Journal
INFORMATION SCIENCES
Volume 382, Issue -, Pages 415-440Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2016.12.012
Keywords
Partially ordered sets; Fuzzy sets; Rough sets; Three-way decision spaces; Three-way decisions
Categories
Funding
- National Natural Science Foundation of China [11571010, 61179038]
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Decision evaluation functions in three-way decision spaces must meet three axioms, the minimum element axiom, the monotonicity axiom and the complement axiom. Maintaining the complement axiom of decision evaluation functions is crucial to three-way decisions to simplify the decision rules based only on the conditional probability and the loss functions. However, some handy functions do not satisfy the complement axiom. This paper introduces the notion of semi-decision evaluation functions not necessarily satisfying the complement axiom but the minimum element axiom and the monotonicity axiom, and presents some transformation methods from semi-decision evaluation functions to decision evaluation functions. Through numerous examples this paper demonstrates the existence of semi-decision evaluation functions and significance of the transformation methods. (C) 2016 Elsevier Inc. All rights reserved.
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