Appropriate math for evaluating coverage/fit across multiple weighted many-to-many relationships
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Generally speaking, my current problem involves assigning people to jobs. Each job entails a set of tasks, each task requires some array of skills, and each skill is possessed by some subset of people. These would all be many-to-many relationships in database parlance; for example, most tasks require multiple skills, and a single skill can be required by multiple tasks. In addition, these are also weighted relationships; for example, a person can possess a particular skill to a certain degree (represented as a percentage). I currently have a 2-D matrix for each of these three relationships (people to skills, skills to tasks, and tasks to jobs) with percentages for cell values. What I'm ultimately looking for is a measure to represent the degree of fit between people and jobs, or in other words the amount of coverage between their respective skills tasks.
Someone referred me to fuzzy set theory, and although I'm still not sure if it applies 100% I definitely see some parallels to what I'm trying to do. Considering that there are three many-to-many relationships here, I suppose I would need to do multiple operations (i.e. first compare a person's skills to the skills required by a task, and then compare their resulting suitability for that task to the importance of that task to a specific job), but since I don't have any real basis for the order in which I conduct these operations (I could equally first calculate every skill's value to each job, and then compare that with the degree to which different people possess it) it would seem like symmetric difference is a better bet than set difference (since the latter is not associative but the former is).
My knowledge of formal statistics is quite limited, so I'm not aware if there is a simpler solution here. Has anyone ever done a coverage/fit analysis before with similarly complex mappings, i.e. third-degree (?) many-to-many relationships, and if so how did you approach this problem? Is fuzzy symmetric difference applicable to this context?
dataset data-analysis weighted-data fuzzy-logic
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mcmanmcman
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Generally speaking, my current problem involves assigning people to jobs. Each job entails a set of tasks, each task requires some array of skills, and each skill is possessed by some subset of people. These would all be many-to-many relationships in database parlance; for example, most tasks require multiple skills, and a single skill can be required by multiple tasks. In addition, these are also weighted relationships; for example, a person can possess a particular skill to a certain degree (represented as a percentage). I currently have a 2-D matrix for each of these three relationships (people to skills, skills to tasks, and tasks to jobs) with percentages for cell values. What I'm ultimately looking for is a measure to represent the degree of fit between people and jobs, or in other words the amount of coverage between their respective skills tasks.
Someone referred me to fuzzy set theory, and although I'm still not sure if it applies 100% I definitely see some parallels to what I'm trying to do. Considering that there are three many-to-many relationships here, I suppose I would need to do multiple operations (i.e. first compare a person's skills to the skills required by a task, and then compare their resulting suitability for that task to the importance of that task to a specific job), but since I don't have any real basis for the order in which I conduct these operations (I could equally first calculate every skill's value to each job, and then compare that with the degree to which different people possess it) it would seem like symmetric difference is a better bet than set difference (since the latter is not associative but the former is).
My knowledge of formal statistics is quite limited, so I'm not aware if there is a simpler solution here. Has anyone ever done a coverage/fit analysis before with similarly complex mappings, i.e. third-degree (?) many-to-many relationships, and if so how did you approach this problem? Is fuzzy symmetric difference applicable to this context?
dataset data-analysis weighted-data fuzzy-logic
asked 5 mins ago
mcmanmcman
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Generally speaking, my current problem involves assigning people to jobs. Each job entails a set of tasks, each task requires some array of skills, and each skill is possessed by some subset of people. These would all be many-to-many relationships in database parlance; for example, most tasks require multiple skills, and a single skill can be required by multiple tasks. In addition, these are also weighted relationships; for example, a person can possess a particular skill to a certain degree (represented as a percentage). I currently have a 2-D matrix for each of these three relationships (people to skills, skills to tasks, and tasks to jobs) with percentages for cell values. What I'm ultimately looking for is a measure to represent the degree of fit between people and jobs, or in other words the amount of coverage between their respective skills tasks.
Someone referred me to fuzzy set theory, and although I'm still not sure if it applies 100% I definitely see some parallels to what I'm trying to do. Considering that there are three many-to-many relationships here, I suppose I would need to do multiple operations (i.e. first compare a person's skills to the skills required by a task, and then compare their resulting suitability for that task to the importance of that task to a specific job), but since I don't have any real basis for the order in which I conduct these operations (I could equally first calculate every skill's value to each job, and then compare that with the degree to which different people possess it) it would seem like symmetric difference is a better bet than set difference (since the latter is not associative but the former is).
My knowledge of formal statistics is quite limited, so I'm not aware if there is a simpler solution here. Has anyone ever done a coverage/fit analysis before with similarly complex mappings, i.e. third-degree (?) many-to-many relationships, and if so how did you approach this problem? Is fuzzy symmetric difference applicable to this context?
dataset data-analysis weighted-data fuzzy-logic
asked 5 mins ago
mcmanmcman
1
New contributor
mcman is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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Generally speaking, my current problem involves assigning people to jobs. Each job entails a set of tasks, each task requires some array of skills, and each skill is possessed by some subset of people. These would all be many-to-many relationships in database parlance; for example, most tasks require multiple skills, and a single skill can be required by multiple tasks. In addition, these are also weighted relationships; for example, a person can possess a particular skill to a certain degree (represented as a percentage). I currently have a 2-D matrix for each of these three relationships (people to skills, skills to tasks, and tasks to jobs) with percentages for cell values. What I'm ultimately looking for is a measure to represent the degree of fit between people and jobs, or in other words the amount of coverage between their respective skills tasks.
Someone referred me to fuzzy set theory, and although I'm still not sure if it applies 100% I definitely see some parallels to what I'm trying to do. Considering that there are three many-to-many relationships here, I suppose I would need to do multiple operations (i.e. first compare a person's skills to the skills required by a task, and then compare their resulting suitability for that task to the importance of that task to a specific job), but since I don't have any real basis for the order in which I conduct these operations (I could equally first calculate every skill's value to each job, and then compare that with the degree to which different people possess it) it would seem like symmetric difference is a better bet than set difference (since the latter is not associative but the former is).
My knowledge of formal statistics is quite limited, so I'm not aware if there is a simpler solution here. Has anyone ever done a coverage/fit analysis before with similarly complex mappings, i.e. third-degree (?) many-to-many relationships, and if so how did you approach this problem? Is fuzzy symmetric difference applicable to this context?
dataset data-analysis weighted-data fuzzy-logic
dataset data-analysis weighted-data fuzzy-logic
asked 5 mins ago
mcmanmcman
1
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asked 5 mins ago
mcmanmcman
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asked 5 mins ago
mcmanmcman
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asked 5 mins ago
mcmanmcman
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asked 5 mins ago
mcmanmcman
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mcman is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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