On generalized soft equality and soft Lattice structure

Abstract

Abstract. Molodtsov introduced soft sets as a mathematical tool to handle uncertainty associated with real world data based problems. In this paper we propose some new concepts which generalize existing comparable notions. We introduce the concept of generalized soft equality ( denoted as −soft equality ) of two soft sets and prove that the so called lower and upper soft equality of two soft sets imply −soft equality but the converse does not hold. Moreover we give tolerance or dependence relation on the collection of soft sets and soft lattice structures. Examples are provided to illustrate the concepts and results obtained herein.

Generalized operations in soft set theory via relaxed conditions on parameters

“…Employing these notions, they proved results given in [2]. Recently [1], we have generalized some of the above concepts by means of the notions of −soft subset and of −soft equality. One of the advantages of soft set theory is that it provides enough parameters to handle fuzziness in the data.…”

“…In [1] we presented the notions of −null soft set, −soft subset and −soft equality of two soft sets by relaxing the conditions on the underlying parameter subsets of E. Consequently, we generalized already known comparable notions (for example, Definitions 2.2, 2.3, and 2.7 above).…”

“…It was also proved in [1] that lower and upper soft equalities (≈ s and ≈ s ) of two soft sets implies the −soft equality , but −soft equality implies neither lower soft equality nor upper soft equality.…”

A categorical approach to soft S-acts

“…Soft semigroups were touched in [6] and then extensively studied in [10] by means of soft relations. Soft sets were applied to soft ordered semigroups by Jun et al [11] and a lattice structure on soft sets was considered in [1]. Recently on this area some new papers appeared, such as [9,13].…”

A soft version of the Knaster–Tarski fixed point theorem with applications

“…Maji et al [14] introduced some basic algebraic operations on soft sets. Abbas et al [3] proposed tolerance or dependence relation on the collection of soft sets and soft lattice structure. The concept of soft set relations as a soft subset of the Cartesian product of soft sets was introduced by Babitha and Sunil [4].…”