Multi-criteria Group Decision-making Method Research Articles

Multicriteria group decision making for prioritizing IoT risk factors with linear diophantine fuzzy sets and MARCOS method

In a dynamic world of technological advances, the Internet of Things (IoT) is a transformational and widespread force that has revolutionized the way we communicate with our surroundings and regulate our environments. It offers several advantages but also introduces inherent risks. In this study, we provide a comprehensive analysis of the risks associated with IoT and employ the effectiveness of a Linear Diophantine Fuzzy Set to rank the risk factors. Because of the significant uncertainties frequently present in IoT contexts, the use of a fuzzy framework is invaluable in discerning and addressing these risks. The primary contribution is to employ the Measurement of Alternatives and Ranking according to the Compromise Solution (MARCOS) method and linear diophantine fuzzy sets to propose a multi-criteria group decision-making method (MCGDM) for ranking attributes to facilitate risk prioritization, enabling consumers to determine the crucial hazards in their IoT systems. Furthermore, we implement a comparative study and a sensitivity analysis to demonstrate the robustness of our proposed methodology. The insights obtained from our research not only improve the awareness of IoT hazards but also enable organizations and individuals to make informed decisions when navigating IoT fields. By proactively addressing these risks, we endorse the development and secure deployment of IoT technology.

An integrated multi-polar fuzzy N-soft preference ranking organization method for enrichment of evaluations of the digitization of global economy

Digitization represents the ultimate expression of globalization that has revolutionized every facet of global existence, enhancing connectivity, financial terms, trade opportunities, and public services. To further broaden or fortify this digital realm and advance global progress, various strategies for multi-criteria group decision-making (MCGDM) have been developed. This research article extends the literature study on the sensational MCGDM method known as Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE), which shares the burden of selecting the best alternative under many terms and conditions. This article aims to make a positive contribution to the development of the digital world. The main principle of the PROMETHEE technique is to calculate positive and negative flows of the selected options according to the divergence of the alternatives’ scores. It provides us with partial and full rankings of options by determining score degrees, suitable preference functions, and a multi-criteria preference index. To deal with the multi-polarity of the modern world and assign N-ordered levels, this paper proposes the multi-polar fuzzy N-soft (mFNS) PROMETHEE technique. Prior to this, an Analytic Hierarchy Process (AHP) technique is applied to guarantee the credibility of the criterion weights for each criterion. After that, the whole strategy of m-polar fuzzy N-soft PROMETHEE approach to order the selected options is explained, and all the course of action of this remarkable (MCGDM) technique are synchronized in an extensive flowchart, helping us to learn more about the technology keenly. Moreover, the utility of our discussed technology is illustrated by considering two applications of generating electricity through human movement and choosing the best digital currency. The most suitable choice is extracted with the help of the outranked directed graph. The results obtained by mFNS PROMETHEE technique benefits us with the selection of most reliable source to digitized the global economy, in addition, It enables us to rank the alternatives from most preferable to least one, that not only saves time but also produces the better outcomes. Subsequently, the eminence of mFNS PROMETHEE technology is checked by comparability with the prior art. Lastly, the advantages and disadvantages of our proposed technique are supplemented to demonstrate its productivity and shortcomings.

A multi-criteria group decision-making method based on consistency of interval-valued distributed preference relations

In multi-criteria group decision making (MCGDM) with interval-valued distributed preference relations (IDPRs), the consistency of IDPRs is important to guarantee the rationality of IDPRs and the rationality of group-satisfactory solutions. In existing studies, the consistency of the score intervals of IDPRs was considered to ensure the consistency of IDPRs. Meanwhile, a comparison of the score intervals of IDPRs was considered to approximately compare the IDPRs. The transformation from IDPRs into score intervals involved in the consistency and comparison of IDPRs results in information loss and unexpected group solutions. To avoid the influence of information loss on the group solutions, this study proposes an MCGDM method based on the consistency of IDPRs. Six transitive rules were constructed and used to define the distributed transitivity of IDPRs, which differs from existing types of consistency because IDPRs are on a set of discrete grades. With the grade scores, an abstract function with two variables was defined, in which ten conditions were satisfied. Using an abstract function with the scores of the two grades as two parameters, the mechanism of combining the two grades in the two IDPRs was designed by following the principles of mutual independence and probabilistic operation. The consistency of IDPRs is then constructed based on the combination mechanism, which is theoretically proven to satisfy distributed transitivity. In addition, the mean of the odd-order origin moment intervals of an IDPR was used to compare the alternatives. Information loss was avoided from two perspectives. The ultrasonic machine supplier selection problem of a tertiary hospital located in Hefei, Anhui, China was solved using the proposed method to demonstrate its applicability and effectiveness.

Novel Multi-Criteria Group Decision Making Method for Production Scheduling Based on Group AHP and Cloud Model Enhanced TOPSIS

Optimized production scheduling can greatly improve efficiency and reduce waste in the steel manufacturing industry. With the increasing demands on the economy, the environment, and society, more and more factors need to be considered in the production scheduling process. Currently, only a few methods are developed for the comprehensive evaluation and prioritization of scheduling schemes. This paper proposes a novel MCGDM (multi-criteria group decision making) method for the ranking and selection of production scheduling schemes. First, a novel indicator system involving both qualitative and quantitative indicators is put forward. Diverse statistical methods and evaluation functions are proposed for the evaluation of quantitative indicators. The evaluation method of qualitative indicators is proposed based on heterogeneous data, cloud model theory, and group decision-making techniques. Then, a novel Group AHP model is proposed to determine the weights of all evaluation indicators. Finally, a novel cloud-model-enhanced TOPSIS (technique for order of preference by similarity to ideal solution) method is proposed to rank alternative production scheduling schemes. A practical example is presented to show the implementation details and demonstrate the feasibility of our proposed method. The results and comparative analysis indicate that our hybrid MCGDM method is more reasonable, flexible, practical, and effective in evaluating and ranking production scheduling schemes in an uncertain environment.

A novel MCGDM technique based on correlation coefficients under probabilistic hesitant fuzzy environment and its application in clinical comprehensive evaluation of orphan drugs.

Probabilistic hesitant fuzzy sets (PHFSs) are superior to hesitant fuzzy sets (HFSs) in avoiding the problem of preference information loss among decision makers (DMs). Owing to this benefit, PHFSs have been extensively investigated. In probabilistic hesitant fuzzy environments, the correlation coefficients have become a focal point of research. As research progresses, we discovered that there are still a few unresolved issues concerning the correlation coefficients of PHFSs. To overcome the limitations of existing correlation coefficients for PHFSs, we propose new correlation coefficients in this study. In addition, we present a multi-criteria group decision-making (MCGDM) method under unknown weights based on the newly proposed correlation coefficients. In addition, considering the limitations of DMs' propensity to use language variables for expression in the evaluation process, we propose a method for transforming the evaluation information of the DMs' linguistic variables into probabilistic hesitant fuzzy information in the newly proposed MCGDM method. To demonstrate the applicability of the proposed correlation coefficients and MCGDM method, we applied them to a comprehensive clinical evaluation of orphan drugs. Finally, the reliability, feasibility and efficacy of the newly proposed correlation coefficients and MCGDM method were validated.

Interval-valued Pythagorean fuzzy entropy and its application to multi-criterion group decision-making

<abstract><p>Entropy is an important tool of information measurement in the fuzzy set and its inference. The research on information measurement based on interval-valued Pythagorean fuzzy sets mostly involves the distance formula for interval-valued Pythagorean fuzzy numbers, but seldom involves the measurement of fuzziness. In view of this situation, we have aimed to propose new interval-valued Pythagorean fuzzy entropy and weighted exponential entropy schemes. Based on the interval-valued Pythagorean fuzzy weighted averaging operator, a strategy based on weighted exponential entropy is proposed to solve the multi-criteria group decision-making (MCGDM) problem in the interval-valued Pythagorean environment. Two examples illustrate that this paper provides a feasible new method to solve the MCGDM problem in an interval-valued Pythagorean fuzzy (IVPF) environment. Finally, by comparing with the existing methods, it is concluded that the entropy measure of IVPF schemes and the corresponding MCGDM method can select the optimal solution of the practical problem more precisely and accurately. Therefore, the comparative analysis shows that the proposed measurement method has the characteristics of flexibility and universality.</p></abstract>

Assessing the triage and efficacy of strategies of SAARC to improve regional integrity of South Asia using multicriteria group decision making under q-rung orthopair hesitant fuzzy environment

The South Asian Association for Regional Cooperation (SAARC) plays a crucial role in fostering regional integration and cooperation among the countries of South Asia. However, the organization faces various challenges in achieving its objectives due to the complex and dynamic nature of the region. This study aims to assess the triage and efficacy of strategies employed by SAARC in pursuit of regional integrity in South Asia, using a Multi-Criteria Group Decision Making (MCGDM) technique. The assessment process involves several uncertainties which are resolved using q-rung orthopair hesitant fuzzy (q-ROHF) set. A distance measure is developed for q-ROHF sets and is applied to find the best strategy among six well known strategies, viz., SAARC Agreement on Trade in Services (SATIS), SAARC Development Fund (SDF), Establishment of South Asian University (SAU), SAARC Arbitration Council (SARCO), South Asian Preferential Trade Agreement (SAPTA) and South Asian Free Trade Area (SAFTA) through SWARA-TOPSIS based MCGDM technique. The MCGDM method is updated by developing several aggregation operators, viz., Archimedean q-ROHF weighted average, q-ROHF Einstein weighted average, q-ROHF Hamacher weighted average, q-ROHF Frank weighted average along with their geometric forms to combine decision makers’ individual decision. The result shows that the most effective strategy for the economic integration of SAARC is SDF; SATIS comes next as best strategy for economic integration of SAARC. The study reveals that SAU has least impact on the regional economic integration of SAARC. The achieved results reveals the age old proverb that “play on the stomach and sit on the back” – the members of SAARC who are by nature economically poor can afford to take initiative for a successful effective regionalization if it is planned to bring socio economic development of themselves.

Dual Hesitant q-Rung Orthopair Fuzzy Interaction Partitioned Bonferroni Mean Operators and Their Applications

The purpose of this paper is to introduce interaction partitioned Bonferroni mean operators under dual hesitant q-rung orthopair fuzzy environment. Motivated by the idea of q-rung orthopair fuzzy interaction operational laws, partitioned Bonferroni mean, and dual hesitant q-rung orthopair fuzzy sets, for dual hesitant q-rung orthopair fuzzy numbers, we present dual hesitant q-rung orthopair fuzzy interaction operational rules and propose several dual hesitant q-rung orthopair fuzzy interaction partitioned Bonferroni mean aggregation operators, including the interaction partitioned Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers, the weighted interaction partitioned Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers, the interaction partitioned geometric Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers, and the weighted interaction partitioned geometric Bonferroni mean operator for dual hesitant q-rung orthopair fuzzy numbers. Moreover, some properties and special cases associated with these proposed operators are also analyzed. For dual hesitant q-rung orthopair fuzzy numbers, based on the proposed operators, a multicriteria group decision-making method is proposed. Finally, an example for missile purchase problem is illustrated to demonstrate the superiority and feasibility by comparing with other existing multicriteria group decision-making methods.

Software systems supporting remote education – Fuzzy assessment using a multi-criteria group decision-making method

During the COVID-19 pandemic, the demand for systems supporting remote education increased significantly, and after the pandemic this form of education remained in place to supplement the stationary education. Among the tools that comprehensively support remote learning, there are two most popular systems, i.e. Google Workspace for Education and Microsoft Office 365, available in several different variants, differing in the functionalities offered. The aim of the article is to analyse the functionality, as well as to compare and evaluate this software. Since the assessment of e-learning systems is based on the subjective judgements of experts, and the assessment criteria are qualitative in nature, a new MCGDM (Multi-Criteria Group Decision Making) method called NEAT F-PROMETHEE GDSS (New Easy Approach To Fuzzy PROMETHEE – Group Decision Support System) was developed for the purposes of the study. This method captures the uncertain and imprecise qualitative assessments expressed by many experts and aggregates them into an overall quantitative assessment. As a result of the assessment, it was found that all variants of Google Workspace for Education and Microsoft Office 365 meet the basic requirements for tools for conducting remote learning. In addition, the use of the NEAT F-PROMETHEE GDSS method made it possible to create a ranking of individual software variants. Based on the group evaluation, it was determined that the best system in terms of the relationship between the offered capabilities and the cost of use is Google Workspace for Education Plus, with other variants of Google Workspace for Education taking subsequent positions in the ranking. In turn, Microsoft Office 365 solutions received a worse group rating, largely due to the higher cost of use and slightly less ability to control student work.

Spherical fuzzy analytic hierarchy process and linear assignment model based MCGDM method with its application in ranking of states for their business climate

Ranking of the states for business climate is often done by survey analysis and hence prejudiced by untrustworthy and instable responses of the participants. In the present study, we integrate spherical fuzzy set (SFS) and linear assignment model (LAM) with analytic hierarchy process (AHP) to develop a multi criteria group decision making (MCGDM) method to rank Indian states for their business climate and potential index. The proposed MCGDM method is developed using state investment potential index (SIPI) published by the National Council of Applied Economic Research (NCAER), New Delhi to analyse the 'ease of doing business' aspects of various states based on six parameters. We take these six parameters, sub parameters as criteria and sub criteria in proposed MCGDM method and find their global weight using AHP method. Advantages of the proposed method are that it uses SFSs which are more efficient than other extensions of fuzzy sets in handling non-determinacy, and applies LAM to avoid subjectivity in the preferences of decision makers. We also do the sensitivity analysis of the ranking by changing the weights of the criteria and sub criteria to confirm the robustness of the proposed MCGDM method.

Multi-criteria group decision-making methods with dynamic probabilistic linguistic information characterized by multiple consecutive time points

Multi-criteria group decision-making methods with dynamic probabilistic linguistic information characterized by multiple consecutive time points

A multi-criteria group decision-making method with fuzzy preference relations based on filtration-and-weighting-based triangular bounded consistency

In multi-criteria group decision-making (MCGDM) problems with incomplete fuzzy preference relations (FPRs), the consistency based on bounded rationality is preferred to depend on the historical preferences of decision makers to generate complete FPR matrices. There are two factors in influencing the effect of historical preferences on complete FPR matrices and further decision makers’ satisfaction of group solutions. One is the effectiveness of historical preferences and the other is their relative weights. On this basis, this paper proposes a new MCGDM method with FPRs based on the filtration-and-weighting-based triangular bounded consistency (FWBTBC), where historical FPRs between three adjacent pairs of alternatives are characterized by triangles and these two factors are considered comprehensively. A triangle filtration process is designed based on the Grubbs criterion to filter the abnormal triangles in the collected ones. A weight determination process is developed, where a distance measure between remaining triangles is constructed to calculate their weights. Based on the combination of the two processes, the FWBTBC of FPRs is created and then the proposed method is presented. The validity of the proposed method is demonstrated by its application in analyzing a drainage tube supplier selection problem for a tertiary hospital located in Hefei, Anhui, China.

An interval type-2 fuzzy best-worst method and likelihood-based multi-criteria method in group decision-making

In real-world decision-making problems, a group of decision-makers (DMs) with different levels of expertise gathers to investigate the problem from various perspectives. Making the best choice from an analogous shortlist of competitors is challenging, even for an expert group. To address these types of problems, a new multi-criteria group decision-making (MCGDM) methodology under the interval type-2 trapezoidal fuzzy (IT2TrF) environment is proposed. The proposed IT2TrF MCGDM method comprises three phases. In the first phase, the IT2TrF cognitive best-worst method (IT2TrF-CBWM) is introduced to calculate the initial weights of criteria using the interval scale. Subsequently, a new consistency index (CI) and consistency ratio (CR) are presented. In the second phase, an optimization model is proposed to determine the final IT2TrF weights of criteria. Finally, a likelihood-based method for solving MCGDM problems is introduced in the third phase. The validity of the proposed method is illustrated by addressing a healthcare waste (HCW) treatment technology selection problem during the COVID-19 pandemic. Sensitivity and comparative analyses highlight the superiority and effectiveness of the presented MCGDM method.

Archimedean [formula omitted]-norm and [formula omitted]-conorm based intuitionistic fuzzy WASPAS method to evaluate health-care waste disposal alternatives with unknown weight information

Health-care waste (HCW) contains numerous hazardous, infectious, and radioactive contents that may cause serious health issues for society and drastic environmental problems. Therefore, it is crucial to dispose of HCW safely and appropriately. Four commonly used HCW disposal methods are incineration, steam sterilization, microwave, and landfill disposal. To select an appropriate HCW disposal method, there are several conflicting criteria. Furthermore, when information is lacking due to uncertainty and criteria weighing conditions are also unknown, the decision to choose an appropriate HCW disposal method becomes more challenging. So, the objective of this paper is to introduce a novel integrated multi-criteria group decision-making (MCGDM) approach to evaluate HCW disposal methods in which incomplete information is quantified using intuitionistic fuzzy sets (IFSs), unknown criteria weights are evaluated using the maximizing deviation method, and the evaluation of HCW disposal methods is done by applying the Archimedean t-norm and t-conorm-based interactive intuitionistic fuzzy weighted aggregated sum product assessment (WASPAS) method. Herein, the Archimedean t-norm and t-conorm cover a wide range of t-norms and t-conorms, including the Algebraic, Einstein, Hamacher, and Frank, etc., by adopting prescribed combinations of additive generators. The proposed MCGDM approach has been applied to evaluate the above-listed four HCW disposal methods for a case study conducted by Mishra et al. (2020) in the context of India. A sensitivity analysis is performed to examine the impact of changes in the parameters involved in the proposed MCGDM approach. A comparative study is also performed with some well-known multi-criteria decision making(MCDM) and MCGDM methods to demonstrate the consistency and stability of the proposed approach. Findings suggest that the newly developed MCGDM approach is more general, flexible, and provides realistic results to evaluate HCW disposal methods under uncertainty and unknown criteria weight information.

Spatial Bounded Consistency of Intuitionistic Fuzzy Preference Relations

The consistency of intuitionistic fuzzy preference relations (IFPRs) is an important requirement in handling the decision-making problems modeled with IFPRs. Multiplicative consistency and additive consistency are two common types of consistency of IFPRs. These types of consistency of IFPRs are developed in the form of mathematical formulas to satisfy the perfect rationality of decision makers. In real decision-making, the decision makers are generally of bounded rationality rather than perfect rationality due to their own preferences. In consideration of the decision-makers’ preferences, this article proposes a new type of consistency of IFPRs, which is named spatial bounded consistency. A spatial framework is constructed to characterize the relations of three IFPRs among three alternatives. The spatial transitivity of IFPRs is defined based on the restricted max-max transitivity of IFPRs. By following the spatial transitivity of IFPRs, the preferences of decision makers contained in IFPRs are described in two situations. Under the assumption that the preferences of a decision maker are according in handling similar decision-making problems, the historical IFPRs satisfying spatial transitivity are collected to represent decision-makers’ preferences. On this basis, the spatial bounded consistency of IFPRs is then developed. A multicriteria group decision-making (MCGDM) method is designed based on the spatial bounded consistency. A problem of selecting the supplier of breast puncture needle is analyzed to demonstrate the applicability and effectiveness of the developed MCGDM method.

A Multi-Criteria Group Decision-Making Method for Risk Assessment of Live-Streaming E-Commerce Platform

Live-streaming e-commerce is the future development direction of the retail industry. When retailers choose a live-streaming e-commerce platform, they face the test of various risks of the platform, such as insecure control of capital flow, insufficient support of public domain traffic, etc. Therefore, it is necessary to evaluate the risks of the platform to help retailers identify the platform with the lowest risk. Considering the complexity of the risks of live-streaming e-commerce platforms and the ambiguity of the decision-makers thinking, the current method for multi-criteria group decision-making (MCGDM) method in a fuzzy environment rarely discusses the decision-makers weight for the criterion. This paper proposes interval-valued intuitionistic fuzzy multi-criteria group decision-making based on the decision-makers’ professionalism to evaluate the platform’s risks. This method determines the decision-maker’s weight for the criterion based on the professionalism of the decision-maker and uses the technique for order preference by similarity to an ideal solution (TOPSIS) method to rank the alternative platforms. Finally, a risk assessment of the agricultural product live-streaming e-commerce platforms is used as a case study to demonstrate the feasibility and effectiveness of the proposed method. This research will not only provide practical guidance for retailers to choose the live-streaming e-commerce platform with the lowest comprehensive risk but also provide ideas for the research of live-streaming e-commerce from the perspective of risk assessment.

Improving the COPRAS Multicriteria Group Decision-Making Method for Selecting a Sustainable Supplier Using Intuitionistic and Fuzzy Type 2 Sets

Improving the COPRAS Multicriteria Group Decision-Making Method for Selecting a Sustainable Supplier Using Intuitionistic and Fuzzy Type 2 Sets

Integrated multi-criteria group decision-making methods based on q-rung picture fuzzy sets for the identification of occupational hazards.

Practical group decision-making (DM) problems frequently involve challenging circumstances when attempting to assign appropriate values to the data because of the haziness and uncertainty of the surrounding circumstances. In order to address the ambiguity and imprecision that arise in DM issues, q-rung picture fuzzy sets (q-RPFSs) have a more broader structure. In this research, the criteria importance through intercriteria correlation (CRITIC) and the decision-making trial and evaluation laboratory (DEMATEL) techniques are separately integrated with the multi-attributive border approximation area comparison (MABAC) method. The MABAC method, which measures how far each alternative is from the border approximation area, is very stable and useful for resolving real-world problems. The CRITIC technique calculates the criteria weights by taking into account the relationships between attributes, and the DEMATEL methodology is recognized as the best method for determining how several criteria or factors interact with one another. As a result of these justifications, we made the decision to create the CRITIC-MABAC and DEMATEL-MABAC procedures for q-RPFSs. By using the suggested strategies, the primary goal of this article is to determine the occupational risk that has the greatest impact on the health of a hospital's medical staff. We begin by employing the CRITIC technique to determine the criteria weights. In addition, we calculate the weights of the criteria using the DEMATEL approach. The offered methodologies are investigated for their applicability to determine the most serious occupational hazard for hospital employees. We conducted a comparison with three earlier studies to verify the accuracy of the tactics that are offered.

Extended Multicriteria Group Decision Making with a Novel Aggregation Operator for Emergency Material Supplier Selection

How to ensure the normal production of industries in an uncertain emergency environment has aroused a lot of concern in society. Selecting the best emergency material suppliers using the multicriteria group decision making (MCGDM) method will ensure the normal production of industries in this environment. However, there are few studies in emergency environments that consider the impact of the decision order of decision makers (DMs) on the decision results. Therefore, in order to fill the research gap, we propose an extended MCGDM method, whose main steps include the following: Firstly, the DMs give their assessment of all alternatives. Secondly, we take the AHP method and entropy weight method to weight the criteria and the DMs. Thirdly, we take the intuitionistic fuzzy hybrid priority weight average (IFHPWA) operator we proposed to aggregate evaluation information and take the TOPSIS method to rank all the alternatives. Finally, the proposed method is applied in a case to prove its practicability and effectiveness. The proposed method considers the influence of the decision order of the DMs on the decision results, which improves the accuracy and efficiency of decision-making results.

Development of feature extraction method based on interval-valued Pythagorean fuzzy decision theory

Feature extraction is an important step in image processing and the accuracy of the extraction affects the result of subsequent target detection. There are many feature extraction algorithms, but there are few theories and methods about the accuracy of the extraction. Moreover, most of the existing extraction methods are computationally complex, and they will expose deficiencies once they encounter a large number of standard cases. In order to fill this gap, this study proposes a new soft computing multi-criteria group decision-making (MCGDM) method based on interval-valued Pythagorean fuzzy set information to deal with situations where multiple criteria are involved in complex decisions. Thus, the power average operator is used to eliminate the effects of unreasonable input arguments on decision-making results, and the Maclaurin symmetric mean operator is used to comprehensively consider the mutual relationship between input arguments in this article. Combining with the concept of IVPFS, the interval-valued Pythagorean fuzzy power Maclaurin symmetric mean (IVPFPMSM) operator and weighted IVPFPMSM operator are proposed. Then, the TOPSIS method is used to determine the weight vector of decision-making set, and a MCGDM method is developed under the interval-valued Pythagorean fuzzy framework. Next, aiming at the defects of the existing evaluation criteria, we consider the different ranges of membership degree and non-membership degree to propose a new evaluation criterion of MCGDM method. Finally, the proposed method is applied to the optimal selection of characteristic interval of foreign fibers to verify its practicability and effectiveness. The proposed method has certain guiding significance for the extension of decision-making fuzzy operators and the exploration of feature extraction methods.