Abstract
In crisp environment the notions of order of group and cyclic group are well known due to many applications. In this paper, we introduce order of the soft groups, power of the soft sets, power of the soft groups, and cyclic soft group on a group. We also investigate the relationship between cyclic soft groups and classical groups.
Highlights
Most of our real life problems in economics, engineering, environment, social science, and medical science involve imprecise data that contain uncertainties
Maji et al [5] give an application of soft set theory in a decision making problem by using the rough sets and they conducted a theoretical study on soft sets in a detailed way [6]
Chen et al [7] proposed a reasonable definition of parameterizations reduction of soft sets and compared them with the concept of attributes reduction in rough set theory
Summary
Most of our real life problems in economics, engineering, environment, social science, and medical science involve imprecise data that contain uncertainties. There are some well-known theories (probability, fuzzy sets [1], vague sets [2], rough sets [3], etc.) which can be considered as mathematical tools for dealing with uncertainties. The theory of soft sets, proposed by Moldtsov [4], is an extension of set theory for the study of intelligent systems characterized by insufficient and incomplete information. His pioneer paper has undergone tremendous growth and applications in the last few years. Aygunoglu and Aygun [17] introduced the concept of fuzzy soft group and, in the meantime, they studied its properties and structural characteristics. We conclude the study with suggestions for future work
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