Some interval‐valued q‐rung orthopair weighted averaging operators and their applications to multiple‐attribute decision making

Abstract

Q‐rung orthopair fuzzy sets (q‐ROFSs), initially proposed by Yager, are a new way to reflect uncertain information. The existing intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets are special cases of the q‐ROFSs. However, due to insufficiency in available information, it is difficult for decision makers to exactly express the membership and nonmembership degrees by crisp numbers, and interval membership degree and interval nonmembership degree are good choices. In this paper, we propose the concept of interval‐valued q‐rung orthopair fuzzy set (IVq‐ROFS) based on the ideas of q‐ROFSs and some operational laws of q‐rung orthopair fuzzy numbers (q‐ROFNs). Then, some interval‐valued q‐rung orthopair weighted averaging operators are presented based on the given operational laws of q‐ROFNs. Further, based on these operators, we develop a novel approach to solve multiple‐attribute decision making (MADM) problems under interval‐valued q‐rung orthopair fuzzy environment. Finally, a numerical example is provided to illustrate the application of the proposed method, and the sensitivity analysis is further carried out for the parameters.

New q-Rung Orthopair Fuzzy Bonferroni Mean Dombi Operators and Their Application in Multiple Attribute Decision Making

“…Peng et al [18] proposed q-rung orthopair fuzzy weighted distance-based approximation method. Q-rung fuzzy set has been further extended to accommodate uncertain linguistic arguments [19]- [21], interval values [22]. Q-rung orthopair fuzzy set has been applied in evaluation of renewable energy problem [23], teaching quality [24], etc.…”

A new possibility degree measure for interval‐valued q‐rung orthopair fuzzy sets in decision‐making

“…The three experts, whose weights w = (0.32, 0.45, 0.23), from the civil engineering and human resources departments are requested to evaluate them and express their ratings under IVq-ROFNs with q = 1 given in Tables 1-3 (for more details, we refer to see Reference [45]). The overall outcomes of the given alternatives are obtained from the several others existing approaches 6,7,16,24,25,27,28,[31][32][33][34][35][36]41,46 and with the proposed method. The results of them are recorded in Table 3 heart rate and blood pressure), 2 V (body temperature), 3 V (the frequency of the cough), and 4…”

“…For it, a management constitute a committee with three experts who acts as a DM (having weights w = (0.40, 0.35, 0.25)), whose responsibility is to evaluate the given four alternatives { , , , }     . To access it completely, they considered the six attributes approach and the existing approaches 6,7,16,24,25,27,28,[31][32][33][34][35][36]41,46 are listed in Table 5. It is clearly seen that the optimal alternative is 1  .…”

New q-Rung Orthopair Hesitant Fuzzy Decision Making Based on Linear Programming and TOPSIS

“…Liu and Wang [22] developed q-rung orthopair fuzzy Archimedean Bonferroni Mean operator. Ju et al [23] defined some interval-valued q-rung orthopair weighted averaging operators. Wei et al [24] proposed the generalized q-rung orthopair fuzzy Heronian mean operator.…”