Fuzzy Parameterized Hesitant Fuzzy Linguistic Term Soft Sets (FPHFLTSSs) in Multi-Criteria Decision Making
Zahari Md Rodzi1, Abd Ghafur Ahmad2

1Zahari Md Rodzi, School of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia. Faculty of Computer and Mathematical Science, Universiti Teknologi MARA Campus Seremban, 70300 Seremban, Negeri Sembilan, Malaysia.
2Abd Ghafur Ahmad*, School of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Bangi, Selangor, Malaysia.
Manuscript received on February 10, 2020. | Revised Manuscript received on February 20, 2020. | Manuscript published on March 10, 2020. | PP: 909-916 | Volume-9 Issue-5, March 2020. | Retrieval Number: E2519039520/2020©BEIESP | DOI: 10.35940/ijitee.E2519.039520
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: In this research, we suggest the theory of FPHFLTSSs. This theory is combination of hesitant fuzzy linguistic term soft sets (HFLTSSs) and weights of criteria in the set namely fuzzy parameterized where all the information are given in a single set. Then, we address several related concepts and the fundamental operations of this theory, namely the addition, union and intersection. In addition, we introduce the concept of scores in FPHFLTSSs based on arithmetic mean, geometry mean, and fractional of FPHFLTSSs. Next, we introduce the concept of distance between two FPHFLTSSs based on these scores which can be used in TOPSIS approach. Three algorithms are introduced to cater some problems in algorithm discovered in previous study. The first algorithm is an easy and simple step without transforming hesitant linguistic fuzzy elements into hesitant fuzzy elements. This second approach is the extended version of Liu et al. in which they suggested their positive ideal solution (PIS) distance algorithm. For the third algorithm, we suggest FPHFLTSS’s arithmetic mean distances, geometry mean, and fractional distances in TOPSIS approach. Lastly, these algorithms are used for the issue of decision making in FPHFLTSSs environment to show the feasibility and efficiency of our methods. 
Keywords:  A fuzzy parameterized, HFLTSSs, hesitant fuzzy linguistic term sets FPHFLTSSs, TOPSIS.
Scope of the Article: Fuzzy logics