A New Functional Clustering Method with Combined Dissimilarity Sources and Graphical Interpretation

Clustering is an essential task in functional data analysis. In this study, we propose a framework for a clustering procedure based on functional rankings or depth. Our methods naturally combine various types of between-cluster variation equally, which caters to various discriminative sources of functional data; for example, they combine raw data with transformed data or various components of multivariate functional data with their covariance. Our methods also enhance the clustering results with a visualization tool that allows intrinsic graphical interpretation. Finally, our methods are model-free and nonparametric and hence are robust to heavy-tailed distribution or potential outliers. The implementation and performance of the proposed methods are illustrated with a simulation study and applied to three real-world applications.

FRACTIONAL KINETIC EQUATIONS INVOLVING GENERALIZED V-FUNCTION VIA LAPLACE TRANSFORM

In this study, a new and further generalized form of the fractional kinetic equation involving the generalized V$-$function has been developed. We have discussed the manifold generality of the generalized V$-$function in terms of the solution of the fractional kinetic equation. Also, the graphical interpretation of the solutions by employing MATLAB is given. The results are very general in nature, and they can be used to generate a large number of known and novel results.

Complex q-Rung Orthopair Uncertain Linguistic Partitioned Bonferroni Mean Operators with Application in Antivirus Mask Selection

In this paper, complex q-rung orthopair uncertain linguistic sets (CQROULSs) for handling multi-attribute decision making (MADM) issues are proposed so that the assessed estimation of each trait can be presented by CQROULS. Another aggregation operator, called the partitioned Bonferroni mean (PBM) operator, is then considered to manage the circumstances under fuzziness. At that point, the PBM operator is stretched out to CQROULSs in which a complex q-rung orthopair uncertain linguistic partitioned Bonferroni mean (CQROULPBM) operator is then proposed. To wipe out the negative impact of preposterous assessment estimations of characteristics on total outcomes, complex q-rung orthopair uncertain linguistic weighted partitioned Bonferroni mean (CQROULWPBM) operator is further considered. These properties, idempotency, boundedness, and commutativity of the CQROULWPBM operator are obtained. The proposed CQROULSs with the CQROULWPBM operator is novel and important for MADM issues. Finally, an MADM based on CQROULSs is constructed with a numerical case given to delineate the proposed approach and then applied for selecting an antivirus mask for the COVID-19 pandemic. The advantages and comparative analysis with graphical interpretation of the explored operators are also presented to demonstrate the effectiveness and usefulness of the proposed method.

THE LONG-TERM CHANGES OF EMISSION DRIVING FORCES IN EUROPEAN POWER AND HEAT SECTOR AND THEIR IMPACT ON THE DECARBONIZATION PATHWAYS IN EU ENERGY SECTOR SINCE 1990

The Public Electricity and Heat Production (PEHP) is the most emissive sector in European economy. The characteristic features of PEHP contribute to the importance of its mitigation role. In this study, the decarbonization potential of energy sector was retrospectively analyzed. Proposed algorithm contained, at the first layer, the year-by-year data analysis and calculation while at the second graphical interpretation and pattern grouping. Despite the double-layering, the developed approach included the three following stepwise stages: the CO2 emission alternatives scenarios pathways methodology, the CO2 emission driving forces modes and influence weight methodology, and the transformation pattern identifying and grouping. Based on 1990–2017 CO2 emission inventories, the investigation of long-term PEHP decarbonization in 26 European countries was performed, in year-by-year and country-by-country processing. All results and findings have become the foundation for describing achieved decarbonization goals and 27 years mitigation ways. The Energy Consumption (EC) and Emission Factor (EF) have been pointed as a key driving forces of CO2 emission and as a key development indicator of PEHP sectoral transformation structure. Based on the developed country-by-country graphical interpretation interface, the five key patterns of PEHP decarbonization processes in European countries were observed and defined. The algorithm which has been applied and tested in 26 countries for 27 years was proved to be a universal and flexible tool to determine the lack of a utilitarian path of PEHP CO2 emission mitigation in Europe.