Novel similarity measures under complex pythagorean fuzzy soft matrices and their application in decision making problems.

Complex fuzzy soft matrices play a crucial role in various applications, including decision-making, pattern recognition, signals processing, and image processing. The main objective of this study is to introduce the unique notions of complex Pythagorean fuzzy soft matrices (CPFSMs), which provide more flexibility and accuracy in modelling uncertainty. CPFSMs incorporate Pythagorean fuzzy soft matrices, allowing for more sophisticated uncertainty modeling. The key findings of CPFSMs, specific instances, and certain fundamental set-theoretic operations and principles were covered. A set of new distance metrics between two CPFSMs has been defined. In the context of complex Pythagorean fuzzy soft sets and complex Pythagorean fuzzy soft matrices, we created a CPFS decision-making technique. Moreover, the application's numerical example and comparison analysis have been effectively demonstrated. Thus, by integrating the concepts of Pythagorean fuzzy sets, soft matrices, and complex numbers, CPFSMs provide a robust framework with membership and non-membership degrees for complex decision-making modeling and analyzing uncertain data.

Novel complex fuzzy distance measures with hesitance values and their applications in complex decision-making problems.

A complex fuzzy distance measure (CFDMs) plays a significant role in applications involving complex or high-dimensional data where traditional distance measures may not adequately capture the nuances of the data relationships. The significance of CFDMs lies in their ability to handle uncertainty, imprecision, and complexity in various domains. Numerous researchers introduced different concepts of CFDMs, yet these CFDMs fails to convey any information regarding the hesitancy degree associated with an element. The main objective of this paper is to introduce some new distance measures based on complex fuzzy sets, called complex fuzzy hesitance distance measure and complex fuzzy Euclidean Hesitance distance measure, which is the generalization of complex fuzzy normalized Hamming distance measure and complex fuzzy Euclidean distance measure. Some new operations and primay results are discussed in the environment of proposed CFDMs and complex fuzzy operations. Moreover, we discussed the applications of the proposed CFDMs in addressing decision-making problems. We introduced a new decision-making algorithm that integrates CFDMs into decision-making processes, providing a robust methodology for handling real-world complexities. Further, the comparative study of the proposed CFDMs is discussed with some existing CFDMs.

Mathematical Modeling for Inherited Diseases.

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra.

Correction: Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order.

[This corrects the article DOI: 10.1371/journal.pone.0103617.].

Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order.

In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-step generalized differential transform method (MSGDTM). We also show the unique positive solution for this model and present numerical results graphically.

Decomposition of fuzzy soft sets with finite value spaces.

The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter.