Abstract
Three-way decision (3WD) provides a new perspective for solving practical decision-making problems, which is in line with human's cognitive pattern. A covering information system (CIS) is an information system (IS) that consists of multiple coverings in the universe. A CIS with decision attributes which is seen as a covering decision information system (CDIS). This paper proposes three-way group decisions in a CDIS, as well as gives its application on the problem of position competition. First of all, the neighbourhood of every point in a CDIS is defined, and corresponding similarity class of this point is also obtained. Then, because of the uncertainty of risks, loss functions are acquired through group decision-making by means of interval numbers. Next, a method of three-way group decisions in a CDIS is presented. Eventually, the position competition is presented as an example to support our proposed decision-making method.
Highlights
Three-way decision (3WD), proposed by Yao [44], is an extended of decision rough sets
On the basis of the idea of DECISION-THEORETIC ROUGH SETS (DTRSs), the thresholds α and β are obtained by means of loss functions and these equivalence classes
They can separate the universe into three domains-disjoint namely 3WD, it endues a good semantic interpretation of rough sets: the rule generated by the positive region indicates the acceptance of something; the rule generated by the negative region indicates the rejection of something; the rule generated by the boundary region indicates deferment decision which means that something cannot be accepted or rejected from
Summary
Three-way decision (3WD), proposed by Yao [44], is an extended of decision rough sets. X. Xie et al.: Three-Way Group Decision in a CDIS uncertainty measures; Yang and Yao [49] gave a multi-agent decision model by using 3WD’s idea; Yu et al [48] considered various loss functionson based on DTRS model, and proposed a cost evaluation method of clustering pattern and a clustering validity index; Herbert and Yao [6] combined the loss function of DTRS with the game theory of classification measurement, so as to optimize the size of each decision domain; Agbodah [1] studied the loss function evaluated based on multiple experts of 3WDs with DTRSs; Liang and Liu [11]–[13], [20] took into account uncertainty of loss functions, they drew randomness, interval, fuzziness, and triangular fuzzy number into DTRSs, and developed uncertainty 3WD models, so widened range of loss value; Liu et al [14], [17], [23] put forward different DTRSs on uncertain environments; there are many scholars researching 3WD from other perspectives.
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