LCS & GBML Central

Decision-making is the process of finding the best option among the feasible alternatives. In classical multiple criteria
decision-making (MCDM) methods, the ratings and the weights of the criteria are known precisely. However, if decision makers
cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy
set theory can provide a more accurate modeling. In this paper, the interval-valued fuzzy ELECTRE method is presented aiming
at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy set concepts. For the purpose
of proving the validity of the proposed model, we present a numerical example and build a practical maintenance strategy selection
problem.

Having in mind the idea that the computational effort and knowledge gained while solving a problem’s instance should be used
to solve other ones, we present a new strategy that allows to take advantage of both aspects. The strategy is based on a set
of operators and a basic learning process that is fed up with the information obtained while solving several instances. The
output of the learning process is an adjustment of the operators. The instances can be managed sequentially or simultaneously
by the strategy, thus varying the information available for the learning process. The method has been tested on different
SAT instance classes and the results confirm that (a) the usefulness of the learning process and (b) that embedding problem
specific algorithms into our strategy, instances can be solved faster than applying these algorithms instance by instance.

In general, for multi-criteria group decision making problem, there exist inter-dependent or interactive phenomena among criteria
or preference of experts, so that it is not suitable for us to aggregate them by conventional aggregation operators based
on additive measures. In this paper, based on fuzzy measures a generalized intuitionistic fuzzy geometric aggregation operator
is investigated for multiple criteria group decision making. First, some operational laws on intuitionistic fuzzy values are
introduced. Then, a generalized intuitionistic fuzzy ordered geometric averaging (GIFOGA) operator is proposed. Moreover,
some of its properties are given in detail. It is shown that GIFOGA operator can be represented by special t-norms and t-conorms
and is a generalization of intuitionistic fuzzy ordered weighted geometric averaging operator. Further, an approach to multiple
criteria group decision making with intuitionistic fuzzy information is developed where what criteria and preference of experts
often have inter-dependent or interactive phenomena among criteria or preference of experts is taken into account. Finally,
a practical example is provided to illustrate the developed approaches.

Nonlinear optimization algorithms could be divided into local exploitation methods such as Nelder–Mead (NM) algorithm and
global exploration ones, such as differential evolution (DE). The former searches fast yet could be easily trapped by local
optimum, whereas the latter possesses better convergence quality. This paper proposes hybrid differential evolution and NM
algorithm with re-optimization, called as DE-NMR. At first a modified NM, called NMR is presented. It re-optimizes from the
optimum point at the first time and thus being able to jump out of local optimum, exhibits better properties than NM. Then,
NMR is combined with DE. To deal with equal constraints, adaptive penalty function method is adopted in DE-NMR, which relaxes
equal constraints into unequal constrained functions with an adaptive relaxation parameter that varies with iteration. Benchmark
optimization problems as well as engineering design problems are used to experiment the performance of DE-NMR, with the number
of function evaluation times being employed as the main index of measuring convergence speed, and objective function values
as the main index of optimum’s quality. Non-parametric tests are employed in comparing results with other global optimization
algorithms. Results illustrate the fast convergence speed of DE-NMR.