Incomplete Dominance-Based Intuitionistic Fuzzy Rough Sets and Their Application in Estimation of Inflation Rates in the Least Developed Countries

Abstract

Although the concepts of imprecision are captured by both rough sets and intuitionistic fuzzy sets, investigations combining these two ideas and their applications in incompletely ordered information systems are scarce. The semantics of many kinds of missing information still lacks consensus on a global level. Rule extraction is also an important task in a sort of decision system in which condition attributes are treated as intuitionistic fuzzy values and decision attributes are crisp ones. The main goal of this paper is to address semantic issues related to incomplete information. This paper contributes to the following aspects: First, four types of incomplete information are classified (i.e., 'do-not-care value', 'partially-known value', 'class-specific value' and 'non-applicable value'), and then a complete information system is introduced using novel semantics, followed by a ranking approach to create each object's neighborhood using intuitionistic fuzzy values for condition attributes. Further, a dominance-based intuitionistic fuzzy decision table is proposed. Second, the lower and upper approximation sets of an object and crisp classes validated by decision attributes are determined by comparing their relationships. Third, the rule extraction approach is developed using the discernibility matrix and discernibility function to collect knowledge from existing dominance intuitionistic fuzzy decision tables. Finally, the provided approach is used for the estimation of inflation rates in LDCs with inadequate data.