# Hesitant Fuzzy Methods for Multiple Criteria Decision by Xiaolu Zhang, Zeshui Xu

By Xiaolu Zhang, Zeshui Xu

The e-book deals a complete creation to tools for fixing a number of standards determination making and staff choice making issues of hesitant fuzzy info. It experiences at the authors’ most recent learn, in addition to on others’ study, delivering readers with a whole set of selection making instruments, corresponding to hesitant fuzzy TOPSIS, hesitant fuzzy TODIM, hesitant fuzzy LINMAP, hesitant fuzzy QUALIFEX, and the deviation modeling process with heterogeneous fuzzy info. the focus is on determination making difficulties during which the factors values and/or the weights of standards aren't expressed in crisp numbers yet are superior to be denoted as hesitant fuzzy components. the biggest a part of the booklet is dedicated to new tools lately constructed via the authors to resolve choice making difficulties in occasions the place the to be had info is imprecise or hesitant. those tools are awarded intimately, including their program to diversified form of decision-making difficulties. All in all, the e-book represents a beneficial reference advisor for graduate scholars and researchers within the either fields of fuzzy good judgment and determination making.

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L. (2013). Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowledge-Based Systems, 52, 53–64. Zhang, Z. M. (2013). Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. Information Sciences, 234, 150–181. Zhang, X. , & Xu, Z. S. (2014a). Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets. International Journal of Intelligent Systems, 29, 1061–1078. Zhang, X.

In Step 5, we utilize Eq. 4. 4 and thus the most desirable alternative is A5 . 2 Comparison Analysis Recently, Nan et al. (2008) proposed an intuitionistic fuzzy TOPSIS method for solving the MCDM problems with IFNs. We call it the IF-TOPSIS method. Xu and Zhang (2013) made a comparison with the IF-TOPSIS method which is the closest to the proposed approach because the HFEs’ envelopes are IFNs. 6 (Atanassov 1986). Let a set T be a universe of discourse. An intuitionistic fuzzy set (IFS) I is an object having the form I ¼ fht; lI ðtÞ; mI ðtÞijt 2 Tg, where the function lI : T !

Compared with the aggregating operators-based decision methods (Xia and Xu 2011; Zhu et al. 2012; Zhang 2013), this technique is based on the revised closeness index of each alternative to determine the ranking order of all alternatives, which avoids producing the loss of too much information in the process of information aggregation. Furthermore, this developed method is extended to tackle appropriately the MCDM problems under interval-valued hesitant fuzzy environment. 6 Conclusions 29 applicability of the proposed method has been illustrated with an energy police selection problem.