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The concept of sustainable development integrates activities in the economic, environmental and social areas. Energy policy, which is very closely linked to climate protection, is of key importance for achieving the goals of the concept in question. All these elements are connected by the European Green Deal strategy and Agenda 2030. Their implementation requires the evaluation of previous actions undertaken within the framework of sustainable development and the diagnosis of the current state. Therefore, this article presents the results of such research in relation to the key industry connected with this process, which is the energy sector. The research methodology was based on the analysis of 14 indicators that characterize four basic areas (dimensions) related to energy and climate sustainability. These indicators concern energy and climate as well as social and economic issues. This approach makes it possible to comprehensively assess the actions taken so far in the implementation of sustainable economic development in the energy and climate area in the European Union (EU) countries. The entropy-complex-proportional-assessment (COPRAS) methodologies, which belong to the group of multiple criteria decision-making methods, were used for this study. The conducted research allowed for the assessment of the changes in the EU countries in terms of energy and climate sustainability between 2009–2018. In addition, the effects of the introduced changes in individual years and in relation to the studied areas (dimensions) were also evaluated. Based on the results, considering the adopted criteria, the EU countries were divided into groups similar to the level of energy and climate sustainability. The results constitute a valuable set of data, which allows for a wide and in-depth multicriteria analysis. This allows for a very objective and broad assessment of the effects of sustainable development policies in the EU countries and the current state in the context of the European Green Deal strategy and Agenda 2030.

The green supplier selection (GSS) is a significant part in green supply chain management (GSCM). Choosing optimal green supplier can not only realize the sustainable development of enterprises, but also maximize the utilization rate of resources and diminish the negative effect of environmental issues, which conforms to the theme of green development. As a multiple attribute group decision-making (MAGDM) issue, selecting optimal green supplier is of vital important to enterprises. However, how to select the optimal supplier for enterprises is a great challenge. To handle this issue, a novel picture fuzzy COPRAS (COmplex PRoportional Assessment) method is devised. First, some necessary theories related to picture fuzzy sets (PFSs) are briefly reviewed. In addition, a method called CRITIC (Criteria Importance Though Intercrieria Correlation) is utilized to calculate criteria’s weights. Afterwards, the conventional COPRAS method is extended to the PFSs to calculate each alternative’s utility degree. At last, the designed method is exacted to an application which is related to GSS and there also conduct some comparative analysis to demonstrate the designed method’s superiority. The final results show that the proposed model can be utilized to decide the optimum green supplier.

At a time of rapid climate change and an uncertain geopolitical situation caused by the war in Ukraine, the problem of access to energy is a serious issue. The use of renewable energy sources and ensuring the highest possible energy independence are becoming important. They are in line with the seventh Sustainable Development Goal (SDG7). The aim of our research is to compare European countries in terms of the degree of SDG7 implementation and its dynamics from 2005 to 2020. We assess the SDG7 implementation using the COPRAS method and compare its dynamics using the Dynamic Time Warping (DTW) and hierarchical clustering. In years 2005, 2009 and 2020, we present rankings of countries in terms of the SDG7 implementation. Norway, Denmark, Sweden, Croatia, and Estonia were ranked the best, and Luxembourg, Belgium, Bulgaria, Lithuania, Iceland, and Cyprus—the worst. We obtained eight clusters with respect to dynamics of the degree of SDG7 implementation. In Poland, Romania, Belgium, Luxembourg, Latvia, and Ireland, the relative dynamics was increasing, while in the Nordic and South European countries, it was decreasing. The novelty of our research is combining the COPRAS (assessment of SDG7 implementation) and DTW methods (selection of similar countries with respect to its dynamics).

Deep learning (DL), which is a branch of machine learning (ML) and artificial intelligence (AI), has become a fundamental element of contemporary technological advancements. To facilitate such processes, data representation is crucial, often transitioning from crisp sets to generalized forms like fuzzy sets (FS), introduced by Zadeh. This paper extends the concept by defining a special class of FS known as Logarithmic Fractional Fuzzy Sets (Log-FFS). Moreover, a set of aggregation operators (AoPs) is formulated using logarithmic operational principles, such as the Logarithmic Fractional Fuzzy Weighted Average (Log-FFWA) and its variations, with their core properties thoroughly detailed. The study also incorporates known methodologies such as the Complex Proportional Assessment (COPRAS) and an extended TOPSIS method under Log-FFS information. Finally, the proposed approaches are confidently applied to selecting deep learning techniques, demonstrating their capability to yield optimal results.

Sustainable development by emphasizing on satisfying the current needs of the general public without threating their futures, alongside with taking the environment and future generations under consideration, has become one of the prominent issues in different societies. Therefore, identifying and prioritizing the key factors of sustainable architecture according to regional and cultural features could be the first step in sustaining the architecture as a process and an outcome. In this paper, the key indicators of the environmental sustainability in contemporary architecture of Iran has been identified and prioritized. This study has been performed in three phases. First, identifying key factors of environmental sustainability according to the experts’ point of view and transforming the collected data to triangular fuzzy numbers. Subsequently, the best-worst multi-criteria decision-making method (henceforth BWM) under grey system circumstances has determined the weights and priority of the identified criteria. Eventually, identified key factors were prioritized by the complex proportional assessment method (hereafter COPRAS) under the condition of fuzzy sets. The results indicate that the key factors of creating engagement between buildings and other urban systems has the highest priority in the built environment sustainability in contemporary architecture and proving building management systems has the lowest.

Manufacturing robots are used for industrial purposes. Robots used for manufacturing purpose have the power to create products from raw materials and are capable of operating endlessly even in lights-out situations for continuous production. Manufacturing robots can be used in applications like arc welding, spot welding, materials handling, machine tending, painting, machine cutting and so on. Selecting a robot for a given application is complex. However, robot selection is used in selecting a suitable robot for the preferred output with specific application ability. In recent years, many authors used multi-criteria decision-making methods to select a robot that meets the need. This study presents a hybrid model by integrating complex proportional assessment (COPRAS) with the weighted aggregates sum product assessment (WASPAS) methods in intuitionistic dense fuzzy set to select a manufacturing robot for a particular application. Intuitionistic dense fuzzy entropy is used in calculating the weights for the criteria and intuitionistic dense fuzzy COPRAS and WASPAS are used in ranking the best alternatives where in the optimum types of robots are obtained. Here, intuitionistic dense fuzzy sets are used as it is capable of dealing with the intangible factors while selecting a robot. On the basis of the manufacturing robot selection, two comparisons are given. First, the results are compared with various λ values between 0 and 1 and second the results are compared with the fuzzy set, intuitionistic fuzzy set and the dense fuzzy set to show the effectiveness of the proposed methodology with the intuitionistic dense fuzzy set.

Supplier selection is one of the most critical activities of purchasing management in a supply chain because of the key role of supplier’s performance in achieving the objectives of a supply chain. Supplier selection problem requires a trade-off between multiple criteria exhibiting vagueness and imprecision with the involvement of a group of experts. This paper presents a multiple criteria group decision-making approach for supplier selection problem in the context of interval type-2 fuzzy sets. A new method for ranking interval type-2 fuzzy numbers, based on the centroid of fuzzy sets, is proposed and compared with some methods. The proposed ranking method is used for extending complex proportional assessment (COPRAS) method for group decision-making with interval type-2 fuzzy numbers. The developed method uses a stepwise procedure for ranking and evaluating the alternatives, in terms of significance and utility degree, and selects the best solution considering both the positive-ideal and the negative-ideal solutions. To demonstrate the applicability of the proposed approach in supplier selection problems, an illustrative example is presented and the results are analyzed.

With the emergence of outsourcing logistics and the rapid development of the e-commerce business, Third Party Logistics (TPL) plays an indispensable role in modern business. In the TPL provider selection process, uncertain information brings more challenges to decision makers. This paper uses probabilistic linguistic term sets (PLTSs) to describe uncertain decision making information. Firstly, we propose an improved Decision Making Trial and Evaluation Laboratory method, which allows a certain relationship between decision criteria and calculates criteria weights in multi-criteria decision making (MCDM) problems. Then, in order to make full use of uncertain TPL provider information and maximize the values of data, the probabilistic linguistic complex proportional assessment method is proposed and applied to solve the MCDM problems under probabilistic linguistic environment, which needs much less computation than other MCDM methods. Finally, an application example of TPL provider selection is presented to demonstrate the proposed method. A comparative analysis is further conducted to validate the effectiveness of the proposed method.

Double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) is one of the successful extensions of the hesitant fuzzy linguistic term set used for describing the uncertain information in a more prominent manner for solving the group decision-making problems. In DHHFLTS, the membership functions are represented in terms of linguistic membership degrees which are a flexible structure for preference elicitation and enrich the ability for rational decision-making with complex linguistic expressions. Driven by the flexibility of DHHFLTS, in this paper, a new decision framework is developed for solving decision-making problems, which provides scientific and rational decisions based on the preference information. For it, initially, a new aggregation operator is proposed for aggregating decision-makers’ preferences. Later, the importance of the attribute weights in the problems is determined by formulating a mathematical model and the COPRAS method is extended to the DHHFLTS context for prioritizing alternatives. The applicability of the presented approach is demonstrated through a numeric example related to green supplier selection. A comparative analysis with existing studies is also administered to test the effectiveness and verify the method.

Data mining is a thoroughly advanced method that evaluates and makes more sense of a variety in electronic commerce (e-commerce)-related knowledge, discovering useful ideas, predicting user actions, and assisting enterprises selection in modifying competitive strategy, minimizing cost, and attaining the finest results. Data mining has already become more popular in recent years. In this research paper, we propose a multi-attribute group decision-making (MAGDM) method under T -spherical fuzzy environment for selecting an optimal data mining strategy which is an important part of modern decision-making research. The information aggregation operators play an important role in solving MAGDM problems. Some point aggregation operators based on the 2-tuple linguistic T -spherical fuzzy numbers, including 2-tuple linguistic T -spherical fuzzy point weighted averaging (2TL T -SFPWA) operator, 2-tuple linguistic T -spherical fuzzy point weighted geometric (2TL T -SFPWG) operator, 2-tuple linguistic T -spherical fuzzy generalized point weighted averaging (2TL T -SFGPWA) operator and 2-tuple linguistic T -spherical fuzzy generalized point weighted geometric (2TL T -SFGPWG) operator, are proposed which competently capture all the aspects of human opinions expressible in terms of yes, no, cessation and denial with no limitation. The proposed aggregation operators are valid and have some basic properties which are keenly analyzed. Furthermore, the complex proportional assessment (COPRAS) method is developed on the basis of 2-tuple linguistic T -spherical fuzzy point aggregation operators. Finally, a numerical example is illustrated for demonstrating the effectiveness of the proposed work along with comparative analysis which verifies the reliability and efficacy of its outcomes. In the end, we conclude some results from the numerical analysis, i.e., to balance the long-term development of e-commerce, data mining can mine massive amounts of data which boosts the growth of e-commerce in future.