Search Results (8)

The fusion of multi-polarized petrographic images of rock thin sections involves the fusion of feature information from microscopic images of rock thin sections illuminated under both plane-polarized and orthogonal-polarized light. During the fusion process of rock thin section images, the inherent high resolution and abundant feature information of the images pose substantial challenges in terms of computational complexity when dealing with massive datasets. In engineering applications, to ensure the quality of image fusion while meeting the practical requirements for high-speed processing, this paper proposes a novel fast fusion Transformer. The model leverages a soft matching algorithm based on intuitionistic fuzzy sets to merge redundant tokens, effectively mitigating the negative effects of asymmetric dependencies between tokens. The newly generated artificial tokens serve as brokers for the Query (Q), forming a novel lightweight fusion strategy. Both subjective visual observations and quantitative analyses demonstrate that the Transformer proposed in this paper is comparable to existing fusion methods in terms of performance while achieving a notable enhancement in its inference efficiency. This is made possible by the attention paradigm, which is equivalent to a generalized form of linear attention, and the newly designed loss function. The model has been experimented on with multiple datasets of different rock types and has exhibited robust generalization capabilities. It provides potential for future research in diverse geological conditions and broader application scenarios. Full article

Social-Ecological Systems (SESs) are systems with close linkage between nature and societies. Coastal lagoons are SESs crucial for the ecosystem services (ESs) provided, especially in the Mediterranean Basin, facing threats from anthropogenic activities and climate change. Management strategies focusing solely on ecological elements’ improvement have not yielded the desired outcomes, as they often neglect the needs and perspectives of stakeholders. Participatory approaches promote engagement and awareness to develop sustainable and effective management strategies. Aiming to contribute to the preservation and sustainable management of the Nestos Delta coastal lagoons, a Natura 2000 site in Greece, this study explores the application of intuitionistic fuzzy sets (IFS) to capture the inherent uncertainty in stakeholder opinions against complex environmental challenges. Through this participatory approach, stakeholder perspectives were assessed and quantified to rank management alternatives. Ecological health and economic values were prioritized, endorsing the adoption of natural and soft interventions; conflicts and a knowledge gap regarding non-provisioning ESs were revealed, highlighting the necessity of inclusive consultation processes. This approach offers the potential to facilitate consensus-building and enhance the legitimacy of coastal lagoon management decisions. Full article

Octahedron sets, which extend beyond the previously defined fuzzy set and soft set concepts to address uncertainty, represent a hybrid set theory that incorporates three distinct systems: interval-valued fuzzy sets, intuitionistic fuzzy sets, and traditional fuzzy set components. This comprehensive set theory is designed to express all information provided by decision makers as interval-valued intuitionistic fuzzy decision matrices, addressing a broader range of demands than conventional fuzzy decision-making methods. Multi-criteria decision-making (MCDM) methods are essential tools for analyzing and evaluating alternatives across multiple dimensions, enabling informed decision making aligned with strategic objectives. In this study, we applied MCDM methods to octahedron sets for the first time, optimizing decision results by considering various constraints and preferences. By employing an MCDM algorithm, this study demonstrated how the integration of MCDM into octahedron sets can significantly enhance decision-making processes. The algorithm allowed for the systematic evaluation of alternatives, showcasing the practical utility and effectiveness of octahedron sets in real-world scenarios. This approach was validated through influential examples, underscoring the value of algorithms in leveraging the full potential of octahedron sets. Furthermore, the application of MCDM to octahedron sets revealed that this hybrid structure could handle a wider range of decision-making problems more effectively than traditional fuzzy set approaches. This study not only highlights the theoretical advancements brought by octahedron sets but also provides practical evidence of their application, proving their importance and usefulness in complex decision-making environments. Overall, the integration of octahedron sets and MCDM methods marks a significant step forward in decision science, offering a robust framework for addressing uncertainty and optimizing decision outcomes. This research paves the way for future studies to explore the full capabilities of octahedron sets, potentially transforming decision-making practices across various fields. Full article

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. In this analysis, we use the massive dominant and more consistent principle of power aggregation operators (PAOs) based on general t-norm and t-conorm, which manage awkward and inconsistent data in real-world dilemmas such as medical diagnosis, pattern recognition, cleaner production evaluation in gold mines, the analysis of the cancer risk factor, etc. The principle of averaging, geometric, Einstein, and Hamacher aggregation operators are specific cases of generalized PAOs. We combine the principle of complex intuitionistic fuzzy soft (CIFS) information with PAOs to initiate CIFS power averaging (CIFSPA), CIFS weighted power averaging (CIFSWPA), CIFS ordered weighted power averaging (CIFSOWPA), CIFS power geometric (CIFSPG), CIFS weighted power geometric (CIFSWPG), and CIFS ordered weighted power geometric (CIFSOWPG), and their flexible laws are elaborated. Certain specific cases (such as averaging, Einstein, and Hamacher operators) of the explored operators are also illustrated with the help of different t-norm and t-conorm operators. A MADM process is presented under the developed operators based on the CIFS environment. Finally, to investigate the supremacy of the demonstrated works, we employed a sensitivity analysis and geometrical expressions of the initiated operators with numerous prevailing works to verify the efficiency of the proposed works. This manuscript shows how to make decisions when there is asymmetric information about enterprises. Full article

In a conventional interpretation of decision-making based on ambiguity, a decision-maker must prefer the best possible opportunity including various feasible possibilities. However, the dilemma of picking the best possible alternative has continued to be a substantial task to resolve. In this manuscript, we improve the existing complex intuitionistic fuzzy soft set (CIFSS), which includes the grade of truth and falsity with the rule that the sum of the real and imaginary parts of both grades is confined to [0, 1]. CIFS is a valuable procedure to determine the authenticity and consistency of the elaborated approaches. The fundamental laws and their related examples are also determined. Moreover, by using these laws, we investigated the complex intuitionistic fuzzy soft prioritized weighted averaging operator (CIFSPWAO), the complex intuitionistic fuzzy soft prioritized ordered weighted averaging operator (CIFSPOWAO), the complex intuitionistic fuzzy soft prioritized weighted geometric operator (CIFSPWGO), complex intuitionistic fuzzy soft prioritized ordered weighted geometric operator (CIFSPOWGO), and their related properties are also developed. Based on the developed operators, the multiattribute decision-making (MADM) tool is developed by using the explored operators based on CIFSS. Some numerical examples are also illustrated by using the investigated operators to determine the feasibility and consistency of the developed approaches. Finally, the comparative analysis and their geometrical manifestations are also determined to enhance the excellence of the performed explorations. Full article

In recent years, the complex fuzzy set theory has intensified the attention of many researchers. This paper focuses on developing the algebraic structures pertaining to lattice ordered groups and lattice ordered subgroups for complex intuitionistic fuzzy soft set theory. Furthermore, some of their properties and operations are discussed. In addition, the weighted distance measures between two complex intuitionistic fuzzy soft lattice ordered groups such as weighted hamming, weighted normalized hamming, weighted euclidean and weighted normalized euclidean distance measures were introduced and also some of the algebraic properties of the weighted distance measures are verified. Moreover, the application of complex intuitionistic fuzzy soft lattice ordered groups by using the weighted distance measures is analysed. Full article

A Pythagorean fuzzy soft set (PFSS) model is an extension of an intuitionistic fuzzy soft set (IFSS) model to deal with vague knowledge according to different parameters. The PFSS model is a more powerful tool for expressing uncertain information when making decisions and it relaxes the constraint of IFSS. Hypergraphs are helpful to handle the complex relationships among objects. Here, we apply the concept of PFSSs to hypergraphs, and present the notion of Pythagorean fuzzy soft hypergraphs (PFSHs). Further, we illustrate some operations on PFSHs. Moreover, we describe the regular PFSHs, perfectly regular PFSHs and perfectly irregular PFSHs. Finally, we consider the application of PFSHs for the selection of a team of workers for business and got the appropriate result by using score function. Full article

A decision-making environment is full of uncertainty and complexity. Existing tools include fuzzy sets, soft sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets (PFSs) and so on. Compared with intuitionistic fuzzy sets (IFSs), PFSs proposed by Yager have advantages in handling vagueness in the real world and possess good symmetry. The entropy measure is the most widespread form of uncertainty measure. In this paper, we improve the technique for order preference by similarity to an ideal solution (TOPSIS) method to better deal with multiple-attribute group decision making (MAGDM) problems based on Pythagorean fuzzy soft sets (PFSSs). To better determine the weights of attributes, we firstly define a novel Pythagorean fuzzy soft entropy which is more reasonable and valid. Meanwhile the entropy has good symmetry. Entropy for PFSSs which is used to determine the subjective weights of attributes is also defined. Then we introduce a measure to calculate integrated weights by combining objective weights and subjective weights. Based on the integrated weights, the TOPSIS method is generalized and improved to solve the MAGDM problem. A distance measure taking into account the characteristics of Pythagorean fuzzy numbers (PFNs) is used to calculate distance between alternatives and ideal solutions. Finally, the proposed MAGDM method is applied in the case of selecting a missile position. Compared with other methods, it is shown that the proposed method can rank alternatives more reasonably and have higher distinguishability. Full article