Projected decision background based on q -rung orthopair triangular fuzzy aggregation operators
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ORIGINAL PAPER
Projected decision background based on q-rung orthopair triangular fuzzy aggregation operators Aliya Fahmi1 • Muhammad Aslam2 Received: 8 May 2020 / Accepted: 18 September 2020 Ó Springer Nature Switzerland AG 2020
Abstract The notions of q-rung triangular orthopair fuzzy numbers (q-ROTFNs) to deal with ambiguous data in multi-attribute decision-making (MADM) problems. The purpose of this manuscript is to propose a new concept called q-ROTFNs to handle multipart ambiguous data in real decision-making problems. Then the important laws and their examples of the qROTFNs are also given. Furthermore, the notions of q-rung triangular orthopair operator, q-RTFWA, q-ROTFWA, qROTFHWA, q-ROTFWG, q-ROTFOWG, and q-ROTFHWG operators are proposed and their basic properties are also discussed. Moreover, we mature an original approach to MADM using proposed operators and a numerical example is used to call the flexibility and overtly of the originated operators. In last, the comparison between the proposed method and existing work is also deliberated in part. Keywords Triangular fuzzy number q-ROTFNs q-ROTNF data aggregation operators MCDM
1 Introduction The MADM is intended to choose the best one from limited alternatives by integrating the evaluation information of different alternatives. As a useful evaluation tool for the last few decades, it has widely been applied in many practices such as site selection, medical diagnosis, granular computing techniques, pattern identification, and so forth. The first step of MADM is how to denote the evaluation information for different attributes. Decision makers (DMs) often utilize real numbers to evaluate alternatives, however, sometimes, it is not appropriate for accurate numbers, because the decision surroundings are very complex and DMs are difficult in fully acquainting themselves with the opinion target. Zadeh proposed the inventive notion of the fuzzy set (FS) in 1965. Zadeh (1975) introduced the interval-valued fuzzy. Chen and Chen & Aliya Fahmi [email protected] 1
Department of Management Sciences, School of Mathematics, The University of Faisalabad, Faisalabad, Pakistan
2
Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia
(2014) introduced the probability of the down-trend, the probability of the equal-trend and the probability of the uptrend of the two-factors second-order fuzzy-trend logical relationships in each two-factors second-order fuzzy-trend logical relationship group. Shen et al. (2020) introduced the based on stochastic analysis theory and fuzzy-model-based method. Chen and Niou (2010) calculated the average rating value of each decision maker with respect to the alternatives. Chen et al. (1993) introduced the method requires only simple arithmetic operations, and because it allows bidirectional approximate reasoning. Chen and Hsiao (2000) introduced the perform bidirectional approximate reasoning based on the direction of matching between interval-valued
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