University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065416220190301Ranking triangular interval-valued fuzzy numbers based on the relative preference relation123136454710.22111/ijfs.2019.4547ENYu-JieWangDepartment of Shipping and Transportation Management, National Penghu University of Science and Technology, Penghu 880,
Taiwan, Republic of ChinaJournal Article20170801<span class="fontstyle0">In this paper, we first use a fuzzy preference relation with a membership function representing preference degree for<br />comparing two interval-valued fuzzy numbers and then utilize a relative preference relation improved from the fuzzy<br />preference relation to rank a set of interval-valued fuzzy numbers. Since the fuzzy preference relation is a total ordering<br />relation that satisfies reciprocal and transitive laws on interval-valued fuzzy numbers, the relative preference relation is<br />also a total ordering relation. Practically, the fuzzy preference relation is more reasonable on ranking interval-valued<br />fuzzy numbers than defuzzification because defuzzification does not present preference degree between fuzzy numbers<br />and loses messages. However, fuzzy pair-wise comparison for the fuzzy preference relation is more complex and difficult<br />than defuzzification. To resolve fuzzy pair-wise comparison tie, the relative preference relation takes the strengths of<br />defuzzification and the fuzzy preference relation into consideration. The relative preference relation expresses preference<br />degrees of interval-valued fuzzy numbers over average as the fuzzy preference relation does, and ranks fuzzy numbers<br />by relative crisp values as defuzzification does. In fact, the application of relative preference relation was shown in<br />traditional fuzzy numbers, such as triangular and trapezoidal fuzzy numbers, for previous approaches. In this paper, we<br />extend and utilize the relative preference relation on interval-valued fuzzy numbers, especially for triangular intervalvalued fuzzy numbers. Obviously, interval-valued fuzzy numbers based on the relative preference relation are easily andÂ quickly ranked, and able to reserve fuzzy information.</span> <br /><br />https://ijfs.usb.ac.ir/article_4547_2d42cfd6014592f7758ad25007b4a71e.pdf