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The theory of T-spherical fuzzy (T-SF) sets possesses remarkable capability to manage intricate uncertain information. The REGIME method is a well-established technique concerning discrete choice analysis. This paper comes up with a multiple-criteria choice analysis approach supported by the REGIME structure for manipulating T-SF uncertainties. This paper constructs new-created measurements such as superiority identifiers and guide indices for relative attractiveness and fittingness, respectively, between T-SF characteristics. This study evolves the T-SF REGIME I and II prioritization procedures for decision support. The application and comparative studies exhibit the effectiveness and favorable features of the propounded T-SF REGIME methodology in real decisions.

The purpose of this paper is to evolve a novel area-based Pythagorean fuzzy decision model via an approach-oriented measure and an avoidance-oriented measure in support of multiple criteria decision analysis involving intricate uncertainty of Pythagorean fuzziness. Pythagorean membership grades embedded in a Pythagorean fuzzy set is featured by tensible functions of membership, non-membership, indeterminacy, strength, and direction, which delivers flexibility and adaptability in manipulating higher-order uncertainties. However, a well-defined ordered structure is never popular in real-life issues, seldom seen in Pythagorean fuzzy circumstances. Consider that point operators can make a systematic allocation of the indeterminacy composition contained in Pythagorean fuzzy information. This paper exploits the codomains of the point operations (i.e., the quantities that express the extents of point operators) to launch new measurements of approach orientation and avoidance orientation for performance ratings. This paper employs such measurements to develop an area-based performance index and an area-based comprehensive index for conducting a decision analysis. The applications and comparative analyses of the advanced area-based approach to some decision-making problems concerning sustainable recycling partner selection, company investment decisions, stock investment decisions, and working capital financing decisions give support to methodological advantages and practical effectiveness.

This study aims to extend classic VIKOR technique for multicriteria decision-making (MCDM) problems within Pythagorean fuzzy (PF) scenario. First, judgments from decision makers (DMs) are expressed by PF sets that can describe more uncertain and ambiguous information than available fuzzy sets. Second, PF point operators are applied to denote the risk preference of the DM who may express an attitude toward an emerging science and technology. Third, a new generalized distance measurement formula considering all the characteristics of PF sets is proposed, and some attractive properties of distance measure, which outperforms available distance measures, are proved. Fourth, the novel generalized distance measure is employed to relative distance to identify the optimum and worst PF values and then employed in $$L_{p}$$ -metric VIKOR formula to accurately gain the group utility, individual regret, and compromise index. The novel PF-VIKOR algorithm considering DM’s risk preference and a novel distance measure is described in detail, and a blockchain technology solution selection problem is utilized to validate the feasibility of our technique. Then, the sensitivity analysis is implemented to test stability of our PF-VIKOR technique when the parameters in risk preferences and generalized distance measure are adjusted. Fifth, the comparison among various PF-MCDM techniques is performed to validate superiority and practicability of our presented technique.

The purpose of this paper is to propose a useful likelihood measure for determining scalar function order relations and developing a novel likelihood-based optimization ordering model for solving multiple criteria group decision making (MCGDM) problems based on Pythagorean fuzzy (PF) sets. This paper scrutinizes PF order relations based on scalar functions to compare sophisticated uncertain information and establish a precedence order. By way of scalar function order relations, this paper utilizes scalar functions that are associated with Pythagorean membership grades and admissible upper approximations to present a novel likelihood measure in PF contexts. With the aid of useful concepts, such as levels of agreement and disagreement and comprehensive performance values, this paper originates a PF likelihood-based optimization ordering model to acquire the optimal group consensus solution for addressing MCGDM problems. Practical applications and several comparative studies are performed to reveal the practicality and strong points of the proposed methodology in tackling real-world MCGDM issues within uncertain environments of PF sets. This paper finds that the new scalar function-based likelihood measure is more flexible and beneficial than the current probability distribution approach. Furthermore, an easy-to-use algorithmic procedure can realize the proposed methodology to efficaciously process sophisticated PF information and improve the understandability of a decision model via a likelihood comparison approach. The originality and main contributions of this work are fourfold: (1) A PF likelihood measure is introduced as a basis for scalar function order relations; (2) the PF likelihood-based optimization ordering model is established for consensus ranking; (3) a predominant procedure is constructed for addressing PF information; and (4) the likelihood-based decision models are enriched under complex uncertainty.

In this paper, we analyze the delay of the message delivery from a vehicle to a downstream vehicular gateway in a sparse vehicle ad hoc network (VANET). Several research efforts have previously bee...

Residue Number Systems (RNS) can simultaneously improve computing acceleration, area reduction and power saving. For high-reliability applications like automotive electronics, partition-ability empowers the redundant RNS fault tolerance. However the parallel multiple modular redundancy will take a huge number of converters. This is the first paper to incorporate AN codes to the RRNS applied in high-reliable neural networks. From experimental results, the k-modulus redundancy can be reduced from 2 paths to only one, and the residue-to-binary converters can be saved from (k+2)(k+1) to only k+1 for the external-coding structure, and even to only one for the internal-coding structure in the single residue arithmetic-weight error correcting. From BLER simulations, about 130 times of reliability can be achieved for a 16-bit 47N-coded MAC.

In this paper, we generalize the lightweight-slope piecewise-line range-addressable lookup table for efficient approximate computing in any activation/quantization function, and propose an error-correcting algorithm and circuitry using the AN codes for enhancing reliability. A BLER/SNR simulation proves the SEC/DEC capability of the firstly-presented AN-coded neuron. Comparisons with similar state-of-the-art works show that the proposed technique is the most efficient and error-correctable lookup table for any function in a medium resolution within 8-12 bits.

Since it was invented by Satoshi Nakamoto in 2008, Bitcoin has drawn considerable attention both from the financial industry and government supervisory departments, and there is no unanimity on Bitcoin’s nature in the academic field. Some people may think Bitcoin is more like an asset than a currency. And investors’ motivations for incorporating Bitcoin into their portfolios may vary. Might there be a better way to deal with the risk-detection issue associated with such a unique and ambiguous object? The copula-GARCH method has been proven in much of the literature to be a better way than the traditional ways to estimate the value at risk (VaR) of portfolios. When it comes to a portfolio containing Bitcoin, can it still maintain its superiority? In this study, gold and Ethereum were each used to construct a portfolio with Bitcoin. We collected a total of 2,246 daily adjusted closing prices from July 23, 2010, to March 12, 2019. As for the copula-GARCH model, we selected four constant and two time-varying copula models combined with GARCH Student-t residuals to fit the joint distribution of the two assets in the portfolios. The traditional methods refer to the historical simulation, the variance-covariance method, the EWMA method, and the univariate GARCH VaR method. We adopted each method to compute corresponding one-day VaRs. Our results indicated that for the portfolios containing Bitcoin and Ethereum, the copula-GARCH method performed better than traditional methods, while for the portfolio consisting of Bitcoin and gold, traditional methods performed better. Our results may suggest that the copula-GARCH method may not be suitable in the extremely low correlation case.

As a critical component in green supply chain activities, green supplier selection modelled as the typical multicriteria group decision-making (MCGDM) problem, has received tremendous attention both from scholars and practitioners. This article aims to advance an integrated approach for precisely addressing this urgent problem under Pythagorean fuzzy (PF) scenario. Firstly, analytic hierarchy process (AHP) is utilized for computing criterion weights that comprehensively reflect the intention of decision makers (DMs). Secondly, extend the Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) to PF scenario, and apply the newest magnitude comparison method and distance measure of PF sets in the $L_{p} -$ metric equation to accurately acquire the ranking indices, then obtain the different ranks of candidates along with the adjustment of DM's preference value to balance the group utility and individual regret. Thirdly, median ranking method (MRM) is employed to reach a consensus opinion for the differentiated ranks of candidates via the attribute-wise rank and linear programming model. Subsequently, a numerical example for an agri-food company in China is introduced to illustrate the feasibility of our AHP-VIKOR-MRM method. Finally, conduct the comparison with some available MCGDM methods with PF information to interpret the stability and practicability of our presented method.

This paper extends one of the most extensively used multiple criteria decision analysis (MCDA) methods, the technique for order preference by similarity to ideal solutions (TOPSIS), to adapt to highly complicated uncertain environments based on interval-valued Pythagorean fuzzy (IVPF) sets. In contrast to classical TOPSIS methods, this paper develops a novel concept of Pearson-like IVPF correlation coefficients instead of distance measures to not only construct a useful and effective association measure between two IVPF characteristics but also depict the outranking relationship of IVPF information. Moreover, this paper proposes the (weighted) IVPF correlation-based closeness coefficients to establish a Pearson-like correlation-based TOPSIS model to manage MCDA problems within the IVPF environment. In particular, there is a definite improvement in determining the closeness coefficient required in the TOPSIS procedure. This paper considers anchored judgments with respect to the positive- and negative-ideal IVPF solutions and provides new approach- and avoidance-oriented definitions for the IVPF correlation-based closeness coefficient, which is entirely different from the traditional definition of relative closeness in TOPSIS. Furthermore, this paper proposes a comprehensive IVPF correlation-based closeness index to balance the consequences between ultra-approach orientation and ultra-avoidance orientation and acquire the ultimate compromise solution for decision support and aid. The feasibility and practicability of the developed methodology are illustrated by a practical MCDA problem of rehabilitation treatment for hospitalized patients with acute stroke. The application results, along with experimentations and comparative analyses, demonstrate that the developed methods are rational and effective.

Acceleration and reliability are two critical issues of artificial intelligent circuits and systems. In this paper we propose a novel structure of deep neural network in testing stage that converts the trained weights to optimized ternary-coded binary. Within each shallow layer a constant-shift sub-layer with almostfree cost is inserted to transfer all multipliers to a carry save adder/subtractor. Then the activation functions are simplified to piecewise lines with nice slopes for calculation by an adder only. Since input-side layers tend to have self-healing ability, only output-side layers are equipped by AN codes that can be encoded and decoded almost without extra cost in our structure. From experiments and evaluations, our structure can have a higher resolution with error-correcting capability and a performance similar to the BNN.

Background Translational regulation is one important aspect of gene expression regulation. Dysregulation of translation results in abnormal cell physiology and leads to diseases. Ribosome profiling (RP), also called ribo-seq, is a powerful experimental technique to study translational regulation. It can capture a snapshot of translation by deep sequencing of ribosome-protected mRNA fragments. Many ribosome profiling data processing tools have been developed. However, almost all tools analyze ribosome profiling data at the gene level. Since different isoforms of a gene may produce different proteins with distinct biological functions, it is advantageous to analyze ribosome profiling data at the isoform level. To meet this need, previously we developed a pipeline to analyze 610 public human ribosome profiling data at the isoform level and constructed HRPDviewer database. Results To allow other researchers to use our pipeline as well, here we implement our pipeline as an easy-to-use software tool called RPiso. Compared to Ribomap (a widely used tool which provides isoform-level ribosome profiling analyses), our RPiso (1) estimates isoform abundance more accurately, (2) supports analyses on more species, and (3) provides a web-based viewer for interactively visualizing ribosome profiling data on the selected mRNA isoforms. Conclusions In this study, we developed RPiso software tool (http://cosbi7.ee.ncku.edu.tw/RPiso/) to provide isoform-level ribosome profiling analyses. RPiso is very easy to install and execute. RPiso also provides a web-based viewer for interactively visualizing ribosome profiling data on the selected mRNA isoforms. We believe that RPiso is a useful tool for researchers to analyze and visualize their own ribosome profiling data at the isoform level.

This paper aims at developing a novel generalized distance measure of Pythagorean fuzzy (PF) sets and constructing a distance-based compromise approach for multiple criteria decision analysis (MCDA) within PF environments. The theory of Pythagorean fuzziness provides a representative model of nonstandard fuzzy sets; it is valuable for representing complex vague or imprecise information in many practical applications. The distance measure for Pythagorean membership grades is important because it can effectively quantify the separation between PF information. Based on the essential characteristics of PF sets (membership, non-membership, strength, and direction), this paper proposes several distance measures, namely, new Hamming and Euclidean distances and a generalized distance measure that is based on them for Pythagorean membership grades and for PF sets. Moreover, the useful and desirable properties of the proposed PF distance measures are investigated to evaluate their advantages and form a solid theoretical basis. In addition, to evaluate the performance of the proposed distance measures in practice, this paper establishes a PF-distance-based compromise approach for addressing MCDA problems that involve PF information. The effectiveness and practicability of the developed approach are further evaluated through a case study on bridge-superstructure construction methods. According to the application results and comparative analysis, the proposed PF distance measures are accurate and outperform other methods in handling the inherent uncertainties of evaluation information. Furthermore, the PF-distance-based compromise approach can accommodate the much higher degrees of uncertainty in real-life decision scenarios and effectively determine the priority ranking among candidate alternatives for managing complicated MCDA problems.

This paper aims to utilize the core structure of linear programming technique for multidimensional analysis of preference (LINMAP) to propose a parametric LINMAP methodology for addressing multiple criteria group decision-making problems based on Pythagorean fuzzy sets. To compare Pythagorean membership grades, this paper presents a Hamming distance-based approach for identifying closeness-based order relations based on Pythagorean fuzzy closeness indices. The concept of comprehensive closeness measures is introduced to measure individual order consistency and inconsistency between subjective preference relations and objective order relations. In the spirit of LINMAP, this paper determines individual goodness of fit and poorness of fit and further constructs a novel parametric LINMAP model. The applicability of the developed approach is explored by a practical application of railway project investment. Some comparative analyses are conducted to demonstrate the usefulness and advantages of the proposed methodology.

The aim of this paper is to develop a novel outranking method using a risk attitudinal assignment model under complex uncertainty based on Pythagorean fuzzy (PF) sets and interval-valued Pythagorean fuzzy (IVPF) sets. Additionally, this paper applies the proposed methodology to address financial decision-making problems to investigate its applicability and effectiveness in the real world. These developed methods and techniques can provide a new viewpoint for capturing the amount of information conveyed by PF and IVPF values and can fully take into account the decision maker’s attitude towards risk-taking in the face of high uncertainty. Considering the diverse attitudes toward risk neutrality, risk seeking, and risk aversion, this paper introduces novel measures of risk attitude-based score functions within the PF/IVPF environments and investigates their desirable and useful properties. These properties provide a means of establishing linear orders and admissible orders in the PF/IVPF contexts. This means that the proposed measures can overcome some drawbacks and ambiguities of the previous techniques through score and accuracy functions and can address incomparable PF/IVPF information more effectively. As an application of the risk attitude-based score functions, this paper develops novel risk attitudinal assignment models to establish a useful outranking approach for solving multiple criteria decision-making problems. Two algorithms for PF and IVPF settings are developed based on the concepts of a precedence frequency matrix and a precedence contribution matrix for conducting multiple criteria evaluation and the ranking of alternatives. A financing decision on aggressive/conservative policies of working capital management is presented to demonstrate the applicability of the proposed outranking approach in real situations. Moreover, a comparison to the technique of risk attitudinal ranking methods is investigated to validate the advantages of the proposed methodology. Furthermore, a comparative analysis with a newly developed outranking method, the IVPF-ELECTRE (for the elimination and choice translating reality), is conducted via an application to the investment problem of software development projects. Compared with these benchmark approaches, the proposed methods can produce a more reasonable and persuasive result for ranking the order relationships of alternatives in the highly uncertain context. The practical studies and comparative discussions demonstrate an excellent performance of the developed methodology that is effective and flexible enough to accommodate more-complex decision-making environments.

We present an interactive system using one RGB-D sensor, which allows a user to use bare hands to perform sand drawing. Our system supports the common sand drawing functions, such as sand erosion, sand spilling, and sand leaking. To use hands to manipulate the virtual sand, we design four key hand gestures. The idea is that the gesture of one hand controls the drawing actions. The motion and gesture of the other hand control the drawing positions. There are three major steps. First, our system adopts a vision-based bare-hand detection method which computes the hand position and recognizes the hand gestures. Second, the drawing positions and the drawing actions are sent to a sand drawing subsystem. Finally, the subsystem performs the sand drawing actions. Experimental results show that our system enables users to draw a rich variety of sand pictures.

Technological innovation is critically important for high-tech firms in laying the groundwork for corporate growth and competitive advantages. It is hoped that evaluating risk accurately and effectively will contribute to assign appropriate priorities of technological innovation projects and to enhance the success rate for the whole project. In considering the issue of risk evaluation, the essential question that arises concerns strong fuzziness, ambiguity, and inexactness during the process of assessing risks. However, comparatively little research has focused on accommodating higher degrees of uncertainty in evaluating risks associated with technological innovation projects. Because the existing risk evaluation methods (such as models using net present values, internal rates of return, fuzzy logic, real options, and stochastic simulation) have certain limitations, this paper takes the powerfulness of interval-valued Pythagorean fuzzy (IVPF) sets into account to handle imprecise and ambiguous information and to characterize complex uncertainty in practical risk evaluation problems. This paper aims to propose an IVPF inferior ratio (IR)-based assignment model and to establish a novel risk evaluation method of technological innovation for the purpose of appropriately tackling highly uncertain information in intricate and varied circumstances. The proposed method provides an effective way to fuse complicated information about risk assessments and to identify an aggregate ranking of technological innovation projects that has the closest agreement with all indicator-wise precedence ranks. The feasibility and applicability of the IVPF IR-based assignment model are illustrated via a real-world case concerning the risk evaluation of technological innovation in high-tech enterprises. Furthermore, the practicality and effectiveness of the developed methodology are verified through a comparative analysis with other relevant approaches.

Post-acute care (PAC) is an interdisciplinary healthcare service used to assist in returning patients to their community after they receive acute medical services. To establish a fully developed PAC service model, the National Health Insurance Administration in Taiwan attempts to recruit professional medical service institutions (consisting of medical centers and regional and district hospitals) in a trial program for improving the rehabilitation quality of patients with cerebrovascular diseases (CVDs) and to reduce the re-hospitalization rate. The evaluation and selection of adequate medical service institutions are critical in the program for enhancing the effectiveness of hospital-based PAC in acute stroke management. However, because of the complexity of the national health insurance system and the healthcare system in Taiwan, the determination of pilot hospitals is a highly complicated and ambiguous multiple criteria decision analysis (MCDA) problem. Focusing on the requirement of generating a set of pilot hospitals for the PAC program and tackling imprecise and uncertain information associated with a complex medical circumstance, the purpose of this paper is to develop a novel compromising decision-making method based on the interval-valued Pythagorean fuzzy (IVPF) set theory and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methodology to address the multiple criteria selection problem of pilot hospitals in assisting the establishment of a hospital-based PAC model. Considering the powerfulness of IVPF sets when handling vagueness and complex uncertainty in practical problems, this paper proposes a useful IVPF VIKOR method that is significantly different from the existing VIKOR methodology. The proposed methodology represents a comprehensive integration of high-order uncertainties within a decision environment into the basic VIKOR structure that is designed to lead to both better description and better applicability of MCDA. This paper presents some novel concepts such as remoteness indices and remoteness-based multiple criteria ranking indices and investigates their desirable properties in detail. With the theoretical support of these new concepts, this paper establishes useful remoteness-based group utility indices, individual regret indices, and compromise indices for the assessment of acceptable advantage and acceptable stability. Unlike the current VIKOR-based ranking process, this paper provides a systematic ranking procedure that is capable of improving the efficiency of determining ultimate compromise solutions. Overall, the present study provides several significant contributions, such as structuring the selection problem for hospital-based PAC, extending the IVPF theory and VIKOR to the medical and healthcare fields, simplifying the manipulation procedure in handling IVPF information, constructing valuable concepts of remoteness-based indices, and developing an effective IVPF VIKOR ranking procedure. A real-world example of selecting pilot hospitals in the PAC program for CVDs is provided to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. Furthermore, other valuable MCDA applications with a comparative analysis are conducted to validate the advantages of the proposed method in a variety of fields.

The aim of this paper is to develop a novel consensus ranking method that uses a mixed choice strategy for multiple criteria decision analysis (MCDA) under complex uncertainty based on Pythagorean fuzzy (PF) sets. The majority of MCDA methods have focused almost exclusively on “criterion-specific”choice tasks that are the tasks in which all alternatives are decomposed into distinct components and evaluated on specific criteria. However, in certain MCDA problems in practical applications, category-based choices tend to be more holistic in nature, especially in affective-like aspects. Therefore, this paper incorporates a mixed choice strategy (i.e., a combination of a category-based strategy and a criterion-specific strategy) into the core structure of the developed MCDA method. Furthermore, this paper utilizes the theory of Pythagorean fuzziness to provide a powerful modeling tool for complex and varied decision-making environments. Employing the developed concepts of a PF precedence index based on PF information and a disagreement indicator based on distances between rankings, this paper proposes a novel consensus ranking method by means of a comprehensive disagreement-based assignment model for addressing a mixed-choice-strategy-based MCDA problem in the PF context. As an application of the proposed methodology, a real-world case study of a luxury car selection problem is investigated. The application results, along with a comparative analysis, demonstrate the practicality and effectiveness of the developed approach, which is capable of handling hybrid category-based and criterion-specific choice tasks and managing complex uncertainty in practical situations.

This paper aims to present a novel outranking approach of the preference ranking organization method for enrichment evaluations (PROMETHEEs) based on Pythagorean fuzzy sets for multiple criteria decision analysis. The proposed method utilizes a novel Pythagorean fuzzy precedence index, which is based on the difference of scalar functions under anchored judgments with respect to the superiority/inferiority Pythagorean fuzzy numbers. To appropriately describe the hesitation between indifference and preference in the Pythagorean fuzzy context, this paper introduces useful precedence-based preference functions to establish the precedence relations based on pairwise comparisons. As a multiple criteria measure under Pythagorean fuzzy uncertainty, the concept of overall preference indices is identified at the aggregation stage to exploit certain rules for generating PROMETHEE flows. Next, this paper provides effective Pythagorean fuzzy PROMETHEE I and II ranking procedures to determine partial and complete preorders, respectively, among competing alternatives. The developed Pythagorean fuzzy PROMETHEE-based outranking approach is comparatively validated using a real-world application concerning the selection problem of bridge construction methods. The solution results along with a comparison analysis demonstrate that the proposed methodology outperforms the comparative approach in terms of reasonability and stability.

The evolution strategy with covariance matrix adaptation (CMA-ES) is a well-known algorithm in the family of evolution strategies. It consists of three main mechanisms: derandomized adaptation, cumulative step size, and covariance matrix adaptation. In this paper we aim to improve the CMA- ES and its performance by proper parameter values, better repair mechanism, removal of rank-one update, and a spread- based step size adaptation mechanism. We tested the proposed algorithm by ten test functions in the CEC2019 100-Digit Challenge. The results showed that our algorithm can achieve similar solution quality compared with two recent hybrid adaptive evolutionary algorithms and needs fewer fitness function evaluations.

Mobile electroencephalogram (EEG)-sensing technologies have rapidly progressed and made the access of neuroelectrical brain activity outside the laboratory in everyday life more realistic. However, most existing EEG headsets exhibit a fixed design, whereby its immobile montage in terms of electrode density and coverage inevitably poses a great challenge with applicability and generalizability to the fundamental study and application of the brain-computer interface (BCI). In this study, a cost-efficient, custom EEG-electrode holder infrastructure was designed through the assembly of primary components, including the sensor-positioning ring, inter-ring bridge, and bridge shield. It allows a user to (re)assemble a compact holder grid to accommodate a desired number of electrodes only to the regions of interest of the brain and iteratively adapt it to a given head size for optimal electrode-scalp contact and signal quality. This study empirically demonstrated its easy-to-fabricate nature by a low-end fused deposition modeling (FDM) 3D printer and proved its practicability of capturing event-related potential (ERP) and steady-state visual-evoked potential (SSVEP) signatures over 15 subjects. This paper highlights the possibilities for a cost-efficient electrode-holder assembly infrastructure with replaceable montage, flexibly retrofitted in an unlimited fashion, for an individual for distinctive fundamental EEG studies and BCI applications.

Ever since the introduction of Pythagorean fuzzy (PF) sets, many scholars have focused on solving multicriteria decision-making (MCDM) problems with PF information. The technique for order preference by similarity to ideal solutions (TOPSIS) is a well-known and effective method for MCDM problems. The objective of this study is to extend the TOPSIS to tackle MCDM problems under the PF environment. In this study, we develop a novel distance measure that considers the length, the angle, and the greater space, which reflect the properties of PF sets. Then, we apply the proposed distance measure in PF-TOPSIS to calculate the distances from the PF positive ideal solution and the PF negative ideal solution. Finally, we take the evaluation of emerging technology commercialization as an MCDM problem to illustrate the proposed approaches, and we then compare these approaches to demonstrate the scalar type PF-TOPSIS is the most feasible and effective approach in practice.

Considering the new uncertainty format of Pythagorean fuzzy (PF) sets, this research aims to launch a point operator-based likelihood measure and establish a PF preference ranking organization method for enrichment evaluations (PROMETHEE) to manipulate multiple criteria decision analysis (MCDA) tasks within PF environments. Different from the previous extensions of PROMETHEE into PF circumstances, this research presents dual PF point operators to delineate an innovative likelihood measure as a means to ascertainment of preference relationships. As contrasted with the current probability distribution approach, this research takes advantage of the conception of scalar functions as well as the lower approximated estimations and upper approximated estimations via the dual operators to construct a creative point operator-based likelihood measure. This new likelihood measure has novelty value and possesses several desirable properties, such as boundedness, complementarity, and weak transitivity; thus, it can better reveal the possibility of the dominance relations between PF information. More useful concepts of a likelihood-based predominance index and predominance-based preference functions are proposed to facilitate intra-criteria and inter-criteria comparisons in the forms of PF performance ratings and PF characteristics, respectively. Furthermore, their beneficial and desirable properties are also investigated. On the grounds of these new concepts and measures, a likelihood-based PROMETHEE methodology is exploited to address MCDA problems in uncertain circumstances involving Pythagorean fuzziness. By simultaneously employing the positive and negative predominating flows, the likelihood-based PF PROMETHEE I yields a partial ranking of available alternatives and highlights any possible incomparability between alternatives. Based on the net predominating flow, the likelihood-based PROMETHEE II renders complete ranking orders of alternatives and preclude any incomparability among the competing alternatives. The reasonableness and effectuality of the initiated methodology are demonstrated with the assistance of a realistic case about evaluating financing policies for working capital management and a comparative analysis.

Pythagorean fuzzy (PF) sets involving Pythagorean membership grades can befittingly manipulate inexact and equivocal information in real-life problems involving multiple criteria decision analysis (MCDA). The linear programming technique for multidimensional analysis of preference (LINMAP) is a prototypical compromising model, and it is widely used to carry on decision-making problems in many down-to-earth applications. In LINMAP, the employment of squares of Euclidean distances is a significant technique that is an effective approach to fit measurements. Taking the advantages of a newly developed Euclidean distance model on the grounds of PF sets, this paper initiates a beneficial concept of squared PF Euclidean distances and studies its valuable and desirable properties. This paper aims to establish a squared Euclidean distance (SED)-based outranking approach and develop a novel PF LINMAP methodology for handling an MCDA problem under PF uncertainty. In the SED-based outranking approach, a novel SED-based dominance index is proposed to reflect an overall balance of a PF evaluative rating between the connection and remotest connection with positive- and negative-ideal ratings, respectively. The properties of the proposed index are also analyzed to exhibit its efficaciousness in determining the dominance relations for intracriterion comparisons. Moreover, this paper derives the comprehensive dominance index to determine the overall dominance relation and defines measurements of rank consistency for goodness of fit and rank inconsistency for poorness of fit. The PF LINMAP model is formulated to seek to ascertain the optimal weight vector that maximizes the total comprehensive dominance index and minimizes the poorness of fit under consideration of the lowest acceptable level and specialized degenerate weighting issues. The practical application concerning bridge-superstructure construction methods is conducted to test the feasibility and practicability of the PF LINMAP model. Over and above that, a generalization of the proposed methodology, along with applications to green supplier selection and railway project investment, is investigated to deal with group decision-making issues. Several comparative studies are implemented to further validate its usefulness and advantages. The application and comparison results display the effectuality and flexibility of the developed PF LINMAP methodology. In the end, the directions for future research of this work are represented in the conclusion.

This paper aims to propose novel Chebyshev distance measures for Pythagorean membership grades and establish their based elimination and choice translating reality method (ELECTRE) for addressing multiple criteria decision-making problems under uncertainty of Pythagorean fuzziness. Pythagorean fuzzy (PF) sets have a significant effect on fuzzy modeling for intelligent informatics and decision support because the degrees of membership, non-membership, and indeterminacy, strength of commitment, and direction of commitment featured by PF information are extended for a wider coverage of information span. The theory of PF sets is a powerful tool in dealing with imprecise and ambiguous evaluations for realistic problems and modeling intelligent decision making for complex systems. This paper focuses on both theory and applications of the Chebyshev metric for PF contexts, and special attention is devoted to the theoretical development of Chebyshev distances in connection with Pythagorean membership grades based on various types of representations. To surmount the difficulties confronted by the existing measures, such as low comprehensivity, incomparability in scaling, ignorance of square degrees in metric specification, double weighting, and inappropriate normalization, this paper makes a comprehensive comparison to validate the effectiveness and superiority of the proposed Chebyshev distance measures. To support decision making within complicated PF environments, this paper develops an extended ELECTRE approach based on the Chebyshev distance measure to conduct multiple criteria decision analysis involving PF information for determining partial and complete rankings of candidate alternatives. In particular, this paper constructs novel Chebyshev metric-based preference functions depending on the individual characteristics of the criteria. The developed PF ELECTRE approach leads to using all the information that characterizes a PF set via the concepts of the scalar function and various Chebyshev metric-based comparison indices, such as (net) concordance indices, (net) discordance indices, and the overall precedence index. Practical applications with a comparative analysis in the field of bridge-superstructure construction are conducted to examine the usefulness and advantages of the proposed methodology in the real world.

The purpose of this paper is to develop a novel compromise approach using correlation-based closeness indices for addressing multiple-criteria decision analysis (MCDA) problems of bridge construction methods under complex uncertainty based on interval-valued Pythagorean fuzzy (IVPF) sets. The assessment of bridge construction methods requires the consideration of multiple alternatives and conflicting tangible and intangible criteria in intricate and varied circumstances. The concept of IVPF sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real-world applications. Inspired by useful ideas concerning information energies, correlations, and correlation coefficients, this paper constructs new concepts of correlation-based closeness indices for IVPF characteristics and investigates their desirable properties. These indices can be utilized to achieve anchored judgments in decision-making processes and to reflect a certain balance between connections with positive and negative ideal points of reference. Moreover, these indices can fully consider the amount of information associated with higher degrees of uncertainty and effectively fuse imprecise and ambiguous evaluative ratings to construct a meaningful comparison approach. By using the correlation-based closeness index, this paper establishes effective algorithmic procedures of the proposed IVPF compromise approach for conducting multiple-criteria evaluation tasks within IVPF environments. The proposed methodology is implemented in a practical problem of selecting a suitable bridge construction method to demonstrate its feasibility and applicability. The practicality and effectiveness of the proposed methodology are verified through a comparative analysis with well-known compromise methods and other relevant nonstandard fuzzy models.

This paper presents a new compromising approach to multiple criteria group decision-making (MCGDM) for the treatment of uncertainty which is based on Pythagorean fuzzy (PF) sets. The present work intends to propose a novel linear programming technique for multidimensional analysis of preference (LINMAP) by way of some useful concepts related to PF dominance relations, individual consistency and inconsistency levels, and individual fit measurements. The concept of PF scalar function-based dominance measures is defined to conduct intracriterion comparisons concerning uncertain evaluation information based on Pythagorean fuzziness; moreover, several valuable properties are also investigated to demonstrate its effectiveness. For the assessment of overall dominance of alternatives, this paper provides a synthetic index, named a comprehensive dominance measure, which is the aggregation of the weighted dominance measures by combining unknown weight information and PF dominance measures of various criteria. For each decision-maker, this paper employs the proposed measures to evaluate the individual levels of rank consistency and rank inconsistency regarding the obtained overall dominance relations and the decision-maker's preference comparisons over paired alternatives. In the framework of individual fit measurements, this paper constructs bi-objective mathematical programming models and then provides their corresponding parametric linear programming models for generating the best compromise alternative. Realistic applications with some comparative analyses concerning railway project investment are implemented to demonstrate the appropriateness and usefulness of the proposed methodology in addressing actual MCGDM problems.

This paper aims at developing a novel preference ranking organization method for enrichment evaluations (PROMETHEE) using a Pythagorean fuzzy combinative distance-based precedence approach under complex uncertainty based on Pythagorean fuzzy sets. This paper introduces a new generalized distance measure for adequately expressing differences between Pythagorean fuzzy information and utilizing fundamental parameters of Pythagorean membership grades. This paper defines the useful concept of precedence indices for determining the desirability of evaluative ratings about competing alternatives on a criterion. In Pythagorean fuzzy contexts, this paper establishes a combinative distance-based precedence approach for reflecting an overall balance between the connection with approach-oriented anchor values and the remotest connection with avoidance-oriented anchor values. This paper presents six types of new preference functions and proposes the comprehensive preference index for measuring the intensity of a pairwise preference. Based on the concepts of a dominant flow, a dominated flow, and an outranking flow, this paper develops a Pythagorean fuzzy PROMETHEE-based method and validates its feasibility and applicability using a multiple criteria decision-making problem of bridge-superstructure construction methods. A sensitivity analysis is carried out to investigate the effects of various parameter settings on the partial preordering and complete preordering of alternatives. Furthermore, a comparative analysis is performed with other relevant methods to evaluate the effectiveness of the proposed methodology.

An interval-valued intuitionistic fuzzy set contains membership and non-membership values that are crisp intervals and represent an extension of the ordinary fuzzy sets that are widely used because of their usefulness in handling imprecise or uncertain information. The linear programming technique for multidimensional analysis of preference (LINMAP) is a representative decision-making method with respect to preference information for given alternatives. In this paper, we present a new linear programming technique with weight assessment, an extended LINMAP method, for addressing multiple criteria group decision-making problems in the interval-valued intuitionistic fuzzy framework. With consideration given to the degrees of relative agreement and the importance weights of multiple decision makers, this paper presents an inclusion-based hybrid averaging operation with an inclusion comparison approach for forming a collective decision environment. The concept of inclusion-based indices that relate to anchor dependency with multiple points of reference is developed as the core of the extended LINMAP method. We also establish a linear programming model to handle the incomplete preference information for alternatives. The optimal weights of the criteria can be determined, and the priority order of the alternatives can be obtained according to the resulting comprehensive inclusion-based indices. The feasibility and applicability of the proposed methods are illustrated with an example addressing graduate admission, and a comparative analysis is performed with another interval-valued intuitionistic fuzzy LINMAP approach to validate the effectiveness of the proposed methodology.

Intuitionistic fuzzy sets are suitable for capturing imprecise or uncertain decision information in multiple criteria decision analysis. In addition, optimism and pessimism generally affect the manner in which subjective judgments are construed. This paper proposes an outranking model, a QUALIFLEX method, for relating optimism and pessimism within the intuitionistic fuzzy decision environment. This paper treats the influences of optimism and pessimism differently by using the unipolar bivariate model. In addition, the proposed method investigates all possible permutations of alternatives with respect to the consequences of all criteria. A ranking procedure is employed to compare intuitionistic fuzzy values by using the inclusion comparison probability.

This study proposes a new approach that recovers the system from deadlock states to its former live states, and reaches the same number of states as the original uncontrolled model by adding monitors (and control arcs) with no new problematic siphons. We further propose a lossless approach by coloring some arcs to avoid the material loss. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Interval-valued fuzzy sets have been developed and applied to multiple criteria analysis. However, the influence of optimism and pessimism on subjective judgments and the cognitive dissonance that accompanies the decision making process have not been studied thoroughly. This paper presents a new method to reduce cognitive dissonance and to relate optimism and pessimism in multiple criteria decision analysis in an interval-valued fuzzy decision environment. We utilized optimistic and pessimistic point operators to measure the effects of optimism and pessimism, respectively, and further determined a suitability function through weighted score functions. Considering the two objectives of maximal suitability and dissonance reduction, several optimization models were constructed to obtain the optimal weights for the criteria and to determine the corresponding degree of suitability for alternative rankings. Finally, an empirical study was conducted to validate the feasibility and applicability of the current method. We anticipate that the proposed method can provide insight on the influences of optimism, pessimism, and cognitive dissonance in decision analysis studies.

The use of evolutionary algorithms for global optimization has increased rapidly during the past several years. But evolutionary computations have a common drawback: they need a huge number of function evaluations. This makes them inadequate for structural optimization. To overcome this difficulty, the authors propose a method that integrates the evolutionary algorithm with data mining and approximate analysis to find the optimal solution in structural optimization. The approximate analysis is used to replace exact finite element analyses and the data mining is employed to identify feasible solutions. These combined efforts can reduce the computational time and search the feasible region intensively. As a result, the efficiency and quality of structural optimization using evolutionary algorithms will be increased. Some test problems show that the proposed method not only finds the global solution but is also less computationally demanding.

In this paper, we developed a system which enables users to draw pictures of sand and water on a two-dimensional surface in a virtual environment. By mixing water and sand for artwork creation, we can create different styles of pictures. Our system has three major subsystems: water animation system, sand animation system and rendering system. In the simulation part, we compute the motion of sand and water based on the interactions for water-water, sand-water and sand-sand. In the rendering part, we attempt to balance the rendering quality and the computation cost. We render water using a ray tracing method and the sand is rendered with shadow. Thus, the rendered results of water and sand look like 2.5D. We tested our system and the experimental results showed that the users could create a variety of pictures of sand and water.

Metasurfaces created artificially with metal nanostructures that are patterned on surfaces of different media have shown to possess “unusual” abilities to manipulate light. Limited by nanofabrication difficulties, so far most reported works have been based on 2D metal structures. We have recently developed an advanced e-beam process that allowed for the deposition of 3D nanostructures, namely vertical split-ring resonators (VSRRs), which opens up another degree of freedom in the metasurface design. Here we explore the functionality of beam steering with phase modulation by tuning only the vertical dimension of the VSRRs and show that anomalous steering reflection of a wide range of angles can be accomplished with high extinction ratio using the finite-difference-time-domain simulation. We also demonstrate that metasurfaces made of 3D VSRRs can be made with roughly half of the footprint compared to that of 2D nano-rods, enabling high density integration of metal nanostructures.

The complex nature of the realistic decision-making process requires the use of Pythagorean fuzzy (PF) sets which have been shown to be a highly promising tool capable of solving highly vague and imprecise problems. Multiple criteria decision analysis (MCDA) methods within the PF environment are very attractive approaches for today's intricate decision environments. With this study, an effective compromise model named as the PF technique for order preference by similarity to ideal solutions (TOPSIS) is proposed based on some novel PF correlation-based concepts to overcome the complexities and ambiguities involved in real-life decision situations. In contrast to the existing distance-based definitions, this paper develops new closeness indices based on an extended concept of PF correlations. This paper employs the proposed PF correlation coefficients to construct two types of closeness measures. A comprehensive concept of PF correlation-based closeness indices can then be established to balance the consequences yielded by the two closeness measures. Based on these useful concepts, an effective PF TOPSIS method is proposed to address MCDA problems involving PF information and determine the ultimate priority orders among competing alternatives. Feasibility and practicability of the developed approach are illustrated by a medical decision-making problem of inpatient stroke rehabilitation. Finally, the proposed methodology is compared with other current methods to further explain its effectiveness.

Shortest-path (minimum travel time) routing has been adopted over the past few decades. However, many studies have shown that a driver’s route and the shortest path diAer widely in significant ways, and that most drivers use several criteria in selecting their routes. Since route choice criteria have been the subject of controversy, this study develops an individual behavioral-based mechanism for exploring the crucial criteria aAecting drivers’ route-selection decisions. On the basis of the weight-assessing model and the habitual domain theory, this study presents the dynamic change of route choice criteria according to their dynamic weights. Furthermore, the eAects of information on drivers’ route-formulating behaviors are investigated as well in order to provide some valuable suggestions for implementing Advanced Traveler Information Systems (ATIS) in the future. An empirical study in Taipei City was conducted to show the feasibility and applicability of our proposed method and the empirical results indicate excellent performance in practice. ” 2001 Elsevier Science Ltd. All rights reserved.

This study develops an identification procedure for general fuzzy measures using genetic algorithms. In view of the difficulty in data collection in practice, the amount of input data is simplified through a sampling procedure concerning attribute subsets, and the corresponding detail design is adapted to the partial information acquired by the procedure. A specially designed genetic algorithm is proposed for better identification, including the development of the initialization procedure, fitness function, and three genetic operations. To show the applicability of the proposed method, this study simulates a set of experimental data that are representative of several typical classes. The experimental analysis indicates that using genetic algorithms to determine general fuzzy measures can obtain satisfactory results under the framework of partial information.

Weights of criteria are the important factors in decision-making. However, from a behavioral perspective, traditional weighting methods account for too few factors to deal with decisions properly. Based on the behavior mechanism and the theory of habitual domains, this study is undertaken to develop a new weight-assessing model that treats decision-making as a dynamically adjusting process proceeding from the ideal to actual states. The new model is built upon the dynamic analysis for the connectivities between criteria instead of the static analysis of traditional models. Finally, we have studied Taipei City motorcycle users, mode-choice behavior through questionnaire in order to show the applicability of the new model. From the empirical results, it is found that our weight-assessing method has significant application potential in practice.

The efficiency of Simple Genetic Algorithm (SGA) can be improved by some strategies. They are elitest strategy, multi-point crossover, identification of passive design variables, gradual increase of penalty parameter, and bit-wise local search. Topology optimization using GA is also discussed in this paper and examples are given. Five numerical examples show the efficiency and the optimum solutions of GA are greatly improved by these strategies. © 1997 John Wiley & sons, Ltd.

Fuzzy automata are regarded as an important device in fuzzy systems due to the advantage of powerful mathematical computation. This dynamic machine has been applied in various fields, such as pattern recognition, controller design, etc. However, most of the applications pertain to the engineering. Considering higher-order sets with imprecision, this paper makes use of Atanassov fuzzy sets and proposes the Atanassov fuzzy automata to solve problems in social science. The Atanassov fuzzy automata are powered by the implication and the composition to deal with Atanassov fuzzy relations. Derived from different t-norms and t-conorms, several types of implications and compositions are presented and compared. Based on the Atanassov fuzzy automata, an integrated model of advertising involvement is constructed as an illustration in order to manifest the feasibility and effectiveness of the proposed dynamic system. The presented device explores new directions for the permeation of Atanassov fuzzy automata to application areas in social science. Key words: Atanassov fuzzy set, Atanassov fuzzy automata, implication, composition, advertising involvement.

As the importance of patient safety increases for hospital management, improvements in patient safety are needed to reduce the high incidence of medical errors. Research on patient safety and medical errors shows that errors and the resulting adverse events are mainly the result of health-care providers, equipment and the quality management system. Most studies focused their research on the risk of the individual patient in health care. However, when facing patient safety problems, a hospital manager must consider the risk to the organization while making decisions about improvements. The risks will be relative to the cost-effectiveness of a health-care organization. Here we used a TOPSIS (technique for order preference by similarity to ideal solution) approach to manage the risk of a health-care organization in linguistic terms in the environment of interval-valued fuzzy numbers (IVFNs). Rather than calculating the distance between the alternatives and the positive/negative ideal solution in a TOPSIS approach, we use the similarity measure between IVFNs of the alternatives’ risk and the risk of the positive/negative ideal solution to help hospital managers analyze risks in an uncertain and complex situation and more easily determine the best alternative. Key words: Risk management, decision making, patient safety, interval-valued fuzzy numbers, TOPSIS, similarity measure.

The global financial crisis brought a serious collapse involving a "systemic" meltdown. Internet technology and globalization have increased the chances for interaction between countries and people. The global economy has become more complex than ever before. Mark Buchanan [12] indicated that agent-based computer models will prevent another financial crisis and has been particularly influential in contributing insights. There are two reasons why culture-sensitive agent on the financial market has become so important. Therefore, the aim of this article is to establish a culture-sensitive agent and forecast the process of change regarding herding behavior in the financial market. We based our study on the Kirman's Ant Model[4,5] and Hofstede's Natational Culture[11] to establish our culture-sensitive agent based model. Kirman's Ant Model is quite famous and describes financial market herding behavior from the expectations of the future of financial investors. Hofstede's cultural consequence used the staff of IBM in 72 different countries to understand the cultural difference. As a result, this paper focuses on one of the five dimensions of culture from Hofstede: individualism versus collectivism and creates a culture-sensitive agent and predicts the process of change regarding herding behavior in the financial market. To conclude, this study will be of importance in explaining the herding behavior with cultural factors, as well as in providing researchers with a clearer understanding of how herding beliefs of people about different cultures relate to their finance market strategies.

A design optimization procedure using a sequential linear programming technique is proposed in this paper to design minimum weight structures subjected to frequency response and static displacement constraints. The merit of the proposed approach is that the reanalyses of the static and dynamic responses, as well as the computations of the static and dynamic sensitivity data, are performed in a reduced approximate model. A significant saving of computer time for large scale structures is expected. Two numerical examples show good results of this method.