Roughness and Fuzziness Associated with Soft Multi-Sets and their Application to MADM

Abstract

In this paper, we tried to hybrid soft sets with multisets. We define some basic properties of soft multiset and present some important results. We define some binary relations, equivalence relations and an indiscernibility relation on soft multiset with examples. The concept of an approximation space associated with each parameter in a soft multiset is discussed and an approximation space associated with the soft multiset is defined. We introduce the novel concepts of roughness and fuzziness associated with soft multiset. We use soft multiset in multi-valued information system. Furthermore, we present an algorithm to cope with uncertainties in multi-attribute decision making (MADM) problems by utilizing soft multisets and related concepts. The efficiency of the algorithm is verified by a case study to find the optimal choice of the real-world problems having uncertainties.

Keywords

• Soft multi-set
• roughness and fuzziness
• multiu-valued information systems
• MADM

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