pythagorean fuzzy sets

Medical information is complex and confidential, making accurate diagnosis challenging, especially with varying expert opinions. This study proposes a hybrid multicriteria decision-making (MCDM) approach combining the Pythagorean fuzzy method based on removal effects of criteria (PF-MEREC) and stepwise weight assessment ratio analysis (SWARA). By integrating both objective and subjective weight assessments, the approach ranks alternatives using TOPSIS. This method offers a novel solution to early childhood cancer diagnosis, demonstrating its practicality and efficiency through sensitivity analysis. The results align with the standards of the American Cancer Society and the National Cancer Institute, showcasing its potential to improve diagnosis and treatment planning.

Process capability analysis (PCA) is a completely effective statistical tool for ability of a process to meet predetermined specification limits (SLs). Unfortunately, especially the real case problems include many uncertainties, it is one of the critical necessities to define the parameters of PCIs by using crisp numbers. So, the results obtained may be incorrect, if the PCIs are calculated without taking into account the uncertainty. To overcome this problem, the fuzzy set theory (FST) has been successfully used to design of PCA. We also know that fuzzy set extensions have an important role in modelling the case that include uncertainty, incomplete and inconsistent information and they are more powerful than traditional FST to model uncertainty. Defining of main parameters of PCIs such as SLs, mean (µ) and variance (σ2) by using the flexible of fuzzy set extensions rather than precise values due to uncertainty, time, cost, inspectors hesitancy and the results based on fuzzy sets for PCIs contain more, flexible and  sensitive information. In this study, two of well-known PCIs called Cp and Cpk have been re-designed at the first time by using one of fuzzy set extensions named Pythagorean fuzzy sets (PFSs). Defining PCIs with more than one membership function instead of an only one membership function is enabling to evaluate the process more  broadly more flexibility. For this aim, the main parameters of PCIs have been defined  and analyzed by using PFSs. Finally, four new PCIs based on PFSs such as Csp, Cspk, Cfp and Cfpk have been derived. The proposed new PCIs based on PFSs have been also applied on manufacturing process and capability for gears have been analyzed. It is shown that the flexibility of the PFSs on PCIs enables the PCA to give more realistic,  more sensitive, and more comprehensive results.

Multiple criteria decision analysis (MCDA) has been widelyinvestigated and successfully applied to many fields, owingto its great capability of modeling the process of actualdecision-making problems and establishing proper evaluationand assessment mechanisms. With the developmentof management and economics, real-world decision-makingproblems are becoming diversified and complicated to anincreasing extent, especially within a changeableand unpredictable environment. Multi-criteria decision making is a decision-making technique that explicitly evaluates numerous contradictory criteria. TOPSIS is a well-known multi-criteria decision-making process. The goal of this research is to use TOPSIS to solve MCDM problems in a Pythagorean fuzzy environment. The distance between two Pythagorean fuzzy numbers is utilised to create the model using the spherical distance measure. To construct a ranking order of alternatives and determine the best one, the revised index approach is utilised. Finally, we look at a set of MCDM problems to show how the proposed method and approach work in practise. In addition, it shows comparative data from the relative closeness and updated index methods.

Fermatean Fuzzy Sets (FFSs) provide an effective way to handle uncertainty and vagueness by expanding the scope of membership and Non-Membership Degrees (NMDs) of Intuitionistic Fuzzy Set (IFS) and Pythagorean Fuzzy Set (PFS), respectively. FFS handles uncertain information more easily in the process of decision making. The concept of composite relation is an operational information measure for decision making. This study establishes Fermatean fuzzy composite relation based on max-average rule to enhance the viability of FFSs in machine learning via soft computing approach. Some numerical illustrations are provided to show the merit of the proposed max-average approach over existing the max-min-max computational process. To demonstrate the application of the approach, we discuss some pattern recognition problems of building materials and mineral fields with the aid of the Fermatean fuzzy modified composite relation and Fermatean fuzzy max-min-max approach to underscore comparative analyses. In recap, the objectives of the paper include: 1) discussion of FFS and its composite relations, 2) numerical demonstration of Fermatean fuzzy composite relations, 3) establishment of a decision application framework under FFS in pattern recognition cases, and 4) comparative analyses to showcase the merit of the new approach of Fermatean fuzzy composite relation. In future, this Fermatean fuzzy modified composite relation could be studied in different environments like picture fuzzy sets, spherical fuzzy sets, and so on.

Different extensions of fuzzy sets like intuitionistic, picture, Pythagorean, and spherical have been proposed to model uncertainty. Although these extensions are able to increase the level of accuracy, imposing rigid restrictions on the grades are the main problem of them. In these types of fuzzy sets, the value of grades and also the sum of them must be in the closed unit interval of [0, 1]. The sum condition seriously restricts the eligible values for grades. q-rung orthopair and T-spherical fuzzy sets have been introduced to establish a framework to tackle the mentioned problem for two-grade and three-grade fuzzy sets, respectively. Reducing the value of grades by means of power operator is the backbone idea of the both sets. However, these fuzzy sets are suffering from two drawbacks. The first one arises from the fact that there is no automatic structure to identify a proper power. Also, information loss is the other one which affects the accuracy of the decision-making process. This problem is a damaging consequence of changing the values of the grades. This paper introduces a novel reducing strategy to improve q-rung orthopair and T-spherical fuzzy sets by tackling the mentioned drawbacks. The proposed strategy solves out the former problem by establishing an automatic framework for finding a proper power which guarantee enough reduction of the values. The automatic framework is used for reducing the value of the maximum grade. Besides, the novel strategy reduces the rest of the grades according to their distance with the the maximum grade and it’s reduction rate. This paper proves mathematically that the ratio between the grades before and after of the reduction process will be intact, which results in solving information loss problem. Moreover, the higher accuracy level of the novel reduction strategy in comparison with the preceding methods, q-rung orthopair and T-sipherical fuzzy sets, is shown via different examples.

In the decision theory, there are many useful tools for operations in logistics and Supply Chain Management (SCM). One of the vital trivets of logistics operations is warehouse management which is also one of the parts of a supply chain. Deciding on the location of a warehouse has a critical issue especially during an outbreak. In this study, we aimed that to figure out differences between the perceived importance of the considered criteria in the decision process regarding warehouse location in the medical sector in terms of the changing dynamics after the Covid-19 pandemic. Pursuing this goal, the results of a preliminary study which was resulted from the gathered data of a decision-making group including industry professionals before the pandemic outbreak were accepted as an anchor to obtain a comparison with the current state. To construct a proper representation of the post-Covid state, a similar methodology was used, and similar decision-makers data were collected with the preliminary study in the identification of the importance figures and causal relationships between criteria. According to comparative results of pre-and post-Covid studies, it is found that there are significant changes in the perceived role of adjacency to target markets and customs criteria in medical warehouse location decisions. It is obvious that the results will shed light on medical sector professionals’ decision process while adapting to the current pandemic conditions.

The aim of this manuscript is to present a new concept of hesitant q-rung orthopair fuzzy sets (Hq-ROFSs) by combining the concept of the q-ROFSs as well as Hesitant fuzzy sets. The proposed concept is the generalization of the fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and Pythagorean fuzzy sets as well as intuitionistic hesitant fuzzy sets (IHFSs) and hesitant Pythagorean fuzzy sets (HPFSs).Furthermore some basic operational laws of hesitant q-rung orthopair fuzzy have been investigated. The score and accuracy functions are defined which play a vital role in decision making process for making comparison between the hesitant q-rung orthopair fuzzy numbers (Hq-ROFNs). Under the Hq-ROF environment, Hq-ROF weighted averaging (Hq-ROFWA) and Hq-ROF weighted geometric (Hq-ROFWG) operators are introduced and various properties of these aggregation operators are studied. Additionaly, a numerical application shows that how the proposed operators are utilized to solve multi-criteria decision making (MCDM) problems in which experts added their optimistic and pessimistic preferences. Finally the analysis of proposed method with other methods is presented which show that the method presented in this paper is more flexible and superior than existing methods.