Summary Attribute importance measurement is the core of multi‐attribute decision making. This study aims at resolving the problem of attribute importance computation. Based on the data system and the inclusion degree of sets, we propose a data deletion method based on knowledge reliability. By taking the hidden knowledge in the data system as the carrier, we further discuss the changing rules of knowledge factors in the subsystems and propose an attribute importance measurement method based on the data effect (abbreviated DE‐AIM). Furthermore, we analyze the values and structure features of DE‐AIM through a theoretical proof and an example calculation. Finally, we compare DE‐AIM with other attribute importance measurements by combining with concrete cases and several data sets from UCI. All the results indicate that DE‐AIM not only has good structural features and interpretability but also can reflect different decision preference by changing parameters. The method has wide applications in many fields such as resource management, artificial intelligence, complex system optimization, expert systems, and concurrency computation.

Fuzzy programming approach has wide application in many fields such as project management, multi-attribute decision making, and comprehensive evaluation. Its solving methods have attracted many attentions. In this paper we present a new approach, based on the genetic algorithm, for dealing with a programming problem with fuzzy-valued objective function and constraints. Firstly, we propose the concept of generalized equilibrium value of fuzzy number, and analyze the properties, further give the operation rules; secondly, we establish a generalized equilibrium value-based fuzzy programming method combined with genetic algorithm; finally, we analyze the characteristic of the above mentioned method through a nonlinear fuzzy programming problems.

By using the restricted and complementary relationship of the principle and secondary indexes, providing the description of the compound quantification of the fuzzy number, and analyzing the essential characteristic of fuzzy decision, we propose a kind of fuzzy genetic algorithm based on the principle index (PO-FGA for short) to deal with the fuzzy optimization and programming problems with fuzzy coefficients, fuzzy variables and fuzzy constraints. The concrete solution method is presented in accordance with the strategy of the unconditional penality transformation with conditional constrains. Then consider its convergence by using Markov chain theory and analyze its performance through two examples. All these indicate that this kind of algorithm is of faster speed of convergence, smaller number of iterations, has lower chances of trapping into the state of premature convergence and can be widely used in many problems of optimization.

In view of the slowness and the locality of convergence for Simple Genetic Algorithm (SGA for short), Composite Genetic Algorithm, as an improved genetic algorithm, is proposed based on extreme pre-judgement. The implementation is also given. The convergence and computing efficiency are analyzed from different aspects by the methods of Markov chain and simulation. All the results indicate that the new type of algorithm possess better convergence with the strategy of reserving the optimal individuals and could avoid efficiently the premature phenomenon. So it will be applied to the optimization problems with large-scale and high-accuracy.

Ranking and comparing fuzzy numbers is an important part in many fuzzy optimization problems such as intelligent control and manufacturing system production line scheduling with uncertainty environments. In this paper, based on the level characteristic function and α -average of level cut sets of fuzzy number, we establish the IM α -metric method for measuring fuzzy number as a whole, and introduce the concept of ID α -difference that describes the reliability of IM α -metric value. Further, the basic properties and the separability of IM α -metric and ID α -difference are discussed. Finally, we give a mathematical model to solve fuzzy optimization problems by means of IM α -metric.