A Rudimentary Approach to Develop Context for Convexity cum Concavity on Soft Expert Set with Some Generalized Results

Soft set theory is considered as the preeminent tool to tackle the problems involving vagueness by controlling all complexities of optimization theory, fuzzy set theory and interval theory. Some models have been developed to solve problems in decision making and medical diagnosis with one expert by using this theory. This causes a problem with those who use questionnaires in their research. Soft expert set overcomes this problem and facilitates the user to know the opinion of all experts in one model. The concept of convexity plays a key role to deal optimization, pattern recognition-classification and many other related topics in operation research, numerical analysis and other disciplines of mathematical sciences. In this study, a mathematical cum abstract technique is employed to develop basic concept of convex and concave soft expert sets to deal with their important applications. Some classical results on convexity cum concavity are modified under uncertain multi-decisive environment with the support of explicatory proofs.