p-SC invariance approximation of fuzzy numbers

In this paper, the aim is to find the nearest trapezoidal fuzzy numberto a given fuzzy number which preserves the convex combinationof support and core intervals of that fuzzy number. This allows the decisionmaker to select the preferred approximation of a fuzzy numberfrom a class of trapezoidal approximations.Nowadays, the fuzzy concepts are widely used in many real-world engineeringapplications, such as population models, control chaotic systems, economicsand finance, artificial intelligence, computer science, expert systems, managementscience, operations research, pattern recognition, robotics and others.Because of the existence of fuzzy parameters, computational complexity isthe cost of fuzzy system and this matter has captured the attention of researchersfor introducing methods and decreasing this cost. In general, mostof the fuzzy-based algorithms use a defuzzification process that maps a fuzzyparameter into a crisp one. Obviously, in most cases, too much importantinformation is lost by converting fuzzy sets into a set of real numbers. Itseems that we should accept some criteria and apply a framework for constructinga defuzzyfication process. Van Leekwijck et al. in [21] presenteda set of criteria for defuzzification strategies and classified the most widelyused defuzzification techniques into different groups and they examined theprototypes of each group with respect to the defuzzification criteria.