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The article presents new types of fuzzy sets, such as the hypersoft set, indeterminate soft set, indeterminate hypersoft set, and tree soft set. Definitions and examples of these sets are provided, as well as practical applications. Other fuzzy extensions of the soft set are also mentioned, and the possibility of investigating and applying new forms of soft sets in combination with fuzzy sets and their extensions is suggested. The author of the article is Florentin Smarandache from the University of New Mexico. The text was published in the Octogon Mathematical Magazine and Journal of Fuzzy Extension and Applications. [Extracted from the article]

Every development activity is always related to human or community aspects. This can also lead to changes in the characteristics of the community. The community's increasing awareness and critical attitude need to be accommodated to avoid the emergence of social conflicts in the future. This research is to find out how the public perception about the impact of development on the environment. Two methods are used, i.e., MDA (Maximum Dependency Attribute) and MSMD (the Multi soft set multivariate distribution function). The MDA is to determine the most influential attribute and the Multi soft set multivariate distribution function (MSMD) is to group the selected data into classes with similar characteristics. This will help the police producer plan the right mediation and take quick activity to make strides in the quality of the social environment. The experiment conducted level of impact based on the clustering results with the greatest number of member clusters is cluster 1 (very low impact) with 32.25 % of total data following cluster 5 (Very High impact) with 24.25 % of total data. The experiment obtains the level of impact based on the clustering results. The greatest number of member clusters is cluster 1 (extremely low impact) with 32.25 % of total data following cluster 5 (Very High impact) with 24.25 % of total data. The scatter area impact is spread at districts 6, 7, 10, 11, the most of very high impact and districts 1,2,3,4,5,8 the lowest impact.

We introduce a new concept of certainty and coverage of a parameter of the soft set and present a new decision making approach for the soft set over the universe using the certainty of a parameter. Also, we point out the drawbacks of the reduct definition by pointing out the delusion of Proposition 14 given by Herawan et al. [20] and provide the revised definition of the reduct of the multi soft set.

Clustering refers to the method grouping the large data into the smaller groups based on the similarity measure. Clustering techniques have been applied on numerical, categorical and mix data. One of the categorical data clustering technique based on the soft set theory is Maximum Attribute Relation (MAR). The MAR technique allows calculating all of pair multi soft set made. However, the computational complexity is still an issue of the technique. To overcome the drawback, the paper proposes the alternative algorithm to decrease the complexity so get the faster response time. In this paper, to get the similar results as MAR without calculating all pair of soft set is proved. The alternative algorithm is implemented in MATLAB Software, and then experimental is run on the 10 benchmark datasets. The results show that the alternative algorithm improves the computational complexity in term of response time up to 36.46%. [ABSTRACT FROM AUTHOR]