Multiobjective Satisfactory Design by Simultaneous Equations with Several Unknowns.

On equations with sets as unknowns.

We shall present here a number of results in set theory concerning the decomposition of a set E in various ways as sum (union) of its subsets . These results have connection with problems on countably additive measure functions in abstract sets, but they may also bear on the problems of the axiomatics of set theory and generally on foundations of set theory itself . Some of these results employ...

A satisfactory strategy of multiobjective two person matrix games with fuzzy payoffs

The multiobjective two person matrix game problem with fuzzy payoffs is considered in this paper. It is assumed that fuzzy payoffs are triangular fuzzy numbers. The problem is converted to several multiobjective matrix game problems with interval payoffs by using the $alpha$-cuts of fuzzy payoffs. By solving these problems some $alpha$-Pareto optimal strategies with some interval outcomes are o...

NC Solving of a System of Linear Ordinary Differential Equations in Several Unknowns

Multiobjective controller design by solving a multiobjective matrix inequality problem

In this study, linear matrix inequality (LMI) approaches and multiobjective (MO) evolutionary algorithms are integrated to design controllers. An MO matrix inequality problem (MOMIP) is first defined. A hybrid MO differential evolution (HMODE) algorithm is then developed to solve the MOMIP. The hybrid algorithm combines deterministic and stochastic searching schemes. In the solving process, the...

Multiobjective design of sewer networks

The sewer layout in flat areas significantly influences the construction and operational costs as well as reliability of the network performance. To find an optimum design of sewer networks for flat areas, this study presents a multi-objective optimization problem with the objective functions of 1- the cost and 2- the reliability. The reliability criterion is defined as the effect of a clogging...