An intuitionistic fuzzy score function and distance measure-based decision-making model for prioritizing sustainable strategies for electronic waste management

In complex decision-making environments, the uncertainty and hesitancy of evaluation information, coupled with differences among evaluators, lead to asymmetric characteristics in decision information and preferences. Traditional methods struggle to effectively handle scenarios where interval uncertainty and hesitant information coexist, nor can they suppress asymmetric biases caused by extreme evaluations or imbalanced information distributions. To address this, this paper proposes a Symmetric Perception Decision Framework based on credibility-based interval hesitant fuzzy information. First, a Robust Credibility-Based Interval Hesitant Fuzzy Score Function (R-CHFSF) is constructed. This function quantifies asymmetric information by integrating interval width, distribution dispersion, and hesitancy characteristics. An adaptive penalty mechanism is introduced to suppress unreasonable asymmetric amplification effects caused by anomalous intervals or extreme evaluations. Second, the R-CHFSF is embedded into DEMATEL and TODIM methods to construct an integrated model combining causal analysis and ranking decisions, forming a closed-loop decision mechanism that simultaneously regulates information asymmetry and preference asymmetry. Empirical analysis using online movie reviews demonstrates that this framework effectively suppresses interference from excessively asymmetric evaluations, enhances the robustness and interpretability of ranking results, and validates its effectiveness in asymmetry regulation and decision stability.

Fermatean Cubic Fuzzy Score Function in Multi-objective Transportation Problems

Novel Fermatean fuzzy score function enriched decision support framework for biomedical waste recycling

A HyperFunction associates each input with a set of admissible outputs, extending conventional functions by allowing multi-valued rather than single-valued mappings. A SuperHyperFunction further generalizes this concept by employing iterated powersets for both its domain and codomain, enabling the representation of hierarchical, multi-level output structures and HyperStructural multi-valued behavior within complex systems. Although HyperFunctions and SuperHyperFunctions offer expressive tools for modeling hierarchical functional relationships, their study in the existing literature remains relatively limited. This paper extends the fuzzy score function and fuzzy cost function within the frameworks of HyperFunctions and SuperHyperFunctions and provides a concise theoretical analysis of their essential properties.

This paper proposes an integrated ranking approach to assess and rank the locations for solar energy plant establishment by combining improved symmetry point of criterion (SPC), pivot pairwise relative criteria importance assessment (PIPRECIA) and multi-attribute multi-objective optimisation based on the ratio analysis (MULTIMOORA) within intuitionistic fuzzy information (IFI) called as the ‘IF-modified SPC-PIPRECIA-MULTIMOORA’. We first estimate the weights of decision experts (DEs) using an IF-score function-based model, and in this line, a new score function is developed with some elegant axioms on IFI. Second, weights of criteria are computed with a combined objective-subjective weighted model, which contains the IF-improved SPC for objective weight and the IF-PIPRECIA for subjective weight of each criterion. Third, a new exponential distance measure for IFI is developed to evade the limitation of extant IF-distance measures and also presents some interesting properties. To confirm the feasibility and effectiveness of the proposed ranking framework, it is implemented in a case study of the solar energy plant site selection problem. Sensitivity assessment is made to see the impact of variation of weighting factor for prioritizing the solar energy plant sites, which depends on the weights of different criteria. Moreover, a comparison with various existing methods is discussed to show the superiority of the developed framework on IFI.

In the digital context, how to achieve symmetrical integration between subjective evaluation and structural stability becomes the key to improving the design effect of iterative product optimization. In this paper, we propose an iterative design method for CIHFS-DEMATEL products that incorporates structural symmetry analysis. The method is based on online review mining and constructs a credibility-based interval hesitant fuzzy set (CIHFS) to symmetrically express the ambiguity and credibility differences in the decision-maker’s subjective evaluation. In turn, a novel exact score function called credibility interval hesitant fuzzy score function (CHFSF), incorporating information symmetric weights, is proposed to realize the bidirectional symmetric mapping between subjective fuzzy inputs and objective exact outputs. Subsequently, the CIHFS-DEMATEL model is introduced to identify the causal paths and a symmetric interaction structure between potential users’ demands. Finally, the demand module mapping matrix is constructed to realize the symmetric decision-making closure loop from demand to solution. Taking the “Intelligent Classified Trash Can” as a case study, we verify the superiority of the method in terms of recognition accuracy, rationality of weight allocation, and structural stability. This study emphasizes the structural symmetry between “input–evaluation–output”, which provides a theoretical foundation and practical framework for the optimal design of products with complex multi-source information.

In this paper, Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) using the fuzzy score function of decision makers’ weights (FSFDMW) in fuzzy set decision making problem is proposed to select the types of grinding machine and air classifier in dry grinding-classification process. Firstly, we consider how to select the main criteria among possible criteria that affect rational alternative decision making by using fuzzy score function with decision makers’ weights, and propose a method to determine the weights of the main criteria by fuzzy score function with decision makers’ weights. Then, we propose a TOPSIS method using fuzzy scoring functions with the decision makers’ weights and choose a suitable types of grinding machine and air classifier for dental gypsum grinding.

Implementing reverse logistics can not only save costs and reduce operational risks for enterprises, but also enhance their core competitiveness. However, how to choose the best reverse logistics supplier is one of the important decisions faced by enterprises, and it is also an urgent problem that modern enterprise management and logistics management need to solve. Hence, this paper proposed a novel multiple criteria group decision-making (MCGDM) approach based on coefficient of variation method, weighted aggregated sum product assessment (WASPAS) method and the proposed aggregation operators under Fermatean fuzzy setting. First, we define the Sugeno-Weber operations on Fermatean fuzzy number (FFN) and then propose four novel aggregation operators including, Fermatean fuzzy Sugeno-Weber weighted averaging operator, Fermatean fuzzy Sugeno-Weber weighted geometric operator and their related ordered weighted operators. Then the proposed Fermatean fuzzy Sugeno-Weber operators are used to integrate the Fermatean fuzzy assessment information provided by decision experts. Next, the coefficient of variation method is propounded based on the Fermatean fuzzy score function to estimate the importance of assessment criteria. Lastly, the improved WASPAS method is put forward to attain the sorting of alternatives. A cased study about the selection of green supplier is provided to discuss the effectiveness and feasibility of the proposed group decision method.

Novel Pythagorean fuzzy score function to optimize fuzzy transportation models

Sustainable benchmarking of e-scooter micromobility systems: A hybrid q-rung orthopair fuzzy score function and distance measure-based ranking approach

Online product reviews provide valuable insights on user experiences and product qualities. However, issues such as information overload and the limited utilization of review features persist, particularly in personalized rankings for popular items like movies. To address these challenges—information overload in online reviews, limited review feature utilization, and personalized decision-making for high-demand products like movies—we introduce a personalized online decision-making framework that integrates a sentiment model for product attributes with an enhanced hesitant fuzzy scoring function. This framework incorporates the concept of symmetry in sentiment analysis. It employs feature words, sentiment terms, and modifiers to assess user sentiments within a hesitant fuzzy setting, utilizing symmetrical relationships between positive and negative sentiments. The improved fuzzy score function efficiently quantifies sentiment values for product features by considering the symmetrical balance of user opinions. Additionally, review quality assessment incorporates both content and reviewer characteristics, resulting in final attribute evaluations. An attribute weighting system, tailored to diverse product types, further captures product specifics and user inclinations, leveraging symmetry to balance varying user preferences. Validation through multi-genre movie sorting demonstrates the method’s capacity to handle review data across varied products and user tastes, offering a robust tool for enhancing online decision quality, especially for high-demand items.

The household waste (HW) disposal and recycling have become a significant challenge due to increasing quantities of generated household wastes and increased levels of urbanization. Selecting locations/sites for building new HW recycling plant comprises numerous sustainability dimensions, thus, this work aims to develop new decision-making model for evaluating and prioritizing the HW recycling plant locations. This paper is categorized into three phases. First, we propose new improved score function to compare the Fermatean fuzzy numbers. Moreover, an example is presented to validate the effectiveness of proposed score function over the extant ones. Second, we introduce new distance measure to estimate the discrimination degree between Fermatean fuzzy sets (FFSs) and further discuss its advantages over the prior developed Fermatean fuzzy distance measures. Third, we introduce an integrated methodology by combining the method with the removal effects of criteria (MEREC), the stepwise weight assessment ratio analysis (SWARA) and the measurement alternatives and the ranking according to compromise solution (MARCOS) approaches with Fermatean fuzzy (FF) information, and named as the “FF-MEREC-SWARA-MARCOS” framework. In this method, the FF-distance measure is used to find the weights of involved decision-making experts. Moreover, an integrated criteria weighting method is presented with the combination of MEREC and SWARA models under the context of FFSs, while the combined FF-MEREC-SWARA-MARCOS model is applied to evaluate and prioritize the locations for HW recycling plant development, which illustrates its feasibility of the developed framework. Comparative study and sensitivity assessment are conducted to validate the obtained outcomes. This work provides a hybrid decision analysis approach, which marks a significant impact to the HW recycling plant location selection process with uncertain information.

Information aggregation based group decision making under Fermatean fuzzy environment for spent lithium-ion battery recycling techniques evaluation

The COVID-19 epidemic has drastically altered the global landscape and thus organizations are finding it difficult to provide a modern and productive work environment to their stakeholders. As a result, personnel have shifted from in-person interactions to working remotely via video conferencing tools (VCTs). Owing to the onset of COVID-19 outbreak, usage of VTCs has gained great interest among people, especially student fraternity and employees as it reduces the hassle of direct interaction. But selecting the right platform for virtual interaction can be challenging, as it involves a number of factors in order to reduce expenses and maximize productivity. The present treatise has focused on devising a mathematical approach to identify the best VCT by structurizing the problem as a multi-criteria group decision making (MCGDM) model. To carry out the research, the notions of two popular techniques, namely Method based on the Removal Effects of Criteria (MEREC) and Weighted Aggregated Sum Product Assessment (WASPAS) have been extended under Picture fuzzy environment with the aid of Picture fuzzy weighted averaging operator to deal with MCGDM situation. Furthermore, to overcome limitations of existing Picture fuzzy score function (PFSF), a novel PFSF has been developed and its significant properties are analyzed through theoretical and numerical justifications, showing its superiority over the existing one. The proposed PFSF can not only overcome the limitations of the existing SF, but also can rank any type of Picture fuzzy numbers irrespective of their membership and non-membership grades. Thereafter, the extended MCGDM techniques have been integrated with the aid of the proposed novel PFSF and applied to assess the best VCT. The proposed technique has identified Google Meet as the best VCT for virtual communication. Consistency and robustness of proposed technique have been validated through comparative and sensitivity analysis.

The aim of this study is to provide neighborhood structures in bipolar fuzzy supra topological space and to show the applicability of bipolar fuzzy supra topology to the medical diagnosis problem. Firstly, we give some properties related to bipolar fuzzy points and their neighborhood structure in bipolar fuzzy supra topological spaces. Then, we consider another important structure, “quasi-coincident”, in the case of bipolar fuzzy points and bipolar fuzzy sets. Then, we introduce the corresponding neighborhood structure called “Q-neighborhood system” by using the quasi-coincident relations. Furthermore, we also investigate the characterization of bipolar fuzzy supra topological space in terms of quasi-neighborhoods. Finally, we present a new method to solve medical diagnosis problems by using the bipolar fuzzy score function.

This research aims to define and investigate the properties of Nano fuzzy Z-open explicitly sets defined in Nano fuzzy topological spaces. Also, there is an attempt to define Nano fuzzy Z-closure Nano fuzzy Z-interior in Nano fuzzy topological spaces. The work has grown by incorporating Nano fuzzy δ open sets, Nano fuzzy δ semi-open sets, Nano fuzzy δ semi-open sets, and Nano fuzzy δ pre-open sets. Also, the work has been concluded with a numerical application of the Nano fuzzy score function in the medical field (to check the proper diagnosis of disease and drug combinations given to the patient).

The major objective of the current investigation is to build an integrated multiple criteria group decision-making (MCGDM) methodology based on combined compromise solution (CoCoSo) andspherical fuzzy set for determining the optimal solar power station. To begin with, an innovative spherical fuzzy score function is brought forward to strengthen the efficiency of the comparison for spherical fuzzy number (SFN). Secondly, several newly operational laws for SFN are defined and some novel aggregation operation based on them are propounded. The corresponding excellent properties of the novel operators are also explored at length. Further, the spherical fuzzy method on the removal effects of criteria (MEREC) technique is presented by the proposed score function to work out the importance of the criteria. Lastly, an MCGDM approach is propounded based on improved spherical fuzzy CoCoSo to obtain the ranking of the solar power station locations. The feasibility and practicability of the proposed SF-MEREC-CoCoSo method are investigated through the comparison study with the extant methods. The sensibility analysis is also executed to discuss the robustness and stability of the propounded methodology.

Sustainability in the mining and raw materials sector is a key target in the EU Green deal agenda. The aim of this work is to determine the degree of importance of risks that may impede sustainable mining, considering UN Sustainable Development Goals (SDGs) indicators and EU initiatives, taking as a case study the mining sector in Greece. A total of 49 risks for sustainable mining, under six categories, were identified by means of expert consultation and review of the literature. The identification and prioritization of potential risks can provide a pathway towards sustainable mining operations. The risks factors weighting is enhanced using a new Fermatean fuzzy score function with Stepwise Weight Assessment Ratio Analysis (SWARA). The proposed model is a powerful tool to handle the uncertainties and inaccuracies in the information regarding the weights of the risks. The main research findings indicate that the most important risks for sustainable mining in Greece are irresponsible mining, the lack of license to operate, and poor environmental monitoring, which are directly connected to the aim and scope of SDG12: responsible consumption and production. In addition, according to the results the category with the highest risk for sustainable mining is the one of “Risk to Environment”. A complete list of risks and risk categories, and their ranking is presented and discussed creating a priority of actions in the framework of European and international initiatives to set a road map to sustainable mining. This work provides a benchmark for future studies, with the aim of providing a tool for evaluating and ranking global risk factors that may affect sustainable mining development.

The support vector machine (SVM) has been combined with the intuitionistic fuzzy set to suppress the negative impact of noises and outliers in classification. However, it has some inherent defects, resulting in the inaccurate prior distribution estimation for datasets, especially the imbalanced datasets with non-normally distributed data, further reducing the performance of the classification model for imbalance learning. To solve these problems, we propose a novel relative density-based intuitionistic fuzzy support vector machine (RIFSVM) algorithm for imbalanced learning in the presence of noise and outliers. In our proposed algorithm, the relative density, which is estimated by adopting the k-nearest-neighbor distances, is used to calculate the intuitionistic fuzzy numbers. The fuzzy values of the majority class instances are designed by multiplying the score function of the intuitionistic fuzzy number by the imbalance ratio, and the fuzzy values of minority class instances are assigned the intuitionistic fuzzy membership degree. With the help of the strong capture ability of the relative density to prior information and the strong recognition ability of the intuitionistic fuzzy score function to noises and outliers, the proposed RIFSVM not only reduces the influence of class imbalance but also suppresses the impact of noises and outliers, and further improves the classification performance. Experiments on the synthetic and public imbalanced datasets show that our approach has better performance in terms of G-Means, F-Measures, and AUC than the other class imbalance classification algorithms.