Search Results (18)

Intuitionistic fuzzy sets (IFSs), proposed in 1983, are one of the most viable and widely explored extensions of Zadeh’s fuzzy sets. In the decade following their introduction, they were extended to interval-valued IFSs (IVIFSs), temporal IFSs, IFSs of the second type (incorrectly called “Pythagorean fuzzy sets” by some authors) IFSs of n-th type, and IFSs over different universes. For each of these extensions, at least one geometrical interpretation has been defined, and for IVIFSs, at least seven different interpretations are known. In the present paper, revisiting some existing results on IVIFSs, some necessary modifications, additions, and corrections to the planar and spatial geometrical interpretations are introduced here for the first time. A new, eighth, geometrical interpretation of IVIFSs is proposed. A basic logic operation and two modal operators are illustrated and a comparison is made between the planar and the new “two-rods” geometrical interpretations of identical IVIFS elements. Finally, a new operator over IVIFSs is proposed for the first time, some of its properties are proven, and its geometrical interpretations are described. Full article

As a non-associative connective in fuzzy logic, the analysis and research of overlap functions have been extended to many generalized cases, such as interval-valued and intuitionistic fuzzy overlap functions (IFOFs). However, overlap functions face challenges in the Pythagorean fuzzy (PF) environment. This paper first extends overlap functions to the PF domain by proposing PF overlap functions (PFOFs), discussing their representable forms, and providing a general construction method. It then introduces a new PF similarity measure which addresses issues in existing measures (e.g., the inability to measure the similarity of certain PF numbers) and demonstrates its effectiveness through comparisons with other methods, using several examples in fractional form. Based on the proposed PFOFs and their induced residual implication, new generalized PF rough sets (PFRSs) are constructed, which extend the PFRS models. The relevant properties of their approximation operators are explored, and they are generalized to the dual-domain case. Due to the introduction of hesitation in IF and PF sets, the approximate accuracy of classical rough sets is no longer applicable. Therefore, a new PFRS approximate accuracy is developed which generalizes the approximate accuracy of classical rough sets and remains applicable to the classical case. Finally, three multi-criteria decision-making (MCDM) algorithms based on PF information are proposed, and their effectiveness and rationality are validated through examples, making them more flexible for solving MCDM problems in the PF environment. Full article

Linguistic q-Rung orthopair fuzzy set is a new extension of the linguistic Pythagorean fuzzy set, which effectively represents the fuzzy and uncertain decision-making information based on qualitative modeling. However, its operational rules are unable to process pure linguistic exponential calculations, in which the exponents are represented using linguistic q-Rung orthopair fuzzy values and the bases are represented as linguistic terms or interval linguistic numbers. This greatly restricts its application in decision making under complex environments. As the complement of the existing linguistic q-Rung orthopair fuzzy operational rules, this paper defines linguistic q-Rung orthopair fuzzy calculation rules, including division, subtraction, and exponent operations. Based on theorem-based proofs, the relevant properties of the calculation rules have been analyzed, such as commutative law, distributive law, symmetry, and so on. Moreover, in order to facilitate the application of linguistic q-Rung orthopair fuzzy theory, this paper introduces the concept of dual linguistic q-Rung orthopair fuzzy value. Building on this foundation, a series of weighted aggregation operators for the calculations involving linguistic q-Rung orthopair fuzzy values and dual linguistic q-Rung orthopair fuzzy values have been designed. In conclusion, a novel pure linguistic multi criteria decision-making methodology is introduced in this work. The validity and utility of the proposed method are demonstrated via a real-world application in the decision process of energy resource exploitation. Full article

Task scheduling is a critical challenge in cloud computing systems, greatly impacting their performance. Task scheduling is a nondeterministic polynomial time hard (NP-Hard) problem that complicates the search for nearly optimal solutions. Five major uncertainty parameters, i.e., security, traffic, workload, availability, and price, influence task scheduling decisions. The primary rationale for selecting these uncertainty parameters lies in the challenge of accurately measuring their values, as empirical estimations often diverge from the actual values. The integral-valued Pythagorean fuzzy set (IVPFS) is a promising mathematical framework to deal with parametric uncertainties. The Dyna Q+ algorithm is the updated form of the Dyna Q agent designed specifically for dynamic computing environments by providing bonus rewards to non-exploited states. In this paper, the Dyna Q+ agent is enriched with the IVPFS mathematical framework to make intelligent task scheduling decisions. The performance of the proposed IVPFS Dyna Q+ task scheduler is tested using the CloudSim 3.3 simulator. The execution time is reduced by 90%, the makespan time is also reduced by 90%, the operation cost is below 50%, and the resource utilization rate is improved by 95%, all of these parameters meeting the desired standards or expectations. The results are also further validated using an expected value analysis methodology that confirms the good performance of the task scheduler. A better balance between exploration and exploitation through rigorous action-based learning is achieved by the Dyna Q+ agent. Full article

Mining is a high-risk industry where occupational accidents are common due to its complex nature. Therefore, providing a more holistic and dynamic risk assessment framework is essential to identify and minimize the potential risks and enhance safety measures. Unfortunately, traditional risk assessment methods have limitations and shortcomings, such as uncertainty, differences in experience backgrounds, and insufficiency to articulate the opinions of experts. In this paper, a novel risk assessment method precisely for such cases in the mining sector is proposed, applied, and compared with traditional methods. The objective of this study is to determine the risk scores of Turkish Coal Enterprises, based on non-fatal occupational accidents, which operates eight large-scale open-cast coal mine enterprises in Türkiye. The causes of the accidents were categorized into 25 sub-criteria under 6 main criteria. The risk scores for these criteria were computed using the Pythagorean fuzzy Analytical Hierarchy Process (PFAHP) method. The first shift (8–16 h) (0.6341) for the shift category is ranked highest out of the 25 sub-risk factors, followed by maintenance personnel (0.5633) for the occupation category; the open-cast mining area (0.5524) for the area category, the 45–57 age range (0.5279) for employee age category, and the mining machine (0.4247) for the reason category, respectively. The methodologies proposed in this study not only identify the most important risk factors in enterprises, but also provide a mechanism for risk-based rankings of enterprises by their calculated risk scores. The enterprises were risk-based ranked with the fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) method and Paksoy approach based on interval type-2 fuzzy sets (IT2FSs). The findings indicate that the first three risk score rankings of enterprises are the same for both approaches. To examine the consistency of the applied methods, sensitivity analyses were performed. The results of the study also indicate that the proposed approaches are recommended for effective use in the mining sector due to their ease of application compared to other methods and their dynamic nature in the risk assessment process. Full article

A Fermatean fuzzy set (FRFS) is the extension of a fuzzy set, an intuitionistic fuzzy set, and a Pythagorean fuzzy set, and is used in different fields. Unlike other fuzzy structures, the sum of cubes of membership grades in FRFSs approximates a unit interval, increasing uncertainty. In this study, we intend to provide unique operational rules and aggregation operators (AOs) inside a Fermatean fuzzy environment. To develop a fair remedy for the membership degree and non-membership degree features of “Fermatean fuzzy numbers (FRFNs)”, our solution introduces new neutral or fair operating principles, which include the concept of proportional distribution. Based on the suggested operating principles, we provide the “Fermatean fuzzy fairly weighted average operator and the Fermatean fuzzy fairly ordered weighted averaging operator”. Our suggested AOs provide more generalized, reliable, and exact data than previous techniques. Combining the recommended AOs with multiple decision-makers and partial weight information under FRFSs, we also devised a technique for “multi-criteria decision-making”. To illustrate the application of our novel method, we provide an example of the algorithm’s effectiveness in addressing decision-making challenges. Full article

Airports located in densely populated areas often face challenges due to asymmetrical traffic patterns. Efficient management and careful planning are required to handle the disproportionate flow of passengers, aircraft, and ground services. The significance of symmetry and asymmetry in civil aviation extends to international regulations and agreements. By harmonizing standards and practices among different nations, it is possible to achieve symmetry in safety measures and operational procedures, thereby promoting a unified and secure global aviation system. Conversely, asymmetry in regulations, infrastructure development, or technological advancements among countries can create obstacles in establishing a cohesive and equitable international aviation framework. This article discusses the weaknesses of the existing score function in handling the MADM problem in an Interval-Valued Pythagorean Fuzzy (IVPF) environment. To tackle this issue, an enhanced score function is developed as a solution. The article proposes the IVPF Dombi hybrid arithmetic and IVPF Dombi hybrid geometric operators based on IVPF information. Furthermore, the article proves some fundamental properties of these operators. In the context of recently introduced techniques using IVPF settings, an effective method is developed for selecting the best airline. Additionally, a comparative investigation is carried out to demonstrate the legitimacy and viability of this unique strategy in comparison to earlier approaches. Full article

The linguistic interval-valued Pythagorean fuzzy (LIVPF) sets, which absorb the advantages of linguistic terms set and interval-valued Pythagorean fuzzy sets, can efficiently describe decision makers’ evaluation information in multi-attribute group decision-making (MAGDM) problems. When investigating aggregation operators of linguistic interval-valued Pythagorean fuzzy (LIVPF) information, we have to consider two important issues, viz. the operational rules of LIVPF numbers and aggregation functions. The classical Archimedean t-norm and t-conorm (ATT) are a famous t-norm and t-conorm, which can produce some special cases. Recently, ATT has been widely applied in different fuzzy decision-making information. Hence, in this paper, for the first issue, we propose some novel operational rules of LIVPF numbers based on ATT. The new operational laws are flexible and can generate some useful operations. For the second issue, we choose a powerful function, i.e., the extended power average (EPA) operator as the aggregation function. The prominent advantages of EPA are that it not only considers the relationship among input arguments, but also dynamically changes the weights of input arguments by employing a parameter. Hence, our proposed novel aggregation operators for LIVPFNs are flexible and is suitable to handle MAGDM problems in actual life. Afterward, we further present a novel MAGDM method under LIVPF conditions. The main finding of our study is a new MAGDM method, which is more powerful and flexible than existing ones. Finally, we apply the method in a sustainable building materials selection to show its effectiveness. Additionally, comparison analysis is provided to demonstrate the advantages and superiorities of the proposed method. Full article

Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set $\left(C_{PFSs}\right)$ as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of $C_{PFSs}$, set operators, aggregation operators, and developed an algorithm based on distance measures for ($C_{PFSs}$), which are applied in a disease diagnostic decision-making problem. Full article

Single-minute exchange of dies (SMED) is one of the most significant lean tools which reduces the required time for setup operations. The consideration of appropriate ergonomic interferences during the SMED implementation improves working conditions, productivity, and flexibility. The SMED literature has an opportunity for expansion with ergonomic assessment. Moreover, ergonomic assessment studies have various limitations in terms of a broad hierarchy of ergonomic factors and their weighting. Therefore, this study enriches the literature by providing the ergonomic assessment of the setup process through integrating multi-criteria decision-making (MCDM) into SMED. In this context, a wide hierarchy of ergonomic risk factors is compiled for ergonomic assessment. The Interval Valued Pythagorean Fuzzy Analytic Hierarchy Process (IVPF-AHP) method is used to determine the weights of factors. Then, Fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is used to prioritize setup tasks in terms of ergonomic factors by using the Interval Valued Pythagorean Fuzzy Sets (IVPFSs). The proposed model was validated by applying it to a real-life manufacturing system in the white goods supplier industry. The application results justify the proposed model with a setup time reduction of 58% and an ergonomic improvement of 19%. Full article

The T-spherical fuzzy set (TSFS) is a modification of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), q-rung orthopair fuzzy set (q-ROFS), and picture fuzzy set (PFS), with three characteristic functions: the membership degree (MD) denoted by $S$, the nonmembership degree (NMD) denoted by $D$, and the abstinence degree (AD) denoted by $I$. It can be used to solve problems of uncertain information with no restrictions. The distance measure (DM) is a tool that sums up the difference between points, while the similarity measure (SM) is a method applied to calculate the similarity between objects within an interval of $\left[0,1\right]$. The current work aims to introduce novel DMs and SMs in the environment of TSFSs to show the limitations of the previously defined DMs and SMs. The suggested DMs and SMs provide more room for all three degrees to be selected without restriction. We investigated the effectiveness of the proposed DMs and SMs by applying a pattern-recognition technique, and we determined their applicability for multicriteria decision making (MCDM) using numerical examples. The newly proposed DMs and SMs are briefly compared to existing DMs and SMs, and appropriate conclusions are drawn. Full article

This study introduces an integrated decision-making methodology to choose the best “waste-to-energy (WTE)” technology for “municipal solid waste (MSW)” treatment under the “interval-valued Pythagorean fuzzy sets (IPFSs)”. In this line, first, a new similarity measure is developed for IPFSs. To show the utility of the developed similarity measure, a comparison is presented with some extant similarity measures. Next, a weighting procedure based on the presented similarity measures is proposed to obtain the criteria weight. Second, an integrated approach called the “interval-valued Pythagorean fuzzy-complex proportional assessment (IPF-COPRAS)” is introduced using the similarity measure, linear programming model and the “complex proportional assessment (COPRAS)” method. Furthermore, a case study of WTE technologies selection for MSW treatment is taken to illustrate the applicability and usefulness of the presented IPF-COPRAS method. The comparative study is made to show the strength and stability of the presented methodology. Based on the results, the most important criteria are “greenhouse gas (GHG)” emissions (P3), microbial inactivation efficacy (P7), air emissions avoidance (P9) and public acceptance (P10) with the weight/significance degrees of 0.200, 0.100, 0.100 and 0.100, respectively. The evaluation results show that the most appropriate WTE technology for MSW treatment is plasma arc gasification (H4) with a maximum utility degree of 0.717 followed by anaerobic digestion (H7) with a utility degree of 0.656 over various considered criteria, which will assist with reducing the amount of waste and GHG emissions and also minimize and maintain the costs of landfills. Full article

Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding data is not generally symmetric on the grounds that it does not provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due to their parameter variableness, they have been well applied in MADM under fuzzy construction. Recently, the Aczel-Alsina AOs on intuitionistic fuzzy sets (IFSs), interval-valued IFSs and T-spherical fuzzy sets have been proposed in the literature. In this article, we develop new types of Pythagorean fuzzy AOs by using Aczel-Alsina t-norm and Aczel-Alsina t-conorm. Thus, we give these new operations Aczel-Alsina sum and Aczel-Alsina product on Pythagorean fuzzy sets based on Aczel-Alsina t-norm and Aczel-Alsina t-conorm. We also develop new types of Pythagorean fuzzy AOs including Pythagorean fuzzy Aczel-Alsina weighted averaging and Pythagorean fuzzy Aczel-Alsina weighted geometric operators. We elaborate some characteristics of these proposed Aczel-Alsina AOs on Pythagorean fuzzy sets, such as idempotency, monotonicity, and boundedness. By utilizing the proposed works, we solve an example of MADM in the information of the multinational company under the evaluation of impacts in MADM. We also illustrate the comparisons of the proposed works with previously existing AOs in different fuzzy environments. These comparison results demonstrate the effectiveness of the proposed Aczel-Alsina AOs on Pythagorean fuzzy sets. Full article

In the face of practical problems such as the increasing demand for shared bicycles and the number of faulty vehicles which are hard to handle and repair in time, shared bicycles operators tend to outsource recycling services to suppliers. To solve the problem of recycling supplier selection, this paper constructs a novel evaluation index system involving the three traditional dimensions and introduces an interval-valued Pythagorean fuzzy (IVPF) hybrid weighted decision-making model based on the self-confidence level. Subsequently, the self-confidence IVPF hybrid weighted average geometric operator and self-confidence IVPF ordered hybrid weighted average geometric operator are proposed by integrating the self-confidence level of experts, the superiority of the weighted and geometric average rules. The significant merit of the developed operators is that they can incorporate the self-confidence level of the expert as well as effectively combine the characteristics of the weighted and geometric average mechanism. A multi-attribute decision-making (MADM) framework is then constructed by using the proposed aggregation approach. Finally, on the basis of the established evaluation index system, a case concerning the green recycling supplier selection of shared bicycles is applied to display the superiority and practicability of the presented method. Full article

The VIKOR model has been considered a viable tool for many decision-making applications in the past few years, given the advantages of considering the compromise between maximizing the utility of group and minimizing personal regrets. The q-rung interval-valued orthopair fuzzy set (q-RIVOFS) is a generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS) and has emerged to solve more complex and uncertain decision making problems which IFS and PFS cannot handle. In this manuscript, the key innovation is to combine the traditional VIKOR model with q-RIVOFS to develop the q-rung interval-valued orthopair fuzzy VIKOR model. In the new developed model, to express more information, the attribute’s values in MAGDM problems are depicted by q-RIVOFNs. First of all, some basic theories and aggregation operators of q-RIVOFNs are simply introduced. Then we develop the origin VIKOR model to q-RIVOFS environment and briefly express the computing steps of this new established model. Thereafter, the effectiveness of the model is verified by an example of supplier selection of medical consumer products and through comparative analysis, the superiority of the new method is further illustrated. Full article