Research About Decision-making Methods Based On Interval Number Information

As an important part of modern decision-making theory, theory and methods of multi-attribute decision-making have been widely applied to many social areas, such as economics, engineering and management, and so on. In real world, because of complexity and inaccuracy of objective reality, uncertainty of human mind, classical accurately mathematical tool cannot play to its advantages. Interval number theory, as an important branch of uncertain theory, has a good theoretical value and real meaning. For decades, decision-making methods about interval number information have attracted widely attention by many scholars at home and abroad, therefore, under the information environment of interval number, some aggregating operators have been discussed and apply them into decision-making problems. The mainly works are as follows:1. The development processes of interval number and its decision-making methods have been introduced, and then the paper discusses the domestic and foreign current research situation, and presents the general framework of the overall article.2. The processes that interval number turns into positive interval number and normal distribution interval number have been introduced, and their operations and properties have also been proved. Classical WA and WG operators have been extended into interval number information environment, and propose IVWA operator and IVWG operator. By constructing order relationship in interval number, extend OWA operator and OWG operator to IVOWA operator and IVOWG operator.3. Introduce center factor and deviation factor in interval number, we measure the discrimination information between different interval number by defining the concept of cross-entropy, and discuss their relevant properties. For the multi-attribute decision-making problem of interval number, the paper consider three situations of attribute weight, which are attribute weight is completely known, partly known and unknown completely, construct non-linear programming model combined with cross-entropy, and give the calculate formulas of attribute weight under different situations, propose three different decision-making algorithms. At the same time, the article discuss the method which convert the situation of attribute weight is unknown completely into partly known, and give corresponding decision-making algorithm to improve scientificity of decision-making. By practical examples, the feasibility and reasonability of all decision-making algorithms has been shown.4. Define the contain degree and possibility degree in normal distribution interval number, and prove their relevant properties. For multi-attribute decision-making problem of normal distribution interval number, according to the situation of attribute weight information, the article divides attribute weight into three situations respectively:completely known, partly known and unknown completely, and constructs non-linear programming models combined with contain degree and possibility degree, and give the calculate formulas of attribute weight, propose three different decision-making algorithms under different situations. Finally, the paper applies all kinds of decision-making algorithms into practical examples and verifies their effectiveness.