SUMMARY
The aim of this paper is to introduce the notion of soft multi-set topology (SMS-topology) defined on a soft multi-set (SMS). Soft multi-set and soft multi-set topology are fundamental tools in computational intelligence, which have a large number of applications in soft computing, fuzzy modeling and decision-making under uncertainty. The idea of power whole multi-subsets of a SMS is defined to explore various rudimentary properties of SMS-topology. Certain properties of SMS-topology like SMS-basis, MS-subspace, SMS-interior, SMS-closure and boundary of SMS are explored. Furthermore, the multi-criteria decision-making (MCDM) algorithms with aggregation operators based on SMS-topology are established. Algorithm i (i = 1, 2, 3) are developed for the selection of best alternative for biopesticides, for the selection of best textile company, for the award of performance, respectively. Some real life applications of the proposed algorithms in MCDM problems are illustrated by numerical examples. The the reliability and feasibility of proposed MCDM techniques is shown by comparison analysis with some existing techniques.