### Journals Information

Mathematics and Statistics Vol. 8(3), pp. 244 - 253
DOI: 10.13189/ms.2020.080302
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## Application of Parameterized Hesitant Fuzzy Soft Set Theory in Decision Making

Zahari Md Rodzi 1,2,*, Abd Ghafur Ahmad 2
1 School of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Malaysia
2 Faculty of Computer and Mathematical Science, Universiti Teknologi MARA Campus Seremban, Malaysia

ABSTRACT

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.

KEYWORDS
Fuzzy Soft Set, Fuzzy Hesitant, Fuzzy Parameterized Hesitant Fuzzy Soft Sets

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Zahari Md Rodzi , Abd Ghafur Ahmad , "Application of Parameterized Hesitant Fuzzy Soft Set Theory in Decision Making," Mathematics and Statistics, Vol. 8, No. 3, pp. 244 - 253, 2020. DOI: 10.13189/ms.2020.080302.

(b). APA Format:
Zahari Md Rodzi , Abd Ghafur Ahmad (2020). Application of Parameterized Hesitant Fuzzy Soft Set Theory in Decision Making. Mathematics and Statistics, 8(3), 244 - 253. DOI: 10.13189/ms.2020.080302.