Rough set theory has been extensively discussed in machine learning and pattern recognition. It provides us another important theoretical tool for feature selection. In this paper, we construct a novel rough set model for feature subset selection. First, we define the fuzzy decision of a sample by using the concept of fuzzy neighborhood. A parameterized fuzzy relation is introduced to character...

The notion of fuzzy is context dependent, so for each context very often there is a fuzzy theory. Present papers use the notion of neighborhood systems to unify them. A neighborhood system is an association that assigns to each datum a list of data (a neighborhood). Rough sets and topological spaces are special cases. A “real world” fuzzy set should allow small amount of perturbation, so it sho...

In this paper, we introduce generalized connectivity in L-fuzzy topological spaces by à Lukasiewicz logic and prove K. Fan’s theorem.

One of the methods for solving definite integrals is modified trapezoid method, which is obtained by using Hermitian interpolation (see e.g. [12]). In this article, we have used modified trapezoid quadrature method and Generalized differential to solve the Fredholm fuzzy integral equations of the second kind. This method leads to solve fuzzy linear system. Finally the proposed method is illustr...

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Syst Appl 36:6833–6842, 2009) is incorrect. The main aim of this paper is to propose a new approac...

This paper describes a fault tree technique based on generalized fuzzy numbers to a possibility distribution of reliability indices for power systems. Due to uncertainty in the collected data, all the failure probabilities are represented by generalized trapezoidal fuzzy number. In this paper, the fault-tree incorporated with the generalized trapezoidal fuzzy number and minimal cut sets approac...

Generalized predictive control with flexible constraints is investigated. To apply fuzzy technique, the flexible parts in the inequality constraints are fuzzified as fuzzy constraints. The optimization problem of the generalized predictive control with flexible inequality constraints is converted into two sub-problems to get the lower and upper bound of the objective values, and then the object...

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. Cheng (Cheng, C. H. (1998). A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets and Systems, 95, 307–317) pointed out that the proof of the statement ‘‘Ranking of generalized fuzzy numbers does not depe...