Fuzzy Einstein Hybrid Geometric Operator Research Articles

Leakage failure probability assessment of submarine pipelines using a novel pythagorean fuzzy bayesian network methodology

Obtaining precise and adequate failure data can be challenging in the probabilistic risk assessment of process industries, like submarine pipelines. This study proposes a novel approach, the Pythagorean fuzzy Bayesian network methodology, to tackle the challenge of obtaining prior data in the assessment of leakage risk in submarine pipelines. First, the qualitative evaluation of experts is converted by Pythagorean fuzzy sets. Next, the enhanced Pythagorean trapezoidal fuzzy Einstein hybrid geometric operator is integrated with the subject-objective weighting approach to consolidate the expert opinions in order to obtain prior probabilities. Following this, the leaky Noisy-OR gate in the Bayesian network is utilized to access the conditional probabilities, which depict the uncertain logical connection of events. Ultimately, the Bayesian network is utilized for inference and analysis to anticipate the probability of system failure and detect any vulnerabilities. Furthermore, a case study is performed to demonstrate the practicality of the approach. The reliability of the methodology is verified by results comparison and analysis. The suggested approach and evaluation findings can offer valuable guidance for the safety supervision of the submarine pipeline network.

Algorithms for decision-making process using complex Pythagorean fuzzy set and its application to hospital siting for COVID-19 patients

Since the start of COVID-19, a fair amount of work has been undertaken by scholars around the world to model its progression. It became clear from the start of pandemic that its progression is affected by various factors within different communities. Subsequently, the necessary means and the range of measures used to effectively control the virus would vary from place to place. And we have been witness to different approaches adopted around the world to maintain the virus under check both in the short term and the long term. So, in this unexpected situation, it is a great challenge for the world health organization (WHO) to save the lives of COVID-19 patients. For this, several mathematical models have been made for better understanding the coronavirus contagion. Mostly, these models are based on classical integer-order derivative using real numbers which cannot capture the fading memory. Thus, in this unexpected situation, fuzzy sets (FSs) are considered due to their inherent capability to deal with uncertainty. Fuzzy sets (FSs) theory has the ability to manage uncertain situations. Thus, the goal of this research is to present newly mathematical methods based on complex Pythagorean fuzzy sets (CPyFSs) and their operators, namely complex Pythagorean fuzzy Einstein weighted geometric operator, and induced complex Pythagorean fuzzy Einstein hybrid geometric operator to reduce the spreading rate of COVID-19. At the end of the paper an illustrative example is constructed to show the effectiveness, reliability of the new techniques.

Induced generalized pythagorean fuzzy aggregation operators and their application based on t-norm and t-conorm

In this paper, we present some new operators, namely induced Pythagorean fuzzy Einstein ordered weighted geometric operator, induced Pythagorean fuzzy Einstein hybrid geometric operator, induced generalized Pythagorean fuzzy Einstein ordered weighted geometric operator, induced generalized Pythagorean fuzzy Einstein hybrid geometric operator. Moreover, these operators are applied to decision-making, in which the specialists of the problems deliver their favorites to display the practicality, and value of the new presented work. We also study the applicability in a decision-making concerning strategic choice of the best information system and give an example to show the effectiveness of the developed methods.

Generalized intuitionistic fuzzy aggregation operators based on confidence levels for group decision making

The focus of our this paper is to develop a series of Einstein hybrid aggregation operators using confidence level, such as confidence intuitionistic fuzzy Einstein hybrid averaging operator, confidence intuitionistic fuzzy Einstein hybrid geometric operator, generalized confidence intuitionistic fuzzy Einstein hybrid averaging operator and generalized confidence intuitionistic fuzzy Einstein hybrid geometric operator. The main advantage of the new operators is that these operators not only provide information to the experts of the problems, but these methods also consider the degrees of the experts of the problems that they are familiar with the selection option. The new approaches provide more general, more accurate and precise results as compared to the existing methods. Finally, the proposed operators have been applied to decision-making problems to show the validity, practicality and effectiveness of the new approach.

New approach to multiple attribute group decision-making based on Pythagorean fuzzy Einstein hybrid geometric operator

The objective of the present work is divided into two folds. Firstly, Pythagorean fuzzy Einstein hybrid geometric operator has been introduced along with their properties, namely idempotency, boundedness and monotonicity. Actually, Pythagorean fuzzy Einstein weighted geometric aggregation operator weighs only the Pythagorean fuzzy arguments, and Pythagorean fuzzy Einstein ordered weighted geometric aggregation operator weighs only the ordered positions of the Pythagorean fuzzy arguments instead of weighing the Pythagorean fuzzy arguments themselves. To overcome these limitations, we introduce the concept of Pythagorean fuzzy Einstein hybrid geometric aggregation operator, which weighs both the given Pythagorean fuzzy value and its ordered position. Thus, the main advantage of the proposed operator is that it is the generalization of their existing operators. Therefore, this method plays a vital role in real-world problems. Finally, we applied the proposed operator to multiple-attribute group decision-making.

Geometric aggregation operators with interval-valued Pythagorean trapezoidal fuzzy numbers based on Einstein operations and their application in group decision making

The aim of this paper is to investigate information aggregation methods under interval-valued Pythagorean trapezoidal fuzzy environment. Some Einstein operational laws on interval-valued Pythagorean trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. Based on Einstein operations, we define interval-valued Pythagorean trapezoidal fuzzy aggregation operators, such as interval-valued Pythagorean trapezoidal fuzzy Einstein weighted geometric operator, interval-valued Pythagorean trapezoidal fuzzy Einstein ordered weighted geometric operator and interval-valued Pythagorean trapezoidal fuzzy Einstein hybrid geometric operator. Furthermore, we apply the proposed aggregation operators to deal with multiple attribute group decision making problem. Finally we construct a numerical example for multiple attribute group decision making problem and compare the result with existing methods.

Evaluation of emergency risk management capability based on hesitant fuzzy Einstein operator

Scientific and objective evaluation of emergency risk management capability is of vital importance to the improvement of emergency management system. A three-perspective evaluation system of emergency risk management capability is proposed, which includes the risk identification, risk reduction, an d risk treatment. Considering the hesitation of people’s judgment about complex situations, a new fuzzy comprehensive evaluation model based on hesitant fuzzy Einstein hybrid geometric operator is developed. Finally, a practical example is given to verify the developed approaches and to demonstrate its practicality and effectiveness.

Some intuitionistic trapezoidal fuzzy aggregation operators based on Einstein operations and their application in multiple attribute group decision making

Information aggregation is a key problem in decision making. The aim of this paper is to investigate information aggregation methods under intuitionistic trapezoidal fuzzy environment. Some Einstein operational laws on intuitionistic trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. Then, some intuitionistic trapezoidal fuzzy aggregation operators based on Einstein operations are proposed, such as intuitionistic trapezoidal fuzzy Einstein weighted averaging operator, intuitionistic trapezoidal fuzzy Einstein ordered weighted averaging operator, induced-intuitionistic trapezoidal fuzzy Einstein ordered weighted averaging operator, intuitionistic trapezoidal fuzzy Einstein hybrid averaging operator, intuitionistic trapezoidal fuzzy Einstein weighted geometric operator, intuitionistic trapezoidal fuzzy Einstein ordered weighted geometric operator, induced intuitionistic trapezoidal fuzzy Einstein ordered weighted geometric operator and intuitionistic trapezoidal fuzzy Einstein hybrid geometric operator. Furthermore, we apply the proposed aggregation operators to deal with multiple attribute group decision making in which decision information takes the form of intuitionistic trapezoidal fuzzy numbers. Finally, an illustrative example is given to demonstrate its practicality and effectiveness.