Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making

Football players' strength training method using image processing based on machine learning

This work addresses the declining physical fitness levels observed in both football players and the general population. The objective is to investigate the impact of functional strength training on the physical capabilities of football players and to develop a machine learning-based approach for posture recognition. A total of 116 adolescents aged 8 to 13 participating in football training are randomly assigned to either an experimental group (n = 60) or a control group (n = 56). Both groups underwent 24 training sessions, with the experimental group engaging in 15-20 minutes of functional strength training after each session. Machine learning techniques, specifically the backpropagation neural network (BPNN) in deep learning, are utilized to analyze the kicking actions of football players. Movement speed, sensitivity, and strength are employed as input vectors for the BPNN to compare the images of players' movements, while the similarity between the kicking actions and standard movements served as the output result to enhance training efficiency. The experimental group's kicking scores are compared to their pre-experiment scores, demonstrating a statistically significant improvement. Moreover, statistically significant differences are observed in the 5*25m shuttle running, throwing, and set kicking between the control and experimental groups. These findings highlight the significant enhancement in strength and sensitivity achieved through functional strength training in football players. The results contribute to the development of training programs for football players and the overall improvement of training efficiency.

An Extension TOPSIS Method Based on the Decision Maker’s Risk Attitude and the Adjusted Probabilistic Fuzzy Set

The paper studies an extension TOPSIS method with the adjusted probabilistic linguistic fuzzy set in which the decision maker’s behavior tendency is considered. Firstly, we propose a concept of probabilistic linguistic q-rung orthopair set (PLQROS) based on the probability linguistic fuzzy set (PLFS) and linguistic q-rung orthopair set (LQROS). The operational laws are introduced based on the transformed probabilistic linguistic q-rung orthopair sets (PLQROSs) which have the same probability. Through this adjustment method, the irrationality of the existing methods in the aggregation process is avoided. Furthermore, we propose a comparison rule of PLQROS and the aggregated operators. The distance measure of PLQROSs is also defined, which can deal with the symmetric information in multi-attribute decision making problems. Considering that the decision maker’s behavior has a very important impact on decision-making results, we propose a behavioral TOPSIS decision making method for PLQROS. Finally, we apply the practical problem of investment decision to demonstrate the validity of the extension TOPSIS method, and the merits of the behavior decision method is testified by comparing with the classic TOPSIS method. The sensitivity analysis results of decision-maker’s behavior are also given.

Multiple attribute decision making method based on DEMATEL and fuzzy distance of trapezoidal fuzzy neutrosophic numbers and its application in typhoon disaster evaluation

 Trapezoidal fuzzy neutrosophic decision making plays an important role in decision-making processes with uncertain, indeterminate, and inconsistent information. In this paper, we propose a new multi-attribute decision-making method based on decision-making trial and evaluation laboratory (DEMATEL), fuzzy distance, and linear assignment method (LAM), and we express evaluation values as the trapezoidal fuzzy neutrosophic numbers (TrFNNs). First, attribute weights are obtained using the DEMATEL method and the new fuzzy distance of TrFNNs based on graded mean integration representation is defined. Then, alternatives are ranked using the LAM in operations research. In addition, we make two comparative analyses in the end to illustrate the feasibility and rationality of our method. Finally, an illustrative example about typhoon disaster assessment is presented to show the advantages of the proposed method.

The reference ideal TOPSIS method for linguistic q-rung orthopair fuzzy decision making based on linguistic scale function

The linguistic q-rung orthopair fuzzy set is a powerful tool in representing linguistic assessments. Considering that the traditional decision making methods cannot deal with the situation that the best choice may not be the minimum or the maximum but between them, we propose an innovative TOPSIS method with linguistic q-rung orthopair fuzzy numbers based on the reference ideal theory. Firstly, the new operations of linguistic q-rung orthopair fuzzy sets are introduced based on the linguistic scale function. In addition, we propose the Minkowski distance measure of linguistic q-rung orthopair fuzzy numbers to make up for the defects of the existing distance measures based on the linguistic scale function. By using the new operations of linguistic q-rung orthopair fuzzy numbers, we propose the linguistic q-rung orthopair fuzzy weighted averaging operator and the linguistic q-rung orthopair fuzzy weighted geometric operator to aggregate linguistic decision information. Furthermore, we develop a reference ideal TOPSIS method to the linguistic q-rung orthopair fuzzy decision making problems. Finally, an example concerning the postgraduate entrance qualification assessment is given to illustrate the feasibility of the proposed method. Some comparative analysis is also given to show the efficiency of the method, in addition, the sensitivity analysis and stability analysis of the proposed method are also given.

Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals

The intuitionistic fuzzy set (IFS) is applied in various decision-making problems to express vagueness and showed great success in realizing the day-to-day problems. The principal aim of this article is to develop an approach for solving multi-criteria matrix game with intuitionistic fuzzy (I-fuzzy) goals. The proposed approach introduces the indeterminacy resolving functions of I-fuzzy numbers and discusses the I-fuzzy inequalities concept. Then, an effective algorithm based on the indeterminacy resolving algorithm is developed to obtain Pareto optimal security strategies for both players through solving a pair of multi-objective linear programming problems constructed from two auxiliary I-fuzzy programming problems. It is shown that this multi-criteria matrix game with I-fuzzy goals is an extension of the multi-criteria matrix game with fuzzy goals. Moreover, two numerical simulations are conducted to demonstrate the applicability and implementation process of the proposed algorithm. Finally, the achieved numerical results are compared with the existing algorithms to show the advantages of our algorithm.

On the Analysis and Computation of Topological Fuzzy Measure in Distributed Monoid Spaces

The computational applications of fuzzy sets are pervasive in systems with inherent uncertainties and multivalued logic-based approximations. The existing fuzzy analytic measures are based on regularity variations and the construction of fuzzy topological spaces. This paper proposes an analysis of the general fuzzy measures in n-dimensional topological spaces with monoid embeddings. The embedded monoids are topologically distributed in the measure space. The analytic properties of compactness and homeomorphic, as well as isomorphic maps between spaces, are presented. The computational evaluations are carried out with n = 1, considering a set of translation functions with different symmetry profiles. The results illustrate the dynamics of finite fuzzy measure in a monoid topological subspace.