Abstract
The interval concept lattice theory, a new method of mining objects based on interval parameters, can more accurately deal with uncertain information than the classical concept lattice theory. The optimization of interval parameters has been a problem that is not well solved. From the perspective of three-way decision space, we first combine the theories of interval concept lattice and three-way decision and then put forward interval three-way decision space theory; second, in the interval three-way decision space, the positive region, negative region, and boundary region are divided by extension of interval three-way decision concept; further, the decision loss function and three-way decision rules are extracted. Through adjusting interval parameters of the lattice structure, we could find that when parameter α is roughly 0.6, more credible decision rules will be mined and decision-making becomes more clear than that under the condition α is less than 0.6; finally, we verify the model by a “Green Products Recommendation” example.
Highlights
E last case to motivate our research is that Wei et al [19] give the three-way concept lattices theory and indicate that they can supply much more information than classical concept lattices since they contain the positive information and negative information between objects and attributes simultaneously
Motivated by the commonality of the above two theories, we define the interval three-way decision space according to the interval concept decision loss function that depends on interval parameters α and β
Decision concepts in the interval three-way decision space will change with respect to the interval parameters, which can affect users’ decision-making and benefit interval parameter optimization
Summary
For a pair of thresholds [α, β] with 0 ≤ α < β ≤ 1, the [α, β]-probabilistic lower and upper approximations of X are expressed as follows: apr (X). According to the lower and upper approximation, the following probabilistic positive, negative, and boundary region can be given as follows: U. where (apr(α,β)(X))c U − apr(α,β)(X). E false acceptance rates in different regions are as follows:. The false acceptance rate in the positive region is as follows: IAEPOS(α,β)(X), X. Rejecting all entities of [x] will lead to an error. The false rejection rate in the negative region is as follows: IRENEG(α,β)(X),. (iii) When the confidence coefficient is too low to warrant an acceptance, at the same time, and too high to warrant a rejection, we choose a third option, noncommitment. Due to allowing certain levels of error, a probabilistic rough set model may have a smaller boundary region than a classical rough set model. e sizes of the three regions are controlled by the pair of thresholds [α, β]
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