High-dimensional and incomplete (HDI) data are involved frequently in big data-related industrial applications. Latent factor (LF) analysis aims at extracting the knowledge of great value from such extremely sparse HDI data efficiently. Non-negative LF models based on the single LF-dependent, non-negative, and multiplicative update rules exactly are the representative of LF analysis. However, these models face low generalization dilemma due to incompatible with general unconstrained optimization techniques. To address this issue, this article proposes a novel momentum-accelerated and biased unconstrained non-negative latent factor (MBUNLF) model, which matches with unconstrained optimization techniques. The proposed MBUNLF model is built on three main ideas: (a) Improving the generalization through a non-negative mapping function; (b) Capturing information among different entities through linear biases; (c) Accelerating convergence during the training process through generalized momentum method. Empirical studies on six datasets from industrial applications indicate that the proposed MBUNLF model outperforms nine state-of-the-art models when processing HDI data, reducing the root mean square error by 19.47% on average. It demonstrates the validity of the MBUNLF model in extracting non-negative LFs from HDI data.

High-Dimensional and Incomplete (HDI) tensors contain a wealth of knowledge and patterns, which are typically utilized to characterize complex relationships between entities in a variety of industrial applications. Currently, the neural network-based tensor factorization model has shown superiority when handling the missing data in HDI tensors. However, it only uses the outer product of latent factors (LFs) of entities and neglects the interactions between the LF. In addition, the simple linear operation does not consider the nonlinear structure of the HDI tensor. To overcome the aforementioned issues, an Attention-mechanism-based Neural Latent-Factorization-of-Tensors (ANLFT) model is provided in this article. It encompasses three primary ideas: (a) incorporating the theory of neural networks with the latent factorization of tensor to construct the nonlinear structure in the HDI tensor effectively; (b) adopting the attention mechanism to depict the interactions between LF; (c) using the position-transitional particle swarm optimization backward propagation learning ( \(\rm{P}^{2}\) BP) scheme to train the ANLFT model efficiently. The experimental results on eight HDI datasets show that the ANLFT model can obtain higher estimation performance gain than state-of-the-art models. The convergence performance of the proposed model is also competitive with that of state-of-the-art models.

Time-varying quality-of-service (QoS) data is often used to measure the performance of Web services. It is vital to capture the temporal pattern hidden in such time-varying QoS data for estimating unknown ones. A Nonnegative Latent Factorization of Tensors (NLFT) model is highly effective and efficient in describing temporal patterns. However, an NLFT model assigns a single bias into each order of the target QoS data tensor, making it unable to accurately describe the fluctuations of time-varying QoS data, thus impairing its estimation performance. To address this issue, this paper proposes an Extended linear Biases Nonnegative Latent factorization of tensor (EBNL) model with two-fold ideas: a) incorporating multiple linear biases into the model for describing QoS fluctuations precisely, and b) adopting a particle swarm optimization (PSO) algorithm to make the scale of linear biases self-adaptive. Experiments on two time-varying QoS data generated by real applications indicate that compared with several state-of-the-art QoS estimators, the proposed EBNL model achieves higher estimation accuracy for unknown QoS data.

Evaluating startup companies is an important management process for technology business incubators and it is also a typical multicriteria decision-making (MCDM) problem. There exist various methods that have proposed to solve MCDM problems, but these methods heavily depend on the exact criteria weight values. The decision results of these methods are unstable. Moreover, they cannot provide the improvement suggestions for the nonoptimal startup companies. To overcome these two drawbacks, we propose a novel hesitant fuzzy linguistic decision-making method to solve the problem of evaluating startup companies. To this end, a novel semantic comparison method based on the experts' psychology and the ratio of score value to deviation degree is proposed to compare the hesitant fuzzy linguistic term sets. Then, a novel definition of hesitant fuzzy linguistic information envelopment efficiency (HFLIEE) is proposed, based on which, a novel hesitant fuzzy linguistic information envelopment analysis (HFLIEA) model and a novel preference model are proposed. By solving these models, all the alternatives can be ranked and nonoptimal alternatives can be improved. Finally, the numerical analysis is given to illustrate the applicability of the proposed models and the robustness analyses of the proposed models are provided. At the same time, they are compared with the previous hesitant fuzzy linguistic decision-making methods.

Smart agriculture can enhance agricultural production efficiency, improve the ecological environment, and realize the sustainable development of agriculture. Many countries and companies are working hard to develop or introduce smart agricultural solutions. Because of the shackles of traditional agricultural management methods and fierce competition with a variety of different solutions, it is a difficult task for enterprises to select and implement smart agricultural solutions smoothly. Hence, enterprises must assess alternative solutions and select a feasible solution in advance. This study drew a novel assessment and selection for smart agriculture solutions using an information error-based Pythagorean fuzzy cloud algorithm. First, an evaluation index system built on smart agriculture solutions was constructed from four aspects. Then, a new concept of Pythagorean fuzzy clouds was defined to express the evaluation information for each indicator. Simultaneously, the Pythagorean fuzzy cloud weighted Bonferroni mean (PFCWBM) operator was developed to aggregate the assessment information of multiple indicators. Next, an assessment and selection decision framework for smart agriculture solutions based on the PFCWBM operator was presented. In addition, an example was given to illustrate the effectiveness of the proposed algorithm. Finally, a discussion was conducted to verify the superiority of our approach. The results showed that our algorithm can characterize and evaluate complex information and has high sensitivity and environmental adaptability.

The linguistic intuitionistic fuzzy sets (LIFSs) and linguistic Pythagorean fuzzy sets (LPFSs) are two linguistic orthopair fuzzy sets whose membership grades are pairs of linguistic terms from the predefined linguistic term sets (LTSs). One linguistic term indicates the membership degree (MD), while the other one gives the nonmembership degree (NMD). In each LIFS, the sum of the subscripts of MD and NMD is less than the cardinality of LTS. In the LPFSs, the sum of the squares of the subscripts of MD and NMD is less than the square of the cardinality of LTS. In this paper, we propose a general form of these two linguistic orthopair fuzzy sets, which can be named linguistic q-rung orthopair fuzzy sets. We devise the operational laws, based on which, the linguistic q-rung orthopair fuzzy weighted averaging (LqROFWA) operator and linguistic q-rung orthopair fuzzy weighted geometric (LqROFWG) operator are developed to aggregate the linguistic q-rung orthopair fuzzy numbers (LqROFNs). Then, the novel interactional operational laws that consider the interactions between the MD and NMD from different LqROFNs are given. The partitioned geometric Heronian mean (PGHM) operator can effectively solve the decision-making problems in which the attributes grouped into the same clusters have interrelationships and the attributes belonging to different clusters have no interrelationship. Based on these novel operational laws and PGHM operator, the linguistic q-rung orthopair fuzzy interactional PGHM (LqROFIPGHM) operator and linguistic q-rung orthopair fuzzy interactional weighted PGHM (LqROFIWPGHM) operator are proposed and their properties are discussed. Based on the LqROFIWPGHM operator, an efficient multiattribute group decision-making model is given to deal with the linguistic q-rung orthopair fuzzy information. Finally, the superiorities of the interactional operational laws and LqROFIWPGHM operator are tested using some illustrative examples.

The probabilistic hesitant fuzzy preference relations (PHFPRs) provide the decision makers with an efficient means to express the preference information on pairwise comparisons over alternatives. In this paper, we propose an automatic consistency improving model for PHFPRs. First, we propose a novel normalization algorithm to normalize probabilistic hesitant fuzzy elements (PHFEs) by using probability splitting idea and develop novel operational laws. Then, we define the consistency index to compute the degree of deviation between the PHFPRs and their multiplicative consistent PHFPRs. We also develop a novel consistency threshold estimation method for obtaining the threshold of consistency index and then put forward an automatic consistency improving algorithm for repairing inconsistent PHFPRs. Moreover, two probabilistic hesitant fuzzy aggregation operators are put forward to aggregate preference values in acceptably multiplicative consistent PHFPRs for obtaining the ranking orders of alternatives. Finally, an illustrative example is given to show the implementation process of our proposed automatic consistency improving model and also we compare our proposed model with the existing studies.

As a novel and powerful tool, the notion of probabilistic linguistic term sets (PLTSs) can efficiently model this kind of qualitative assessment information utilizing several possible linguistic terms associated with probabilities or weights over alternatives. Considering that there are no investigation and research on the correlation coefficient and clustering analysis for the concept of PLTSs. Therefore, some correlation coefficient formulas are put forward to measure the relationship between two PLTSs and then they are utilized to develop two novel clustering algorithms to group PLTSs in this paper. We first define some correlation coefficient formulas and their weighted forms to measure the relationship between PLTSs. Then, we extend a fuzzy clustering algorithm for PLTSs and also propose a novel orthogonal clustering algorithm for PLTSs. Finally, we provide a practical example, which performs cluster analysis on the levels of general higher education in different regions of China, to test and verify the usability of our proposed clustering algorithm.