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As an emerging type of large commercial building, commercial complexes play an increasingly important role in contemporary urban development and construction trends. In order to better study the organization of public space relations in commercial complex buildings, this paper selects eight commercial complexes as sample cases to analyze their spatial design in terms of both content public space and external public space based on big data technology. Regarding the design of the commercial complexes’ internal public space movement, the highest accessibility degree reached 95.3%, while the average was 82.5%. Regarding visibility, the highest level was 96.0%, and the average was 83.3%. For large complexes, better spatial relationships can be designed to improve the circulation degree and thus enhance customers’ consumption experience. Regarding the convenience of traffic connection to the external space of commercial complexes, an average of 41.4% of customers consider it very convenient, 23.1% consider it relatively convenient, 27.9% consider it somewhat inconvenient, and 18.0% consider it very inconvenient. Commercial complexes can effectively attract more repeat customers if they can improve the convenient design of transportation connections. The study of public relations of commercial complexes based on big data helps to discover the defects of their public space design and plays a significant role in optimizing spatial design and relationship organization and strengthening their integrated functions.

Abstract Deep learning has achieved tremendous success in various applications owing to its robust feature representations of complex high-dimensional nonlinear data. Financial time-series prediction is no exception. Hence, the volatility trend prediction in financial time series (FTS) has been an active topic for several decades. Inspired by generative adversarial networks (GAN), which have been studied extensively in image processing and have achieved excellent results, we present the ordinal regression GAN for financial volatility trends (ORGAN-FVT) method for the end-to-end multi-classification task of FTS. An improved generative model based on convolutional long short-term memory (ConvLSTM) and multilayer perceptron (MLP) is proposed to capture temporal features effectively and mine the data distribution of volatility trends (short, neutral, and long) from given FTS data. Meanwhile, ordinal regression is leveraged for the discriminator to improve the multi-classification performance, making the model more practical. Finally, we empirically compare ORGAN-FVT with several state-of-the-art approaches on three real-world stock datasets: MICROSOFT(MSFT), Tesla(TSLA), and The People’s Insurance Company of China(PAICC). ORGAN-FVT demonstrated significantly better AUC and F1 scores, at most 20.81% higher than its competitors.

Objective To investigate the effect of autophagy expression levels of different weight‐bearing states and different stages of osteoarthritis in animal models, as well as the corresponding mechanisms. Methods We used the male Sprague–Dawley (SD) rats (12‐week‐old, SPF) to establish the OA animal models by modified Hulth method, and grouped animal models according to the length of time after surgery and different weight‐bearing areas. RT‐qPCR was carried out for detection of autophagy‐related genes such as Atg7, Atg12, P62, etc. Western blot analysis was used to detect the expression levels of corresponding autophagy‐related proteins such as LC3B, P62, etc. T test was performed for statistical analysis to compare different groups, while the differences were deemed statistically significant with P

Na-β″-Al2O3 was prepared with nano-η-Al2O3 powder by a double zeta process, MgO as stabilizer. The compactness, microstructure and mechanical properties of the samples were studied by Archimedes, SEM and three-point bending method, and the β″-Al2O3 phase content and ionic conductivity of the samples were studied by XRD and EIS. The results show that double zeta process is beneficial to improve the uniformity of sample structure. Nano-η-Al2O3 is easier to synthesize Na-β″-Al2O3 solid electrolyte than high purity α-Al2O3, the addition of appropriate MgO can increase the content of the β″-Al2O3 phase and the compactness of the samples, reduce the grain boundary resistance of the sample and improve the ionic conductivity of the electrolyte. Excessive MgO doping results in the growth of pore size in the samples, which will increase the grain resistance and decrease the ionic conductivity. The ionic conductivity of the electrolyte material reaches 0.0396 S·cm-1 at 300 ℃ when the amount of MgO is 2% (mass fraction).

BackgroundPhelanrMcDermid syndrome (PMS) is an uncommon autosomal dominant inherited developmental disorder. The main characteristics are hypotonia, intellectual disability, autism spectrum disorder, autism-like behaviors and tiny facial deformities. Most cases are caused by the deletion of the 22q13 genomic region, including the deletion of SHANK3.MethodsGenetic and phenotype evaluations of ten Chinese pediatric patients were performed. The clinical phenotypes and genetic testing results were collected statistically. We analyzed the deletion of the 22q13 genomic region and small mutations in SHANK3 (GRCh37/hg19) and performed parental genotype verification to determine whether it was related to the parents or was a novel mutation.ResultsThe age of the patients diagnosed with PMS ranged from 0 to 12 years old. Nine of the pediatric patients experienced Intellectual Disability, language motion development delay and hypotonia as prominent clinical features. One subject had autism, two subjects had abnormal electroencephalogram discharge and one subject was aborted after fetal diagnosis. Three patients had a SHANK3 mutation or deletion. All but the aborted fetuses had intellectual disability. Among the ten patients, a deletion in the 22q13 region occurred in seven patients, with the smallest being 60.6 kb and the largest being >5.5 Mb. Three patients had heterozygous mutations in the SHANK3 gene.ConclusionAll ten patients had novel mutations, and three of these were missense or frameshift mutations. For the first time reported, it is predicted that the amino acid termination code may appear before protein synthesis. The novel mutations we discovered provide a reference for clinical research and the diagnosis of PMS.

Background:There were few studies to report whether drinking water sources and habits affected health outcomes. Therefore, this study aimed to examine how boiled water and lifespan water sources affected the risks of cardiovascular disease (CVD) and all-cause mortality in the elderly.MethodsThis study was a 20-year cohort study. All participants aged ≥60 years were eligible. Exposures of interest included lifespan drinking water sources and habits, which were collected using a validated questionnaire. Drinking water sources included wells, surface water, spring, and tap water in childhood, around the age of 60 years, and at present. Drinking habits included boiled and un-boiled water. The main end events included CVD and all-cause mortality.ResultsThere were 33,467 participants in this study. Compared to tap water, drinking well and surface water around the age of 60 years were associated with a higher risk of all-cause mortality (HR: 1.092, 95% CI: 1.051–1.134, P < 0.001; and HR: 1.136, 95% CI: 1.081–1.194, P < 0.001, respectively). However, only drinking spring around aged 60 years and drinking well at present were associated with a lower CVD mortality (HR: 0.651, 95% CI: 0.452–0.939, P = 0.022; and HR: 0.757, 95% CI: 0.665–0.863, P < 0.001, respectively). Boiled water was not associated with mortality.ConclusionsDrinking water from well and surface water around the age of 60 years were associated with increased all-cause mortality. Drinking water from spring around the age of 60 years and well at present was associated with a decreased CVD mortality. However, boiled water was not associated with mortality.

The rapid development of civil UAV promotes the social and economic development, and the frequent “flying illegally” events has brought great challenges to aviation safety and government supervision. The frequency hopping communication system used in UAV data transmission and control link has the advantages of anti-jamming and anti-interception, and its complex electromagnetic environment, which also brings great difficulties to UAV detection. In this paper, the detection of civil UAV is realized by frequency hopping signal monitoring. Firstly, by analyzing the signal characteristics of UAVs, an adaptive noise threshold calculation method is proposed for find the signals from spectrum data. Then, the improved clustering analysis algorithm is proposed based on constructed the waveform shape characteristics and peak characteristics of UAV frequency hopping signal. Finally, according to the designed experimental process, the experimental environment is set up, and the UAV monitoring, discovery and parameter estimation are realized by using the improved clustering analysis algorithm, and compared with K-means, K-means++, DBSCAN, Multi-hop and Auto-correlation methods. The results show that the method has certain robustness and has a good application prospect.

Single-valued neutrosophic set (SVN) can valid depict the incompleteness, nondeterminacy and inconsistency of evaluation opinion, and the Power average (PA) operator can take into account the correlation of multiple discussed data. Meanwhile, Archimedean copula and co-copula (ACC) can significant generate operational laws based upon diverse copulas. In this paper, we first redefine several novel operational laws of single-valued neutrosophic number (SVNN) based on ACC and discuss the associated properties of them. In view of these operational rules, we propound several novel power aggregation operators (AOs) to fuse SVN information, i.e., SVN copula power average (SVNCPA) operator, weighted SVNCPA (WSVNCPA) operator, order WSVNCPA operator, and SVN copula power geometric (SVNCPG) operator, weighted SVNCPG (WSVNCPG) operator, order WSVNCPG operator. At the same time, several significant characteristics and particular cases of these operators are examined in detail. Moreover, we extend these operators to their generalized form named generalized SVNCPA and SVNCPG operator. In addition, a methodology is designed based on these operators to cope with multi-attribute decision-making (MADM) problems with SVN information. Consequently, the effectiveness and utility of the designed approach is validated by a empirical example. A comparative and sensitivity analysis are carried out to elaborate the strength and preponderance of the propounded approach.

A challenge in association rules’ mining is effectively reducing the time and space complexity in association rules mining with predefined minimum support and confidence thresholds from huge transaction databases. In this paper, we propose an efficient method based on the topology space of the itemset for mining associate rules from transaction databases. To do so, we deduce a binary relation on itemset, and construct a topology space of itemset based on the binary relation and the quotient lattice of the topology according to transactions of itemsets. Furthermore, we prove that all closed itemsets are included in the quotient lattice of the topology, and generators or minimal generators of every closed itemset can be easily obtained from an element of the quotient lattice. Formally, the topology on itemset represents more general associative relationship among items of transaction databases, the quotient lattice of the topology displays the hierarchical structures on all itemsets, and provide us a method to approximate any template of the itemset. Accordingly, we provide efficient algorithms to generate Min-Max association rules or reduce generalized association rules based on the lower approximation and the upper approximation of a template, respectively. The experiment results demonstrate that the proposed method is an alternative and efficient method to generate or reduce association rules from transaction databases.

Objective To investigate the effect of tumor necrosis factor alpha (TNF‐α) on the proliferation of fibroblast‐like synoviocytes (FLS) and the expression of programmed cell death factor 5 (PDCD5) in an inflammatory microenvironment, for the further understanding of the mechanism of action of TNF‐α in promoting the proliferation of synovial cells and the apoptosis of the chondrocytes. Methods Articular carriage specimens were obtained from 21 cases with osteoarthritis and 12 cases with femoral neck fractures as healthy controls during arthroplasties. The expression of PDCD5 was evaluated by immunofluorescence analyzed by mean option density (MOD) detected using the software ImagePro Plus. Real‐time PCR was performed to evaluate the transcriptions of PDCD5 and TNF‐α in synovium. FLS cells derived from rheumatoid arthritis patients were cultured in vitro and incubated with different concentrations of TNF‐α. The effects of TNF‐α at different concentrations on the proliferation of FLS cells were detected by Cell Counting Kit‐8 (CCK‐8) assay to evaluate the cell proliferation rate. After incubation with the absence or presence of recombinant human TNF‐α at different concentrations, the FLS cells were isolated for detection of PDCD5 protein and PDCD5 gene. The expression of PDCD5 protein was detected by western‐blot and the transcription of PDCD5 gene from the cells was detected by real‐time quantitative PCR. Results The MOD of PDCD5 as well as TNF‐α of osteoarthritis cartilage sections were significantly increased compared with those of the controls, and in synovium there was a positive correlation between transcriptions of their mRNA. When the concentration of TNF‐α was 1 ng/mL, the cell proliferation rate was not significantly different from that of the control group (P = 0.592), while the proliferation of FLS cells was significantly promoted when the concentration of TNF‐α was 5, 10, 15, or 20 ng/mL, and the proliferation‐promoting rates were 35.64% ± 6.96%, 48.72% ± 7.69%, 45.60% ± 8.85%, and 39.32% ± 6.18%, respectively (P 0.05). The expression of PDCD5 protein was only significantly downregulated when the concentration of TNF‐α was 10 ng/mL (P 0.05). Conclusion The expression of PDCD5 as well as TNF‐α in osteoarthritis cartilage and synovium was significantly higher than in healthy tissues, and TNF‐α can promote the proliferation of FLS cells in patients with rheumatoid arthritis, and inhibit the expression of PDCD5. PDCD5 may be involved in the abnormal proliferation of synoviocytes and the degeneration of chondrocytes stimulated by TNF‐α.

Mining frequent closed itemsets (FCIs) from transaction databases is a fundamental problem in many data mining applications. All the enumeration algorithms enumerate FCIs by adding a singleton item to an itemset and then checking whether it is closure. In order to reduce enumerations, we enumerate FCIs by adding an itemset to the existing FCI itemset. To this end, we first analyze a binary relation on the set of itemsets in transaction databases, show co-occurrence relation among items, and prove that the relation is reflexive and transitive. Next, we use the relation to construct a topology for the set of itemsets and prove that all FCIs are included in the topology. Then, we construct a topology-transaction tree (TT-tree) and provide a topology-transaction miner (TT-Miner) algorithm for enumerating FCIs in the TT-tree. Finally, an extensive experimental evaluation on a number of real and synthetic databases shows that the TT-Miner is an efficient and scalable algorithm compared with the previous methods.

Constructing and managing multi-granular linguistic values are more and more important for linguistic decision making in big data or social computing environments, linguistic variable is the fundamental of constructing and managing multi-granular linguistic values. Based on analysis of linguistic values and drawbacks of symbolic or fuzzy set methods in processing linguistic information, a linguistic value is expressed by a formal linguistic concept, which is constructed by a linguistic term and it's fuzzy sets, i.e., intension (name) and extension (meaning) of the concept are a linguistic term and it's fuzzy sets. A new symbolic translation based on fuzzy sets is provided to obtain formal 2-tuple linguistic concepts, which are continuous formal linguistic concepts. By using linguistic hedges, the hierarchy of multi-granular formal linguistic concepts is constructed, and managing multi-granular linguistic values is carried out by a new transformation function between formal linguistic concepts of the hierarchy. Cases study shows that the proposed method combines advantages of symbolic approaches and fuzzy set methods in linguistic information processing and overcomes their drawbacks due to fuzzy sets and linguistic term as entity in linguistic information processing based on formal linguistic concepts, intensions are utilized to deal with linguistic information and extensions are used to represent meanings and obtain natural or artificial language concepts. It seems that constructing and managing multi-granular linguistic values via formal linguistic concepts is an useful and alternative method in linguistic information processing.

Many association rule mining algorithms have been well-established, such as Apriori, Eclat, FP-Growth, or LCM algorithms. However, the challenge is that the huge size of association rules is extracted by using these algorithms, and it is difficult for users to select satisfied association rules from them. In this paper, a new method is proposed to select satisfied association rules, which is based on the aggregation of fuzzy linguistic satisfied degrees of extracted association rules. To this end, two problems must be solved, one is which interesting measures are utilized to obtain fuzzy linguistic satisfied degrees of association rules and the other is how to aggregate them. For the first problem, many objective and subjective interesting measures have been proposed, which are generally included in [0, 1] or others universes and easily calculated by support, confidence, or other measures, these interesting measures cannot be directly aggregated, because different interesting measures represent different satisfied degrees of association rules. In this paper, a new transformation function is proposed to transform these interesting measures into fuzzy linguistic satisfied degrees, such as dissatisfied, fair, satisfied, and so on. For the second problem, by considering different weights of objective and subjective interesting measures, linguistic aggregation operators are designed to aggregate these fuzzy linguistic satisfied degrees of association rules. Accordingly, satisfied association rules are selected by using order on the aggregation results of linguistic satisfied degrees. In cases' study, Apriori, Eclat, FP-Growth, and LCM algorithms are first utilized to extract association rules with higher support or confidence measures from Chess, Connect, Mushroom, and T40I10D100K databases, then the proposed method is applied to obtain fuzzy linguistic satisfied degrees of extracted association rules and aggregate and select satisfied association rules from those extracted association rules, and comparison and analysis show that the proposed method is a useful and alternative tool to select satisfied association rules from extracted association rules.

As an effective technique to qualitatively depict assessment information, a linguistic intuitionistic fuzzy number (LIFN) is more appropriate to portray vagueness and indeterminacy in actual situations than intuitionistic fuzzy number (IFN). The prominent feature of a Muirhead mean (MM) operator is that it has the powerful ability to capture the correlations between any input-data and MM operator covers other common operators by assigning the different parameter vectors. In the article, we first analyze the limitations of the existing ranking approaches of LIFN and propose a novel ranking approach to surmount these limitations. Secondly, we propound several novel MM operators to fuse linguistic intuitionistic fuzzy (LIF) information, such as the LIF Muirhead mean (LIFMM) operator, the weighted LIF Muirhead mean (WLIFMM) operator and their dual operators, the LIFDMM operator and the WLIFDMM operator. Subsequently, we discuss several desirable properties along with exceptional cases of them. Moreover, two novel multiple attribute group decision-making approaches are developed based upon these operators. Ultimately, the effectuality and practicability of the propounded methods are validated through dealing with a global supplier selection issue, and the comparative analysis and the merits of the presented approaches are demonstrated by comparing them with existing approaches.

Linguistic Pythagorean fuzzy (LPF) set is an efficacious technique to comprehensively represent uncertain assessment information by combining the Pythagorean fuzzy numbers and linguistic variables. In this paper, we define several novel essential operations of LPF numbers based upon Einstein operations and discuss several relations between these operations. For solving the LPF numbers fusion problem, several LPF aggregation operators, including LPF Einstein weighted averaging (LPFEWA) operator, LPF Einstein weighted geometric (LPFEWG) operator and LPF Einstein hybrid operator, are propounded; the prominent characteristics of these operators are investigated as well. Furthermore, a multi-attribute group decision making (MAGDM) approach is presented on the basis of the developed operators under an LPF environment. Ultimately, two application cases are utilized to demonstrate the practicality and feasibility of the developed decision approach and the comparison analysis is provided to manifest the merits of it.

In the paper, we express uncertain assessments information in linguistic multi-criteria decision makings (LMCDMs) as linguistic intuitionistic fuzzy sets, i.e., the decision maker provides membership and non-membership fuzzy linguistic terms to represent uncertain assessments information of alternatives in LMCDMs, and present Hamming distance between two linguistic intuitionistic fuzzy sets. Then we propose the linguistic intuitionistic fuzzy set TOPSIS method for LMCDMs, compared with the traditional TOP-SIS method, we provide different the positive ideal solution, the negative ideal solution and the relative closeness degrees of alternatives, in addition, we design an algorithm to finish the linguistic intuitionistic fuzzy set TOPSIS method for LMCDMs. We utilize a LMCDM problem to illustrate the performance, usefulness and effectiveness of the linguistic intuitionistic fuzzy set TOPSIS method, and compare it with the hesitant fuzzy linguistic multi-criteria optimization and compromise solution (HFL-VIKOR) method, the symbolic aggregation-based method and the hesitant fuzzy linguistic TOPSIS (HFL-TOPSIS) method in the example, results show that the linguistic intuitionistic fuzzy set TOPSIS method is a useful and alternative method for LMCDMs.

The aim of the paper is to discuss some new operations on hesitant fuzzy linguistic terms sets based on Archimedean t-norm and t-conorm. The advantage is that the operations on hesitant fuzzy linguistic terms sets are closed, by studying propositions of the operations on hesitant fuzzy linguistic terms sets, scalar-multiplication addition and power multiplication hesitant fuzzy linguistic terms aggregation operators are proposed. An example is presented to illustrate the practicality of the four well-known scalar-multiplication addition and power multiplication hesitant fuzzy linguistic terms aggregation operators, which are also compared with the symbolic aggregation-based method in the example, results show that scalar-multiplication addition and power multiplication hesitant fuzzy linguistic terms aggregation operators can be applied to fuse hesitant fuzzy linguistic terms sets.

In this paper, we propose a particle-filter-based superpixel (PFS) segmentation method that extends the original tracking problem as a region clustering problem. The basic idea is to approximate superpixel centers by multiple particles to obtain high intra-region similarity. Specifically, we firstly use a density cluster to initialize single-group particles and introduce the association rule for mining other initial candidate particles. In propagation, particles are transferred to neighboring local regions by a moving step aiming to update local candidate particles with a lower energy cost. We evaluate all particles on the basis of their cluster similarity and estimate the largest particles as the final superpixel centers. The proposed method can locate cluster centers in diverse feature space, which alleviates the risk of a local optimum and produces better segmentation performance. Experimental results on the Berkeley segmentation 500 dataset (BSD500) demonstrate that our method outperforms seven state-of-the-art methods.

Motivated by intuitionistic fuzzy sets and fzzy linguistic approach, this article proposes the concept of linguistic intuitionistic fuzzy numbers (LIFNs) where membership and and nonmembership are represented as linguistic terms. In order to process the multiple attribute decision making (MADM) with LIFNs, we introduce the linguistic score index and linguistic accuracy index of the LIFN. Simultaneously, the operation laws for LIFNs are defined and the related properties of the operation laws are studied. Further, some aggregation operators are developed, involving the linguistic intuitionistic fuzzy weighted averaging (LIFWA) operator, linguistic intuitionistic fuzzy ordered weighted averaging (LIFOWA) operator and linguistic intuitionistic fuzzy hybrid averaging (LIFHA) operator, etc., which can be utilized to aggregate preference information taking the form of LIFNs. Based on the LIFWA and the LIFHA operators, we propose an approach to handle MADM under LIFNs environment. Finally, an illustrative example is given to verify the feasibility and effectiveness of the proposed method, which are then compared to other representative methods.

In this paper, properties of operations and algebraic structures of hesitant fuzzy sets are investigated. Semilattices of hesitant fuzzy sets with union and intersection are discussed, respectively. By using ⊕ and ⊗ operators, the commutative monoid of hesitant fuzzy sets is provided, moreover, the lattice and distributive lattice of hesitant fuzzy sets are defined on the equivalence class of hesitant fuzzy sets. Based on the distributive lattice of hesitant fuzzy sets, the residuated lattices of hesitant fuzzy sets are constructed by residual implications, which are induced by intersection and ⊗, respectively. From the theoretical point of view, algebraic structures of hesitant fuzzy sets are useful for approximate reasoning and decision making to deal with hesitancy of information.

This paper puts forward a prediction model based on membrane computing optimization algorithm for chaos time series; the model optimizes simultaneously the parameters of phase space reconstruction (τ,m) and least squares support vector machine (LS-SVM) (γ,σ) by using membrane computing optimization algorithm. It is an important basis for spectrum management to predict accurately the change trend of parameters in the electromagnetic environment, which can help decision makers to adopt an optimal action. Then, the model presented in this paper is used to forecast band occupancy rate of frequency modulation (FM) broadcasting band and interphone band. To show the applicability and superiority of the proposed model, this paper will compare the forecast model presented in it with conventional similar models. The experimental results show that whether single-step prediction or multistep prediction, the proposed model performs best based on three error measures, namely, normalized mean square error (NMSE), root mean square error (RMSE), and mean absolute percentage error (MAPE).

P systems are a class of distributed parallel computing models; this paper presents a novel clustering algorithm, which is inspired from mechanism of a tissue-like P system with a loop structure of cells, called membrane clustering algorithm. The objects of the cells express the candidate centers of clusters and are evolved by the evolution rules. Based on the loop membrane structure, the communication rules realize a local neighborhood topology, which helps the coevolution of the objects and improves the diversity of objects in the system. The tissue-like P system can effectively search for the optimal partitioning with the help of its parallel computing advantage. The proposed clustering algorithm is evaluated on four artificial data sets and six real-life data sets. Experimental results show that the proposed clustering algorithm is superior or competitive to k-means algorithm and several evolutionary clustering algorithms recently reported in the literature.

Hesitant fuzzy linguistic decision making is a focus point in linguistic decision making, in which the main method is based on preference ordering. This paper develops a new hesitant fuzzy linguistic TOPSIS method for group multi-criteria linguistic decision making; the method is inspired by the TOPSIS method and the preference degree between two hesitant fuzzy linguistic term sets (HFLTSs). To this end, we first use the preference degree to define a pseudo-distance between two HFLTSs and analyze its properties. Then we present the positive (optimistic) and negative (pessimistic) information of each criterion provided by each decision maker and aggregate these by using weights of decision makers to obtain the hesitant fuzzy linguistic positive and negative ideal solutions. On the basis of the proposed pseudo-distance, we finally obtain the positive (negative) ideal separation matrix and a new relative closeness degree to rank alternatives. We also design an algorithm based on the provided method to carry out hesitant fuzzy linguistic decision making. An illustrative example shows the elaboration of the proposed method and comparison with the symbolic aggregation-based method, the hesitant fuzzy linguistic TOPSIS method and the hesitant fuzzy linguistic VIKOR method; it seems that the proposed method is a useful and alternative decision-making method.

In this paper, a decision model based on a fuzzy soft set and ideal solution approaches is proposed. This new decision-making method uses the divide-and-conquer algorithm, and it is different from the existing algorithm (the choice value based approach and the comparison score based approach). The ideal solution is generated according to each attribute (pros or cons of the attributes, with or without constraints) of the fuzzy soft sets. Finally, the weighted Hamming distance is used to compute all possible alternatives and get the final result. The core of the decision process is the design phase, the existing decision models based on soft sets mostly neglect the analysis of attributes and decision objectives. This algorithm emphasizes the correct expression of the purpose of the decision maker and the analysis of attributes, as well as the explicit decision function. Additionally, this paper shows the fact that the rank reversal phenomenon occurs in the comparison score algorithm, and an example is provided to illustrate the rank reversal phenomenon. Experiments indicate that the decision model proposed in this paper is efficient and will be useful for practical problems. In addition, as a general model, it can be extended to a wider range of fields, such as classifications, optimization problems, etc.

Multiple attributes group decision making problems aim to find the best alternative for the experts from a solution set of alternatives. Because the attribute value and decision-makers evaluation with respect to the alternatives are usually vague and imprecise, fuzzy multiple attributes group decision making have been widely investigated, in which, ordering fuzzy evaluation results in fuzzy decision making is an important method to find the best alternative for the experts, difference fuzzy expressions for evaluation in fuzzy decision making problems correspond with difference aggregation operator and ranking method. In this paper, we analyze some algebraic properties of a kind of ranking method in fuzzy multiple attributes group decision-making, and prove that the ranking method is pre-ordering, its'drawback in fuzzy decision making is no unique alternative to be best alternative. Then, we provide an equivalence relation on fuzzy evaluation values based on the ranking method, and propose a linearly ordering on equivalence classes of fuzzy evaluation values. Based on the linearly ordering, we propose an improve method to handle fuzzy multiple attributes group decision-making when its ordering is pre-ordering. Some numerical examples illustrate that our method can be used to improve the best alternative of fuzzy decision making when its ordering is pre-ordering.

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. Recently, uncertainty measures of soft sets and fuzzy soft sets have gained attentions from researchers. This paper is devoted to the study of uncertainty measures of fuzzy soft sets. The axioms for similarity measure and entropy are proposed. A new category of similarity measures and entropies is presented based on fuzzy equivalence. Our approach is general in the sense that by using different fuzzy equivalences one gets different similarity measures and entropies. The relationships among these measures and the other proposals in the literatures are analyzed.

Soft set theory and interval set theory are all mathematical tools for dealing with uncertainties. This paper is devoted to the discussion of soft interval set and its application. The notion of soft interval sets is introduced by combining soft set and interval set. Several operations on soft interval sets are presented in a manner parallel to that used in defining operations on soft sets and the lattice structures of soft interval sets are established. In addition, a soft interval set based decision making problem is analyzed.

In this paper, we present a linguistic interval 2-tuple representation model and new linguistic interval 2-tuple aggregation operators, i.e., linguistic interval 2-tuple power average (LI2TPA) operator, linguistic interval 2-tuple weighted power average (LI2TWPA) operator and linguistic interval 2-tuple power ordered weighted average (LI2TPOWA) operator. Some desired properties of the developed operators are also studied. Moreover, we use these aggregation operators to deal with multiple attribute group decision making problems under linguistic interval 2-tuple environment. In the situations where the weighting vector of the decision makers is known, we use the LI2TWPA operator to make multiple attribute group decision. In the situations where the weighting vector of the decision makers is unknown, we use the LI2TPOWA operator to deal with multiple attribute group decision making. A numerical example is provided to show the effectiveness of our method.

In this paper, we develop an improved ranking strategy for fuzzy multiple attribute group decision making. First, we introduce a method for multiple attribute group decision making and show that method can not choose the best alternative, when S() = 0 and . We define then a k-order deviation of the fuzzy sets and propose an improved ranking strategy, we also propose an improved method for fuzzy multiple attribute group decision making. Finally, the results of a numerical example demonstrate the effectiveness of this new method.

Based on the equivalence relation, we can partition a set U, formally, different equivalence relations correspond to different partitions of U. In this paper, based on Yager's work, we discuss how to compare the different partitions, moreover, we obtain some indexes to select a better partition from given partitions. By an illustrative example, we show that our proposed indexes can be used for selecting partitions, feature selection, and help us to gather more information to decision making.