A novel MADM algorithm for landfill site selection based on q-rung orthopair probabilistic hesitant fuzzy power Muirhead mean operator

Abstract

With the rapid development of economy and the acceleration of urbanization, the garbage produced by urban residents also increases with the increase of population. In many big cities, the phenomenon of "garbage siege" has seriously affected the development of cities and the lives of residents. Sanitary landfill is an important way of municipal solid waste disposal. However, due to the restriction of social, environmental and economic conditions, landfill site selection has become a very challenging task. In addition, landfill site selection is full of uncertainty and complexity due to the lack of cognitive ability of decision-makers and the existence of uncertain information in the decision-making process. Therefore, a novel multi-attribute decision making method based on q-rung orthopair probabilistic hesitant fuzzy power weight Muirhead mean operator is proposed in this paper, which can solve the problem of landfill site selection well. This method uses probability to represent the hesitance of decision maker and retains decision information more comprehensively. The negative effect of abnormal data on the decision result is eliminated by using the power average operator. Muirhead mean operator is used to describe the correlation between attributes. Then, an example of landfill site selection is given to verify the effectiveness of the proposed method, and the advantages of the proposed method are illustrated by parameter analysis and comparative analysis. The results show that this method has a wider space for information expression, gives the decision maker a great degree of freedom in decision-making, and has robustness.

Multi-attribute decision-making method based on q-rung orthopair probabilistic hesitant fuzzy schweizer-sklar power weighted hamy mean operator

“…Definition 1. [ 19 ] Let X ={ x 1 , x 2 ,⋯, x n } be a given universe, then the q-order orthogonal probability hesitant fuzzy set on the universe of q-ROPHFS is defined as: …”

“…Definition 2. [ 19 ] Let h = <Γ h ,Ψ h > q , , be any three q-ROPHFE, and λ >0, then the algorithm of q-ROPHFS ics as follows: …”

“…Definition 3. [ 19 ] Let h = <Γ h ,Ψ h > q be a q-ROPHFE, then the score function S ( h ) is defined as: …”

“…Definition 4. [ 19 ] Let h = <Γ h ,Ψ h > q be a q-ROPHFE, its scoring function is η , then the deviation degree D ( h ) is defined as: …”

“…Garg et al [ 18 ] further generalized the probabilistic hesitant fuzzy set from the perspective of membership and non-membership, and proposed probabilistic dual hesitant fuzzy set. Ren et al [ 19 ] broadens the value range of membership degree and non-membership degree, and proposed q-rung orthopair probabilistic hesitant fuzzy set (q-ROPHFS). Expressing the preference of decision-making expert through probability information can more truly reflect the importance of the decision-making opinions given by the decision-making expert, and at the same time, it can describe more decision-making information of the decision makers in actual situations.…”