Search Results (43)

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

The medical diagnosis of many critical diseases is difficult as it usually requires the combined effort of several doctors. At this time, the process of medical diagnosis is actually a group decision-making (GDM) problem. In group medical diagnosis, considering doctors’ weight information and fusing the interaction relation of symptoms remain open issues. To address this problem, a group decision-making method for intuitionistic fuzzy soft environments is proposed for medical diagnosis because the intuitionistic fuzzy soft set (IFSS) integrates the advantages of the soft set and intuitionistic fuzzy set (IFS). Intuitionistic fuzzy soft weighted Muirhead mean operators are constructed by combining Einstein operations with the Muirhead mean (MM) operator, and some properties and results are revealed. A group medical diagnosis model with unknown doctor weight information and incomplete intuitionistic fuzzy soft information is proposed. Similarity measures of the intuitionistic fuzzy soft matrix (IFSM) given by the doctors are used to estimate the incomplete information. To take into account the advantages of objective weight and subjective weight, the combined weights of doctors are calculated based on the IFSMs’ similarity measure and doctors’ grades. The developed operators are then used to combine the evaluation information and handle the correlation of input arguments in the group medical diagnosis process. Finally, a numerical problem is selected to illustrate the superiority of the proposed approach compared to related methods. The combined weights are determined to overcome the shortcomings of the single-weight method to some extent. Meanwhile, the proposed method is more comprehensive, and can provide more flexible and reasonable choices for group medical diagnosis problems. Full article

This paper establishes a new type of space, modified intuitionistic fuzzy soft metric space (MIFSMS). Basic properties and topological structures are defined in the setting of this new notion with valid examples. Moreover, we have given some new results along with suitable examples to show their validity. An application for finding the solution of an integral equation is also given by utilizing our newly developed results. Full article

In this paper, we merge the concepts of soft set theory and a bipolar intuitionistic fuzzy set. A bipolar intuitionistic fuzzy soft ideal in a BCK-algebra is defined as a soft set over the set of elements in the BCK-algebra, with each element associated with an intuitionistic fuzzy set. This relationship captures degrees of uncertainty, hesitancy, and non-membership degrees within the context of BCK-algebras. We investigate basic operations on bipolar intuitionistic fuzzy soft ideals such as union, intersection, AND, and OR. The intersection, union, AND, and OR of two bipolar intuitionistic fuzzy soft ideals is a bipolar intuitionistic fuzzy soft ideal. We also demonstrate how to use a bipolar intuitionistic fuzzy soft set to solve a problem involving decision making. Finally, we provide a general approach for handling decision-making problems using a bipolar intuitionistic fuzzy soft set. Full article

Supplier selection as a multiattribute decision-making (MADM) problem has various inherent uncertainties due to a number of symmetrical variables. In order to handle such information-based uncertainties, rational models like intuitionistic fuzzy sets have already been introduced in the literature. However, a picture fuzzy set (PiFS) with four dimensions of positive, neutral, negative, and rejection is better at capturing and interpreting such kinds of ambiguous information. Additionally, fuzzy parameterization (FPara) is helpful for evaluating the degree of uncertainty in the parameters. This study aims to develop a fuzzy parameterized picture fuzzy soft set (FpPiFSS) by integrating the ideas of PiFS and FPara. This integration is more adaptable and practical since it helps decision makers manage approximation depending on their objectivity and parameterization uncertainty. With the assistance of instructive examples, some of the set-theoretic operations are examined. A decision support framework is constructed using matrix manipulation, preferential weighting, fuzzy parameterized grades based on Pythagorean means, and the approximations of decision makers. This framework proposes a reliable algorithm to evaluate four timber suppliers (initially scrutinized by perusal process) based on eight categorical parameters for real estate projects. In order to accomplish suppliers evaluation, crucial validation outcomes are taken into account, including delivery level, purchase cost, capacity, product quality, lead time, green degree, location, and flexibility. To assess the advantages, dependability, and flexibility of the recommended strategy, comparisons in terms of computation and structure are provided. Consequently, the results are found to be reliable, analog, and consistent despite the use of fuzzy parameterization and picture fuzzy setting. Full article

Large amounts of online reviews from e-commerce sites and social media platforms can help potential consumers to better understand products and play an important part in assisting potential consumers in making purchase decisions. Moreover, while multiple consumers purchase the same product, the index parameters of the product that are of concern among them are usually different, i.e., they have different expectations for the product. Therefore, the question of how to effectively analyze online product reviews and consider multiple consumers’ expectations to select products is an important issue that needs to be addressed. The objective of this study is to propose a product selection method based on intuitionistic fuzzy soft sets and TODIM. Firstly, the online reviews are extracted by the web crawler and are pretreated. Next, the sentiment orientations of each online review concerning product index parameters are recognized using the dictionary-based sentiment analysis algorithm. Then, the evaluation values of sentiment orientations for product index parameters are firstly expressed by intuitionistic fuzzy numbers and are then transformed into intuitionistic fuzzy soft sets. Further, the alternative product set is obtained according to the uni-int decision function and multiple consumers’ expectations, and we then rank the alternative products using the TODIM method. Finally, a case study is provided to illustrate the validity and feasibility of the proposed method. Full article

Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices), proposed by Enginoğlu and Arslan in 2020, are worth utilizing in data classification in supervised learning due to coming into prominence with their ability to model decision-making problems. This study aims to define the concepts metrics, quasi-, semi-, and pseudo-metrics and similarities, quasi-, semi-, and pseudo-similarities over ifpifs-matrices; develop a new classifier by using them; and apply it to data classification. To this end, it develops a new classifier, i.e., Intuitionistic Fuzzy Parameterized Intuitionistic Fuzzy Soft Classifier (IFPIFSC), based on six pseudo-similarities proposed herein. Moreover, this study performs IFPIFSC’s simulations using 20 datasets provided in the UCI Machine Learning Repository and obtains its performance results via five performance metrics, accuracy (Acc), precision (Pre), recall (Rec), macro F-score (MacF), and micro F-score (MicF). It also compares the aforementioned results with those of 10 well-known fuzzy-based classifiers and 5 non-fuzzy-based classifiers. As a result, the mean Acc, Pre, Rec, MacF, and MicF results of IFPIFSC, in comparison with fuzzy-based classifiers, are 94.45%, 88.21%, 86.11%, 87.98%, and 89.62%, the best scores, respectively, and with non-fuzzy-based classifiers, are 94.34%, 88.02%, 85.86%, 87.65%, and 89.44%, the best scores, respectively. Later, this study conducts the statistical evaluations of the performance results using a non-parametric test (Friedman) and a post hoc test (Nemenyi). The critical diagrams of the Nemenyi test manifest the performance differences between the average rankings of IFPIFSC and 10 of the 15 are greater than the critical distance (4.0798). Consequently, IFPIFSC is a convenient method for data classification. Finally, to present opportunities for further research, this study discusses the applications of ifpifs-matrices for machine learning and how to improve IFPIFSC. Full article

Choosing a proper construction project is a vital subject for entrepreneurs to reduce their costs. In real cases, vagueness and uncertain data drive decisions based on uncertainty. The intuitionistic fuzzy sets (IFSs) theory could assist decision-makers (DMs) in inscribing inadequate knowledge. Nevertheless, this paper provides a new integrated decision analysis model with IFSs. The suggested procedure includes a new decision flow under uncertain situations to define the significance of criteria. In this regard, the weighting of subjective DMs is required for this manner; the only input data needed are an alternative evaluation matrix. Then, a case study on sustainable energy project selection is explained to show the purpose of the suggested model. In this regard, four main criteria, technological, economic, social, and environmental, and seven alternatives from different kinds of energies are introduced to select the appropriate energy project. In this model, the weights of criteria are defined based on a new combined method based on two CRITIC and ideal points approaches. The proposed soft computing model computed the ranking of main alternatives by integrating the ARAS and EDAS approaches; the final outcomes indicate that the second alternative has higher values than other alternatives concerning nuclear energy. Afterward, sensitivity and comparative analyses are generated to determine the efficiency and validity of the proposed model. The sensitivity analysis changes the criteria weights. The comparative analysis compares the IF-TOPSIS method and the proposed model and computes the different degrees to confirm the efficiency of the introduced soft computing model. Full article

Artificial intelligence (AI) is a well-known and reliable technology that enables a machine to simulate human behavior. While the major theme of AI is to make a smart computer system that thinks like a human to solve awkward problems, machine learning allows a machine to automatically learn from past information without the need for explicit programming. In this analysis, we aim to derive the idea of Aczel–Alsina aggregation operators based on an intuitionistic fuzzy soft set. The initial stage was the discovery of the primary and critical Aczel–Alsina operational laws for intuitionistic fuzzy soft sets. Subsequently, we pioneer a range of applicable theories (set out below) and identify their essential characteristics and key results: intuitionistic fuzzy soft Aczel–Alsina weighted averaging; intuitionistic fuzzy soft Aczel–Alsina ordered weighted averaging; intuitionistic fuzzy soft Aczel–Alsina weighted geometric operators; and intuitionistic fuzzy soft Aczel–Alsina ordered weighted geometric operators. Additionally, by utilizing certain key information, including intuitionistic fuzzy soft Aczel–Alsina weighted averaging and intuitionistic fuzzy soft Aczel–Alsina weighted geometric operators, we also introduce the theory of the weighted aggregates sum product assessment method for intuitionistic fuzzy soft information. This paper also introduces a multi-attribute decision-making method, which is based on derived operators for intuitionistic fuzzy soft numbers and seeks to assess specific industrial problems using artificial intelligence or machine learning. Finally, to underline the value and reasonableness of the information described herein, we compare our obtained results with some pre-existing information in the field. This comparison is supported by a range of numerical examples to demonstrate the practicality of the invented theory. Full article

The correlation between two disparate variables conquers a significant habitation in statistics. The concept of correlation coefficient (CC) is one of the well-known indicators, but it is not used in interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS) information. It is a generalization of interval-valued intuitionistic fuzzy soft sets and a refined extension of intuitionistic fuzzy hypersoft sets. However, using the CC and weighted correlation coefficient (WCC) has not yet been explored for IVIFHSS information. The core objective of this research is to present the correlation coefficient (CC) and weighted correlation coefficient (WCC) for interval-valued intuitionistic fuzzy hypersoft sets (IVIFHSS) and their mandatory properties. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) is developed based on proposed correlation measures. To ensure the symmetry of the developed scheme, we consider mathematical clarifications of correlation contractions. Based on assessments, it conceded vibrant multi-attribute decision-making (MADM) methodology with the most substantial significance. In addition, a statistical illustration is designated to regulate the operative usage of a decision-making configuration in thermal energy storage techniques. The productivity of the advocated algorithm is more reliable than existing replicas to control the favorable configurations of the premeditated study. Full article

Many of the new $MV$-valued fuzzy structures, including intuitionistic, neutrosophic, or fuzzy soft sets, can be transformed into so-called almost $MV$-valued fuzzy sets, or, equivalently, fuzzy sets with values in dual pair of semirings (in symbols, $(\mathcal{R},{\mathcal{R}}^{*})$-fuzzy sets). This transformation allows any construction of almost $MV$-valued fuzzy sets to be retransformed into an analogous construction for these new fuzzy structures. In that way, approximation theories for $(\mathcal{R},{\mathcal{R}}^{*})$-fuzzy sets, rough $(\mathcal{R},{\mathcal{R}}^{*})$-fuzzy sets theories, or F-transform theories for $(\mathcal{R},{\mathcal{R}}^{*})$-fuzzy sets have already been created and then retransformed for these new fuzzy structures. In this paper, we continue this trend and define, on the one hand, the theory of extensional $(\mathcal{R},{\mathcal{R}}^{*})$-fuzzy sets defined on sets with fuzzy similarity relations with values in dual pair of semirings and power sets functors related to this theory and, at the same time, the theory of cuts with relational morphisms of these structures. Illustratively, the reverse transformations of some of these concepts into new fuzzy structures are presented. Full article

Orthopairs (pairs of disjoint sets) have points in common with many approaches to managing vaguness/uncertainty such as fuzzy sets, rough sets, soft sets, etc. Indeed, they are successfully employed to address partial knowledge, consensus, and borderline cases. One of the generalized versions of orthopairs is intuitionistic fuzzy sets which is a well-known theory for researchers interested in fuzzy set theory. To extend the area of application of fuzzy set theory and address more empirical situations, the limitation that the grades of membership and non-membership must be calibrated with the same power should be canceled. To this end, we dedicate this manuscript to introducing a generalized frame for orthopair fuzzy sets called “$(m,n)$-Fuzzy sets”, which will be an efficient tool to deal with issues that require different importances for the degrees of membership and non-membership and cannot be addressed by the fuzzification tools existing in the published literature. We first establish its fundamental set of operations and investigate its abstract properties that can then be transmitted to the various models they are in connection with. Then, to rank $(m,n)$-Fuzzy sets, we define the functions of score and accuracy, and formulate aggregation operators to be used with $(m,n)$-Fuzzy sets. Ultimately, we develop the successful technique “aggregation operators” to handle multi-criteria decision-making problems in the environment of $(m,n)$-Fuzzy sets. The proposed technique has been illustrated and analyzed via a numerical example. Full article

The present paper comes across the main steps that were laid from Zadeh’s fuzziness and Atanassov’s intuitionistic fuzzy sets to Smarandache’s indeterminacy and to Molodstov’s soft sets. Two hybrid methods for assessment and decision making, respectively, under fuzzy conditions are also presented using suitable examples that use soft sets and real intervals as tools. The decision making method improves on an earlier method of Maji et al. Further, it is described how the concept of topological space, the most general category of mathematical spaces, can be extended to fuzzy structures and how to generalize the fundamental mathematical concepts of limit, continuity compactness and Hausdorff space within such kinds of structures. In particular, fuzzy and soft topological spaces are defined and examples are given to illustrate these generalizations. Full article