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Generalized operations in soft set theory via relaxed conditions on parameters

Abbas Mujahid (Department of Mathematics, Government College University, Lahore, Pakistan + Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia)
Ali Muhammad Irfan (Islamabad Model College for Girls, Islamabad, Pakistan)
Romaguera Salvador (Instituto Universitario de Matemática Pura y Aplicada, Universitat, Politècnica de València, Valencia, Spain)

Soft set theory has been evolved as a very useful mathematical tool to handle uncertainty and ambiguity associated with the real world data based structures. Parameters with certain conditions have been used to classify the data with the help of suitable functions. The aim of this paper is to relax conditions on parameters which lead us to propose some new concepts that consequently generalize existing comparable notions. We introduce the concepts of generalized finite soft equality (gf-soft equality), generalized finite soft union (gf-soft union) and generalized finite soft intersection (gf-soft intersection) of two soft sets. We prove results involving operations introduced herein. Moreover, with the help of examples, it is shown that these operations are proper generalizations of existing comparable operations.

Keywords: soft set, gf-soft subset, gf-soft equality, gf-soft union, gf-soft intersection