The purpose of this work is to present a new theory namely fuzzy parameterized dual hesitant fuzzy soft sets (FPDHFSSs). This theory is an extension of the existing dual hesitant fuzzy soft set whereby the set of parameters have been assigned with respective weightage accordingly. We also introduced the basic operation functions for instance intersection, union, addition and product operations of FPDHFSSs. Then, we proposed the concept of score function of FPDHFSSs of which these scores function were determined based on average mean, geometry mean and fractional score. The said scores function then were divided into the membership and non-membership elements where the distance of FPDHFSSs was introduced. The proposed distance of FPDHFSSs has been applied in TOPSIS which will be able to solve the problem of fuzzy dual hesitant fuzzy soft set environment.

A good investment portfolio is a properly selected group of investment products such as stocks, bonds and cash equivalents. On top of grouping a brilliant portfolio, an excellent portfolio manager will consider the risk of downturn in financial performance as an important event that need to be taken care of at it best. This paper focuses on managing this risk of a welldiversified investment portfolio. The focus is to be narrowed down into finding the assurance value of the risk. This assurance value will be evaluated under specific strategy of buying traded European put option. The most celebrated Black-Scholes model to option pricing will be used in determining the values of these portfolio insurance strategies. General input parameters such as volatility and dividend yields of the portfolio will be taken from the performance of FTSE Bursa Malaysia KLCI (FTSEBMKL) as the portfolio is reflected by the performance on the index. The value results will be then viewed as numerical evaluation of some well-diversified portfolio examples, which will vary in term of specific input parameters of certain cases. This study provides straightforward insurance strategies a portfolio manager would have done in managing risk of downturn in the financial market. This strategy structure could be further enhanced by considering various other financial tools that are available or to be made available in the financial world.

In this paper, by combining hesitant fuzzy soft sets (HFSSs) and fuzzy parameterized, we introduce the idea of a new hybrid model, fuzzy parameterized hesitant fuzzy soft sets (FPHFSSs). The benefit of this theory is that the degree of importance of parameters is being provided to HFSSs directly from decision makers. In addition, all the information is represented in a single set in the decision making process. Then, we likewise ponder its basic operations such as AND, OR, complement, union and intersection. The basic properties such as associative, distributive and de Morgan's law of FPHFSSs are proven. Next, in order to resolve the multi-criteria decision making problem (MCDM), we present arithmetic mean score and geometry mean score incorporated with hesitant degree of FPHFSSs in TOPSIS. This algorithm can cater some existing approach that suggested to add such elements to a shorter hesitant fuzzy element, rendering it equivalent to another hesitant fuzzy element, or to duplicate its elements to obtain two sequence of the same length. Such approaches would break the original data structure and modify the data. Finally, to demonstrate the efficacy and viability of our process, we equate our algorithm with existing methods.

's spread has altered the learning process at all educational levels, resulting in the proliferation of virtual classrooms throughout the world. The purpose of this study is to determine lecturer satisfaction with Microsoft Teams' use in online learning during the COVID-19 pandemic. This way, we can implement the necessary improvements to ensure that students and lecturers are satisfied with their use of Microsoft Teams. Thirty-four lecturers from UiTM Cawangan Negeri Sembilan (UiTMNCS) participated in the study. Five criteria were used consisting of: Basic Microsoft Teams Functions, Discussion, Assessments, Features, and Attendance Form. Data were collected via questionnaires and then distributed to respondents via Google forms. All calculations were performed using the SPSS Statistics 26 software. The findings indicated that Basic Microsoft Teams Functions is the most effective criterion, while Assessments and Attendance Form is the least effective. The sub-criteria rating with the highest score is Creating a TEAM is simple and straightforward, and the lowest score indicates that Microsoft Teams works well even with slow internet. Chi-square test for independent variable shows there is no relationship between gender, residential area, faculties and teaching experience of UiTMCNS lecturers with sub criteria functions in Basic Functions of Microsoft Teams, Discussion, Assessments, Features and Attendance Form. Further research will be proposed to improve the attendance system by integrating it with the Microsoft team's attendance sheet.