On IVF Approximating Spaces
نویسندگان
چکیده
Rough set theory was proposed by Pawlak [1] as a mathematical tool to handle imprecision and uncertainty in data analysis. It has been successfully applied tomachine learning, intelligent systems, inductive reasoning, pattern recognition, mereology, image processing, signal analysis, knowledge discovery, decision analysis, expert systems, and many other fields [2–5]. The basic structure of rough set theory is an approximation space. Based on it, lower and upper approximations can be induced. Using these approximations, knowledge hidden in information systems may be revealed and expressed in the form of decision rules (see [2]). As a generalization of Zadeh’s fuzzy set, interval-valued fuzzy (IVF, for short) sets were introduced byGorzałczany [6] and Türksen [7]. Mondal and Samanta [8] defined topology of IVF sets and studied their properties. By replacing crisp relations with IVF relations, Sun et al. [9] introduced IVF rough sets based on an IVF approximation space, defined IVF information systems, and discussed their attribute reduction. Gong et al. [10] presented IVF rough sets based on approximation spaces and studied the knowledge discovery in IVF information systems. Topological structure is an important base for knowledge extraction and processing. Therefore, an interesting and natural research topic in rough set theory is to study the relationship between rough sets and topologies. The purpose of this paper is to investigate IVF approximating space, that is, a particular type of IVF topological spaces where the given IVF topology coincides with the IVF topology induced by some reflexive IVF relation.
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ورودعنوان ژورنال:
- J. Applied Mathematics
دوره 2013 شماره
صفحات -
تاریخ انتشار 2013