Some distance measures for pythagorean cubic fuzzy sets: Application selection in optimal treatment for depression and anxiety

Pythagorean cubic fuzzy sets represent an advancement beyond conventional interval-valued Pythagorean sets, integrating the principles of Pythagorean fuzzy sets and interval-valued Pythagorean fuzzy sets. Given the critical significance of distance measures in real-world decision-making and pattern recognition tasks, it is noteworthy that there exists a notable gap in the literature regarding distance measures specifically tailored for Pythagorean cubic fuzzy sets. The objectives of this paper are:•To define novel generalized distance measures between Pythagorean cubic fuzzy sets (PCFSs) to tackle intricate decision-making challenges.•These novel distance measures are undergoing testing on a real-world scenario concerning the management of anxiety and depression to evaluate their effectiveness and practical application.•We have illustrated the boundedness and nonlinear characteristics inherent in these distance measures. In addition, we conduct comparative analyses with existing approaches to validate the proposed methodology, thereby providing insights into its advantages and potential applications.

The differential measure for Pythagorean fuzzy multiple criteria group decision-making

Pythagorean fuzzy sets (PFSs) proved to be powerful for handling uncertainty and vagueness in multi-criteria group decision-making (MCGDM). To make a compromise decision, comparing PFSs is essential. Several approaches were introduced for comparison, e.g., distance measures and similarity measures. Nevertheless, extant measures have several defects that can produce counter-intuitive results, since they treat any increase or decrease in the membership degree the same as the non-membership degree; although each parameter has a different implication. This study introduces the differential measure (DFM) as a new approach for comparing PFSs. The main purpose of the DFM is to eliminate the unfair arguments resulting from the equal treatment of the contradicting parameters of a PFS. It is a preference relation between two PFSs by virtue of position in the attribute space and according to the closeness of their membership and non-membership degrees. Two PFSs are classified as identical, equivalent, superior, or inferior to one another giving the degree of superiority or inferiority. The basic properties of the proposed DFM are given. A novel method for multiple criteria group decision-making is proposed based on the introduced DFM. A new technique for computing the weights of the experts is developed. The proposed method is applied to solve two applications, the evaluation of solid-state drives and the selection of the best photovoltaic cell. The results are compared with the results of some extant methods to illustrate the applicability and validity of the method. A sensitivity analysis is conducted to examine its stability and practicality.

Linear-time algorithms for phylogenetic tree completion under Robinson-Foulds distance

BACKGROUND

We consider two fundamental computational problems that arise when comparing phylogenetic trees, rooted or unrooted, with non-identical leaf sets. The first problem arises when comparing two trees where the leaf set of one tree is a proper subset of the other. The second problem arises when the two trees to be compared have only partially overlapping leaf sets. The traditional approach to handling these problems is to first restrict the two trees to their common leaf set. An alternative approach that has shown promise is to first complete the trees by adding missing leaves, so that the resulting trees have identical leaf sets. This requires the computation of an optimal completion that minimizes the distance between the two resulting trees over all possible completions.

RESULTS

We provide optimal linear-time algorithms for both completion problems under the widely-used Robinson-Foulds (RF) distance measure. Our algorithm for the first problem improves the time complexity of the current fastest algorithm from quadratic (in the size of the two trees) to linear. No algorithms have yet been proposed for the more general second problem where both trees have missing leaves. We advance the study of this general problem by proposing a useful restricted version of the general problem and providing optimal linear-time algorithms for the restricted version. Our experimental results on biological data sets suggest that completion-based RF distances can be very different compared to traditional RF distances.

A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis

The intuitionistic fuzzy set, as a generation of fuzzy set, can express and process uncertainty much better. Distance measures between intuitionistic fuzzy sets are used to indicate the difference degree between the information carried by intuitionistic fuzzy sets. Although some distance measures have been proposed in previous studies, they can not satisfy the axioms of distance measure, or exist counter-intuitive cases. In this paper, we give a new distance measure between intuitionistic fuzzy sets, which is based on a matrix norm and a strictly increasing (or decreasing) binary function. The new distance measure not only satisfies the axiomatic definition of distance measure, but also overcomes the counter-intuitive cases. It is proved that the new distance measure is reasonable by numerical examples. Moreover, we give the algorithms for pattern recognition and use it to solve medical diagnosis problems.

Outcome quality assessment by surgical process compliance measures in laparoscopic surgery

OBJECTIVE

The effective and efficient assessment, management, and evolution of surgical processes are intrinsic to excellent patient care. Hence, in addition to economic interests, the quality of the outcome is of great importance. Process benchmarking examines the compliance of an intraoperative surgical process to another process that is considered as best practice. The objective of this work is to assess the relationship between the course and the outcome of surgical processes of the study.

MATERIALS AND METHODS

By assessing 450 skill practices on rapid prototyping models in minimally invasive surgery training, we extracted descriptions of surgical processes and examined the hypothesis that a significant relationship exists between the course of a surgical process and the quality of its outcome.

RESULTS

The results showed a significant correlation with Person correlation coefficients >0.05 between the quality of process outcome and process compliance for simple and complex suturing tasks in the study.

CONCLUSIONS

We conclude that high process compliance supports good quality outcomes and, therefore, excellent patient care. We also showed that a deviation from best training processes led to a decreased outcome quality. This is relevant for identifying requirements for surgical processes, for generating feedback for the surgeon with regard to human factors and for inducing changes in the workflow in order to improve the outcome quality.

Tree-like reticulation networks--when do tree-like distances also support reticulate evolution?

Hybrid evolution and horizontal gene transfer (HGT) are processes where evolutionary relationships may more accurately be described by a reticulated network than by a tree. In such a network, there will often be several paths between any two extant species, reflecting the possible pathways that genetic material may have been passed down from a common ancestor to these species. These paths will typically have different lengths but an 'average distance' can still be calculated between any two taxa. In this article, we ask whether this average distance is able to distinguish reticulate evolution from pure tree-like evolution. We consider two types of reticulation networks: hybridisation networks and HGT networks. For the former, we establish a general result which shows that average distances between extant taxa can appear tree-like, but only under a single hybridisation event near the root; in all other cases, the two forms of evolution can be distinguished by average distances. For HGT networks, we demonstrate some analogous but more intricate results.

Time-series analysis in the medical domain: a study of Tacrolimus administration and influence on kidney graft function

There exists a major concern regarding toxic effects of immunosuppressive medication on the kidney graft during post-transplant care, with observed variation in individual susceptibility to adverse drug effects amongst patients. To date, there has been no possibility to identify susceptible patients prospectively. This study analyzes medical data which includes time series of measures of renal function and trough levels of immunosuppressive drug Tacrolimus, with the main aim of identifying patients susceptible to drug toxicity. We evaluate a plethora of time-series distance measures, determining their appropriateness to the domain based on two criteria: (1) preserving the expected correlations between distances, and (2) ability to detect the expected patterns of interaction between immunosuppressive drug levels and renal function. Besides identifying the most suitable time-series distance measures, we observed that the majority of patients do not exhibit an association between impaired graft function and higher Tacrolimus dosing. On the other hand, the minority of patients determined most sensitive to varying Tacrolimus levels showed a strong tendency to prefer low Tacrolimus dosing.