Abstract
The q-rung orthopair fuzzy number (q-ROFN) has been recently developed by Yager and has been widely applied in handling real-life decision-making problems. To enhance its usefulness in dealing with complex practical issues, this paper first proposes the new concept of q-rung orthopair trapezoidal fuzzy numbers (q-ROTrFNs) which is a new and useful extension of q-ROFNs. Then, we investigate the operation of q-ROTrFNs and develop a new ranking method for q-ROTrFNs. We also propose a new q-rung orthopair trapezoidal fuzzy Hamming distance measure. More important, we develop a useful q-rung orthopair trapezoidal fuzzy modified TODIM group decision-making method. In this method, a new q-rung orthopair trapezoidal fuzzy weighted aggregating (q-ROTrFWA) operator is developed to integrate individual decision matrices into the collective decision matrix, and a q-rung orthopair trapezoidal fuzzy distance measure-based compromise approach is proposed to determine the relative dominance degree of alternatives. It is worth to mention that the modified TODIM method not only expands the freedom of decision makers but also allows decision makers to choose the appropriate risk preference parameter. Finally, a case study on health management of hypertensive patients is conducted to demonstrate the feasibility of the modified TODIM group decision-making method, and the developed method is further verified by comparison analysis with the existing methods and sensitive analysis of different parameters.
Highlights
Due to the complexity and uncertainty in real-life decisionmaking processes, it is difficult for experts to timely and accurately provide the estimated results in form of exact real numbers
Despite the usefulness of Pythagorean fuzzy theory [6, 7], practical applications have shown that Pythagorean fuzzy set (PFS) still have some limitations. erefore, Yager [8] recently developed the concept of generalized orthopair fuzzy set in which uq + vq ≤ 1 (q ≥ 1). e proposed q-ROFSs well incorporate the advantages of intuitionistic fuzzy sets (IFSs) and PFSs and describe a wider range of information within different values of the parameter q. e q-ROFSs have been a research hotspot in recent years, and many excellent research results have been achieved, for example, the q-rung orthopair fuzzy approximate reasoning method [9], integrals
We have introduced the concept of q-ROTrFNs and developed the basic operation of q-ROTrFNs
Summary
Due to the complexity and uncertainty in real-life decisionmaking processes, it is difficult for experts to timely and accurately provide the estimated results in form of exact real numbers. Let c be a random number and c > 0 and a (a, a1, a2, a; ua(max), va(min)) and b (b, b1, b2, b; ub(max), vb(min)) be two q-ROTrFNs; the following equations (13)–(16) hold: Complexity uᾶ (max). Let a (a, a1, a2, a; ua(max), va(min)) and b (b, b1, b2, b; ub(max), vb(min)) be two q-ROTrFNs; the Hamming distance d(a, b) between a and b is show as d(a,. As a classical distance measure, the developed Hamming distance provides a way to quantify the difference between qROTrFNs, which indicates the closeness of two q-ROTrFNs and takes into account the multifactor differences of qROTrFNs
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