There are many researches deals with constructing an efficient solutions for real problem having Multi - objective confronted with each others. In this paper we construct a decision for Multi – objectives based on building a mathematical model formulating a unique objective function by combining the confronted objectives functions. Also we are presented some theories concerning this problem. Areal application problem has been presented to show the efficiency of the performance of our model and the method. Finally we obtained some results by randomly generating some problems.

Multi-document summarization is an optimization problem demanding optimization of more than one objective function simultaneously. The proposed work regards balancing of the two significant objectives: content coverage and diversity when generating summaries from a collection of text documents.

     Any automatic text summarization system has the challenge of producing high quality summary. Despite the existing efforts on designing and evaluating the performance of many text summarization techniques, their formulations lack the introduction of any model that can give an explicit representation of – coverage and diversity – the two contradictory semantics of any summary. In this work, the design of

 Let R be a commutative ring with unity, let M be a left R-module. In this paper we introduce the concept small monoform module as a generalization of monoform module. A module M is called small monoform if for each non zero submodule N of M and for each   f ∈ Hom(N,M), f ≠ 0 implies ker f is small submodule in N. We give the fundamental properties of small monoform modules. Also we present some relationships between small monoform modules and some related modules

Automatic document summarization technology is evolving and may offer a solution to the problem of information overload. Multi-document summarization is an optimization problem demanding optimizing more than one objective function concurrently. The proposed work considers a balance of two significant objectives: content coverage and diversity while generating a summary from a collection of text documents. Despite the large efforts introduced from several researchers for designing and evaluating performance of many text summarization techniques, their formulations lack the introduction of any model that can give an explicit representation of – coverage and diversity – the two contradictory semantics of any summary. The design of gener

      The main problem when dealing with fuzzy data variables is that it cannot be formed by a model that represents the data through the method of Fuzzy Least Squares Estimator (FLSE) which gives false estimates of the invalidity of the method in the case of the existence of the problem of multicollinearity. To overcome this problem, the Fuzzy Bridge Regression Estimator (FBRE) Method was relied upon to estimate a fuzzy linear regression model by triangular fuzzy numbers. Moreover, the detection of the problem of multicollinearity in the fuzzy data can be done by using Variance Inflation Factor when the inputs variable of the model crisp, output variable, and parameters are fuzzed. The results were compared usin