Abstract: The author previously proposed an extension of differential evolution. The proposed method extends the processes of DE to handle interval numbers as genotype values so that DE can be applied to interval-valued optimization problems. The interval DE can employ either of two interval models, the lower and upper model or the center and width model, for specifying genotype values. Ability of the interval DE in searching for solutions may depend on the model. In this paper, the author compares the two models to investigate which model contributes better for the interval DE to find better solutions. Application of the interval DE is evolutionary training of interval-valued neural networks. A result of preliminary study indicates that the CW model is better than the LU model: the interval DE with the CW model could evolve better neural networks.
Abstract: We present a method for the selection of students
in interdisciplinary studies based on the hybrid averaging
operator. We assume that the available information given in
the problem is uncertain so it is necessary to use interval
numbers. Therefore, we suggest a new type of hybrid
aggregation called uncertain induced generalized hybrid
averaging (UIGHA) operator. It is an aggregation operator
that considers the weighted average (WA) and the ordered
weighted averaging (OWA) operator in the same formulation.
Therefore, we are able to consider the degree of optimism of
the decision maker and grades of importance in the same
approach. By using interval numbers, we are able to represent
the information considering the best and worst possible results
so the decision maker gets a more complete view of the
decision problem. We develop an illustrative example of the
proposed scheme in the selection of students in
interdisciplinary studies. We see that with the use of the
UIGHA operator we get a more complete representation of the
selection problem. Then, the decision maker is able to
consider a wide range of alternatives depending on his
interests. We also show other potential applications that could
be used by using the UIGHA operator in educational problems
about selection of different types of resources such as
students, professors, etc.
Abstract: By using a new set of arithmetic operations on interval numbers, we discuss some arithmetic properties of interval matrices which intern helps us to compute the powers of interval matrices and to solve the system of interval linear equations.
Abstract: A manufacturing inventory model with shortages with
carrying cost, shortage cost, setup cost and demand quantity as
imprecise numbers, instead of real numbers, namely interval number
is considered here. First, a brief survey of the existing works on
comparing and ranking any two interval numbers on the real line
is presented. A common algorithm for the optimum production
quantity (Economic lot-size) per cycle of a single product (so as
to minimize the total average cost) is developed which works well
on interval number optimization under consideration. Finally, the
designed algorithm is illustrated with numerical example.