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1
Content available remote Decision-theoretic Rough Sets-based Three-way Approximations of Interval-valued Fuzzy Sets
Lang G., Yang T.
Fundamenta Informaticae
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2015
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Vol. 142, nr 1-4
117--143
EN
In practical situations, interval-valued fuzzy sets are of interest because fuzzy sets of this kind are frequently encountered. In this paper, motivated by the needs for solving imprecise problems, we generalize the concept of shadowed sets for understanding interval-valued fuzzy sets and provide a solution to compute a pair of thresholds by searching for a balance of uncertainty. Then we present three-way approximations of interval-valued fuzzy sets and a formulation for calculating the pair of thresholds using single-valued loss functions. We also compute three-way approximations of interval-valued fuzzy sets using interval-valued loss functions. Afterwards, we employ several examples to illustrate that how to take an action for an object with an interval-valued membership grade using an interval-valued loss function.
2
Content available remote A Multifaceted Analysis of Probabilistic Three-way Decisions
Deng X., Yao Y.
Fundamenta Informaticae
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2014
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Vol. 132, nr 3
291--313
EN
In situations where available information or evidence is incomplete or uncertain, probabilistic two-way decisions/classifications with a single threshold on probabilities for making either an acceptance or a rejection decision may be inappropriate. With the introduction of a third non-commitment option, probabilistic three-way decisions use a pair of thresholds and provide an effective and practical decision-making strategy. This paper presents a multifaceted analysis of probabilistic three-way decisions. By identifying an inadequacy of two-way decisions with respect to controlling the levels of various decision errors, we examine the motivations and advantages of three-way decisions. We present a general framework for computing the required thresholds of a three-way decision model as an optimization problem. We investigate two special cases, one is a decision-theoretic rough set model and the other is an information-theoretic rough set model. Finally, we propose a heuristic algorithm for finding the required thresholds.
3
Content available remote Non-Monotonic Attribute Reduction in Decision-Theoretic Rough Sets
Li H., Zhou X., Zhao J., Liu D.
Fundamenta Informaticae
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2013
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Vol. 126, nr 4
415--432
EN
For most attribute reduction in Pawlak rough set model (PRS), monotonicity is a basic property for the quantitative measure of an attribute set. Based on the monotonicity, a series of attribute reductions in Pawlak rough set model such as positive-region-preserved reductions and condition entropy-preserved reductions are defined and the corresponding heuristic algorithms are proposed in previous rough sets research. However, some quantitative measures of attribute set may be non-monotonic in probabilistic rough set model such as decision-theoretic rough set (DTRS), and the non-monotonic definition of the attribute reduction should be reinvestigated and the heuristic algorithm should be reconsidered. In this paper, the monotonicity of the positive region in PRS and DTRS are comparatively discussed. Theoretic analysis shows that the positive region in DTRS model may be expanded with the decrease of the attributes, which is essentially different from that in PRS model. Hereby, a new non-monotonic attribute reduction is presented for the DTRS model in this paper, and a heuristic algorithm for searching the newly defined attribute reduction is proposed, in which the positive region is allowed to be expanded instead of remaining unchanged in the process of attribute reduction. Experimental analysis is included to validate the theoretic analysis and quantify the effectiveness of the proposed attribute reduction algorithm.
4
Content available remote Modelling Multi-agent Three-way Decisions with Decision-theoretic Rough Sets
Yang X., Yao J. T.
Fundamenta Informaticae
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2012
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Vol. 115, nr 2/3
157-171
EN
The decision-theoretic rough set (DTRS) model considers costs associated with actions of classifying an equivalence class into a particular region. With DTRS, one may make informative decisions in the form of three-way decisions. Current research mainly focuses on single agent DTRS which is too complex for making a decision when multiple agents are involved. We propose a multiagent DTRS model and express it in the form of three-way decisions. The new model seeks for synthesized or consensus decisions when there aremultiple decision preferences and criteria adopted by different agents. Various multi-agent DTRS models can be derived according to the conservative, aggressive and majority viewpoints based on the positive, negative and boundary regions made by each agent. These multi-agent decision regions are expressed by figures in the form of three-way decisions.
5
Content available remote A Multiple-category Classification Approach with Decision-theoretic Rough Sets
Liu D., Li T., Li H.
Fundamenta Informaticae
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2012
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Vol. 115, nr 2/3
173-188
EN
By considering the levels of tolerance for errors and the cost of actions in real decision procedure, a new two-stage approach is proposed to solve the multiple-category classification problems with Decision-Theoretic Rough Sets (DTRS). The first stage is to change an m-category classification problem (m > 2) into an m two-category classification problem, and form three types of decision regions: positive region, boundary region and negative region with different states and actions by using DTRS. The positive region makes a decision of acceptance, the negative region makes a decision of rejection, and the boundary region makes a decision of abstaining. The second stage is to choose the best candidate classification in the positive region by using the minimum probability error criterion with Bayesian discriminant analysis approach. A case study of medical diagnosis demonstrates the proposed method.
6
Content available remote Two Semantic Issues in a Probabilistic Rough Set Model
Yao Y.
Fundamenta Informaticae
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2011
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Vol. 108, nr 3/4
249-265
EN
Probabilistic rough set models are quantitative generalizations of the classical and qualitative Pawlak model by considering degrees of overlap between equivalence classes and a set to be approximated. The extensive studies, however, have not sufficiently addressed some semantic issues in a probabilistic rough set model. This paper examines two fundamental semantics-related questions. One is the interpretation and determination of the required parameters, i.e., thresholds on probabilities, for defining the probabilistic lower and upper approximations. The other is the interpretation of rules derived from the probabilistic positive, boundary and negative regions. We show that the two questions can be answered within the framework of a decision-theoretic rough set model. Parameters for defining probabilistic rough sets are interpreted and determined in terms of loss functions based on the well established Bayesian decision procedure. Rules constructed from the three regions are associated with different actions and decisions, which immediately leads to the notion of three-way decision rules. A positive rule makes a decision of acceptance, a negative rule makes a decision of rejection, and a boundary rules makes a decision of deferment. The three-way decisions are, again, interpreted based on the loss functions
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