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Top1. Introduction
The theory of rough set has been successfully applied to diverse areas, such as pattern recognition, artificial intelligence, machine learning, knowledge acquisition, economy forecast, and data mining (D’eer, Verbiest, Cornelis, & Godo, 2015; Flapan, 2000; Yao & Fu, 2013). Pawlak (2002-2005) rough set model is constructed based on equivalence relations. These relations are studied by many investigators to be used in the complex decision tasks. In multiple criteria decision-making problems, there are preference structures between conditions and decisions (Alharthi & Elsafty, 1998; D’eer, Cornelis, & Yao, 2016). A reduct should be able to preserve the original classification power provided by the whole attribute set (Chan, 1998; Li & Liu, 2002). This power may be interpreted by syntax properties and semantics properties for both positive and boundary rule sets. Instead, we need to consider multiple properties and multiple measures for evaluation.
The classical rough set methods cannot detect the inconsistency related with the preference, such as the price, fuel amount, speed, etc., and these attributes involve preference information, but they are not considered in rough set (Lashin &Medhat, 2005; Pal, Shankar, & Mitra, 2005). Further, rules based on the dominance relation are much more suitable than those based on the indiscernibility relation when they are used to classify new objects (Yao, 2007). Because we may often meet preference information when handling with economic, managing, or financial decision-making problems, the hybrid of rough sets and dominance relation can enlarge the usage of rough set models in economic, management, or financial fields. Greco and other scholars (Creco, Inuiguchi, & Slowinski, 2006; Greco, Matazzo, & Slowinski, 2001) have put forward rough set model and its extended models based on dominance relation by replacing the indiscernibility relation with the dominance relation. Their models can do well with the possible inconsistency that exists in analyzing preference with multiple attributes as well as making decisions related with typical cases.
The granulation structures used by both rough set theory and neighborhood systems and the corresponding approximation structures are studied (Kozae, Elsafty, Swealam, 2012).
Life insurance is characterized by its long period ranging from 15 to 30 years in individual documents, and from one year to 45 years in the collective insurance. Premiums paid in the early years would be technically more than what should be paid despite the fact that the insured persons have paid equal premiums for the duration of insurance (Kilridog & Asuk, 2012). These extra and accumulated sums are collected to be what is called the account reserve which is invested by the best means. The surplus or deficit amount in the formation of this reserve in life insurance is influenced by numerous technical elements related to compensation due for the deaths, rates of investment and productivity and administrative expenses of return and profits to be distributed to policyholders. It is possible after the cessation of the insured to pay premiums, to cancel, modify, determine, reduce the amount or re-effect the recoverable amount of the document to secure a discount after the cancellation or waived, or even by borrowing, contrary to what is the case in the documents of property insurance and responsibility.