A new hybrid framework is proposed for optimization of orderable search spaces. It is based on fuzzy-membership of design variable alternatives to the optimal solution. The method has dynamic behavior since the membership values are assigned as any solution candidates arises during the search and they are summed based on their overlaps in the alternatives scope. A trail matrix is also utilized to indirectly share values of the fuzzy memberships further ranked regarding closeness of an individual to the optimal solution both in the objective function and in the design space scope. The method takes benefit of different random, vector-sum and probability-based walks to move new solutions toward the global optimum. Utilizing a generalized cooling procedure, the related thresholds are tuned to choose between different walk types in searching the design space and also a search refinement strategy is developed. Two variants of such a framework is then proposed and compared with each other in addition to some well-known procedures including genetic algorithm and particle swarm optimization. Test results with some treated problems, reveals the superior performance of the proposed algorithm and its special feature in adaptive tuning the diversity index during the search.

The paper presents a novel type of fuzzy sets, called time-Varying fuzzy Sets (VFS). These fuzzy sets are based on the Gaussian membership functions, they are depended on the error and they are characterized by the displacement of the kernels to both right and left side of the universe of dis- course, the two extremes kernels of the universe are fixed for all time. In this work we focus only on the midpoint movement of the universe, all points of supports (kernels) are shifted by the same distance and in the same direction excepted the two extremes points of supports are always fixed for all computation time. To show the effectiveness of this approach we used these VFS to develop a PDC (Parallel Distributed Compensation) fuzzy controller for a nonlinear and certain system in continuous time described by the T-S fuzzy model, the parameters of the functions de ning the midpoint movements are optimized by a PSO (Particle Swarm Optimization) approach.

In this paper, for a complete lattice L, we introduce interval-valued L-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. Some characterization and properties are discussed.

Under the additional assumption that the errors are normally distributed, the Ordinary Least Squares (OLS) method is the maximum likelihood estimator. In this paper, we propose, for a simple regression, an estimation method alternative to the OLS method based on a so-called Gaussian membership function, one that checks the validity of the verbal explanation suggested by the observer. The fuzzy estimation approach demonstrated here is based on a suitable framework for a natural behavior observed in nature. An application based on a group of MENA countries in 2015 is presented to estimate the employment poverty relationship.