOR]

In the literature, we find that the consensus models proposed for group decision making problems are guided by consensus degrees and/or similarity measures and/or consistency measures refid="ref1"/. When we work in heterogeneous group decision making frameworks, we have importance degrees associated with the experts by expressing their different knowledge levels on the problem. Usually, the importance degrees are applied in the weighted aggregation operators developed to solve the decision situations. In this paper, we study another application possibility, i.e., to use heterogeneity existing among experts to guide the consensus model. Thus, the main goal of this paper is to present a new consensus model for heterogeneous group decision making problems guided also by the heterogeneity criterion. It is also based on consensus degrees and similarity measures, but it presents a new feedback mechanism that adjusts the amount of advice required by each expert depending on his/her own relevance or importance level. [ABSTRACT FROM AUTHOR]

Consensus reaching process (CRP), as an essential part of group decision making (GDM), can facilitate more effective consensus by taking human behaviors into account. Extending the established research on uncertain minimum cost consensus models (MCCMs), this article continues to adopt linear uncertainty distributions (LUDs) to represent decision-maker’s (DM’s) preference, but considers asymmetric costs into a new framework of CRP, where DM’s preference and weight are both adjusted according to democratic consensus. Moreover, in light of the uncertain distance measure, two novel optimization-based consensus models are built in this article: one is to obtain a minimum cost consensus by simultaneously considering asymmetric costs, aggregation function, and consensus measure; while the other provides a more flexible way to address GDM problems without presetting a specific consensus level (CL) threshold. Some 0–1 binary variables are further introduced to reduce the calculation complexity resulted from piecewise functions in the new multicoefficient goal programming models. Finally, an illustrative example and further discussion reveal the feasibility and superiority of our new method. [ABSTRACT FROM AUTHOR]

Model inversion attack (MIA) is a cyber threat with an increasing alert even for deep-learning-based recognition systems (DLRSs). By targeting a DLRS under a scenario of attacker access to the model structure and parameters, MIA generates a data clone for a certain targeted class label. To avoid the possible threats of such MIA-generated data clones, this research work proposes a social IoT approach to a collaborative cyber-defense among the online recognition systems (RSs) sharing the targeted class label. Since, the generation of an MIA-clone is by targeting an RS model and using its structure, parameters, and class labels output scores in an iterative optimization process, the generated clone is partially inherent to the targeted model. Thus, it is expected for an MIA-clone to show a different performance on a secondary RS wherein the same targeted class label is included. It is because, in the MIA generation of the clone, not only the targeted class label but also other class labels, and model parameters and structure affect the process, while the second model has just the targeted class label in common with the target model. Deploying the Social Internet of Recognition Systems (SIoRS), the proposed technique utilizes a collaborative recognition by SIoRC which plays the role of a complementary recognition besides the targeted RS. The recognition output by the targeted RS is further verified by the SIoRS complementary recognition result. To avoid the MIA-targeted data clones, the verification of recognition is by the log-likelihood ratio test between the targeted RS and the SIoRS complementary recognition confidence scores. The proposed technique is evaluated by statistical analysis on deep face RSs in 10000 Monte Carlo runs for each of the conventional, dc-generative adversarial network (GAN) and $\alpha $ -GAN integrated MIA techniques in targeting two different user identities. The $Z$ scores of the fitted normal distribution of the log-likelihood ratios indicate almost 100% detection rate of clones generated by conventional MIA and 95.23% and 86% of clones, respectively, generated by DC-GAN and $\alpha $ -GAN integrated deep MIA techniques. [ABSTRACT FROM AUTHOR]