Research On Multi-attribute Decision-Making Algorithms Under Interval-valued Fermatean Fuzzy Environment

Decision-making is the process of modeling,analyzing,and selecting the best alternative based on established goals and given data.However,the decision-making process often involves uncertainty.The interval-valued Fermatean fuzzy set is a more efficient mathematical tool for dealing with uncertain information.This thesis focuses on multi-attribute decision problems under the interval-valued Fermatean fuzzy environment.It proposes new multi-attribute decision making algorithms in terms of three aspects,such as aggregation operator,score function and three-way decision.The primary work is as follows:(1)An interval-valued Fermatean fuzzy multi-attribute decision making algorithm based on the Dombi aggregation operators is proposed.When non-membership lower(upper)values equal to 0 under the interval-valued Fermatean fuzzy environment,the existing aggregation operators involve information loss.In order to solve this problem,this thesis proposes an interval-valued Fermatean fuzzy Dombi weighted geometric aggregation operator and its ordered weighted geometric aggregation operator based on the Dombi operations.Then,a new intervalvalued Fermatean fuzzy multi-attribute decision-making algorithm is constructed based on the proposed aggregation operators.The experimental results show that compared with existing aggregation operators,the proposed aggregation operators in this thesis do not have the problem of decision information loss when the non-membership lower(upper)values equal to 0.(2)An interval-valued Fermatean fuzzy multi-attribute decision making algorithm based on an improved score function is proposed.The existing score functions cannot distinguish two different interval-valued Fermatean fuzzy numbers in some situations under the interval-valued Fermat fuzzy environment.In order to solve this problem,an improved score function is proposed in this thesis.Then a new multi-attribute decision making algorithm is constructed based on the proposed improved score function.The experimental results show that the score function has the highest differentiation rate and the lowest error rate compared with the existing score functions.(3)The interval-valued Fermatean fuzzy three-way multi-attribute decision making algorithm based on the probability dominance relation is given.For the problem that traditional multi-attribute decision algorithms cannot classify the alternatives in the interval-valued Fermatean fuzzy environment,this thesis proposes an interval-valued Fermatean fuzzy three-way multi-attribute decision algorithm based on the probabilistic dominance relation.The algorithm determines the conditional probability of each alternative based on the probabilistic dominance relation and constructs loss functions from the perspective of the ideal solution.Then,a new intervalvalued Fermatean fuzzy three-way multi-attribute decision making algorithm is constructed based on conditional probabilities and loss functions.The experimental results demonstrate that the proposed algorithm can not only rank but also classify the alternatives.And compared with the existing interval-valued Fermatean fuzzy multiattribute decision making algorithms,the proposed algorithm has a lower error rate.