**8. Conclusions**

Because of the blurring of human thinking, sometimes it becomes difficult for experts to accurately measure the opinions in the area of the usual fuzzy set theory, even in the HIFLTSs and PLTSs. For this purpose, in this article, a new concept called PHILTS was introduced to extend the current HIFLTS and PLTS. To facilitate the calculation of the PHILTSs, a normalization process, basic operations and aggregation operators for PHILTSs are also designed. An extended TOPSIS method and aggregation based method have been proposed to solve decision ranking problems of the group with the multiple conflict criteria in PHILTS. The proposed models are compared with existing model of TOPSIS. The PLTS and HIFLTS are special cases of PHILTS, it grants the freedom to DMs to express their opinions in more dynamic way. Furthermore, the occurrence probabilities of membership and non-membership linguistic term sets greatly affects the decision making, validating the importance of designed theory and models in this manuscript. The probability is one of the best tool to handle uncertainty of future, thus our proposed models are more suitable of decision making related to the possible future scenarios. However, its arithmetic complexity is high.

In the future, all the work which has been done thus far PLTSs and HIFLTSs can be studied for PHILTS and then applied to decision making.

**Author Contributions:** Conceptualization, Z.B., T.R. and J.A.; Formal analysis, Z.B., M.G.A.M., T.R. and J.A.; Investigation, Z.B. and J.A.; Methodology, M.G.A.M.; Resources, T.R.; Software, M.G.A.M.

**Funding:** This work is partially supported by AGI Education, Auckland, New Zealand.

**Acknowledgments:** The authors would like to thank the editors and the anonymous reviewers, whose insightful comments and constructive suggestions helped us to significantly improve the quality of this paper. This research work is partially supported by AGI Education, Auckland, New Zealand.

**Conflicts of Interest:** The authors declare no conflict of interest.
