In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis...In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.展开更多
The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes.It works well for crisp weights,but the problem arises when weights are vague and uncertain.Let us take an examp...The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes.It works well for crisp weights,but the problem arises when weights are vague and uncertain.Let us take an example of computer networks,where the chosen path might no longer be appropriate due to rapid changes in network conditions.The optimal path from among all possible courses is chosen in computer networks based on a variety of parameters.In this paper,we design a new variant of the Floyd-Warshall algorithm that identifies an All-Pair Shortest Path(APSP)in an uncertain situation of a network.In the proposed methodology,multiple criteria and theirmutual associationmay involve the selection of any suitable path between any two node points,and the values of these criteria may change due to an uncertain environment.We use trapezoidal picture fuzzy addition,score,and accuracy functions to find APSP.We compute the time complexity of this algorithm and contrast it with the traditional Floyd-Warshall algorithm and fuzzy Floyd-Warshall algorithm.展开更多
In Pakistan, a hierarchical healthcare system is an efficient way of addressing the issueof limited and insufficient healthcare services. Identifying the various degrees of diseasebased on the doctor's diagnosis i...In Pakistan, a hierarchical healthcare system is an efficient way of addressing the issueof limited and insufficient healthcare services. Identifying the various degrees of diseasebased on the doctor's diagnosis is an important step in developing the hierarchical healthcaretreatment structure. This research presents a framework for dealing with the issueof diagnosis values presented as "picture fuzzy numbers (PFNs)". Specifically, the goal ofthis study is to establish some innovative operational laws and "aggregation operators"(AOs) in a picture fuzzy environment. In this regard, we proposed some new neutral orfair operational laws that incorporate the concept of proportional distribution in orderto achieve a neutral or fair remedy to the positive, neutral and negative aspects ofPFNs. Based on the developed operational laws, we proposed the "picture fuzzy fairlyweighted average operator" and the "picture fuzzy fairly ordered weighted averagingoperator". Compared to previous techniques, the proposed AOs provide more generalizedand reliable. Furthermore, using proposed AOs with multiple decision-makers andpartial weight information under PFNs, a "multi-criteria decision-making" algorithmis developed. Finally, we provide an example to show how the novel approach can aidhierarchical treatment systems. This is essential for merging the healthcare capabilitiesof the general public and optimizing the medical care system's service performance.展开更多
文摘In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.
基金extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through General Research Project under Grant No.(R.G.P.2/48/43).
文摘The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes.It works well for crisp weights,but the problem arises when weights are vague and uncertain.Let us take an example of computer networks,where the chosen path might no longer be appropriate due to rapid changes in network conditions.The optimal path from among all possible courses is chosen in computer networks based on a variety of parameters.In this paper,we design a new variant of the Floyd-Warshall algorithm that identifies an All-Pair Shortest Path(APSP)in an uncertain situation of a network.In the proposed methodology,multiple criteria and theirmutual associationmay involve the selection of any suitable path between any two node points,and the values of these criteria may change due to an uncertain environment.We use trapezoidal picture fuzzy addition,score,and accuracy functions to find APSP.We compute the time complexity of this algorithm and contrast it with the traditional Floyd-Warshall algorithm and fuzzy Floyd-Warshall algorithm.
文摘In Pakistan, a hierarchical healthcare system is an efficient way of addressing the issueof limited and insufficient healthcare services. Identifying the various degrees of diseasebased on the doctor's diagnosis is an important step in developing the hierarchical healthcaretreatment structure. This research presents a framework for dealing with the issueof diagnosis values presented as "picture fuzzy numbers (PFNs)". Specifically, the goal ofthis study is to establish some innovative operational laws and "aggregation operators"(AOs) in a picture fuzzy environment. In this regard, we proposed some new neutral orfair operational laws that incorporate the concept of proportional distribution in orderto achieve a neutral or fair remedy to the positive, neutral and negative aspects ofPFNs. Based on the developed operational laws, we proposed the "picture fuzzy fairlyweighted average operator" and the "picture fuzzy fairly ordered weighted averagingoperator". Compared to previous techniques, the proposed AOs provide more generalizedand reliable. Furthermore, using proposed AOs with multiple decision-makers andpartial weight information under PFNs, a "multi-criteria decision-making" algorithmis developed. Finally, we provide an example to show how the novel approach can aidhierarchical treatment systems. This is essential for merging the healthcare capabilitiesof the general public and optimizing the medical care system's service performance.
