Generalized dice similarity measures for q-rung orthopair fuzzy sets with applications
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ORIGINAL ARTICLE
Generalized dice similarity measures for q-rung orthopair fuzzy sets with applications Naeem Jan1,2 · Lemnaouar Zedam3 · Tahir Mahmood1 · Ewa Rak4 · Zeeshan Ali1 Received: 12 December 2019 / Accepted: 24 April 2020 © The Author(s) 2020
Abstract Recently, Yager has established that the notion of q-rung orthopair fuzzy set (q-ROFS) is more accomplished than pythagorean fuzzy set (PyFS) and intuitionistic fuzzy set (IFS) to cope with awkward and complicated information in real decision theory. This notion works with yes-, no- and refusal-type fuzzy information. The constraint of q-ROFS is that the sum of n-power of the truth grade and the n-power of the falsity grade is bounded to unit interval. Generalized dice similarity measures are complimentary concepts quantifying the difference and closeness of q-ROFSs. In this paper, we suggested a number of novel dice similarity measures (DSMs) in the surroundings of the q-ROFS, and we examined some prevailing dice similarity measures and their limitations. In addition, we took the DSMs broad view to some globalized dice similarity measures (GDSMs), and we examined some of their particular cases. We employed the novel suggested GDSMs to the best selections of items on identification problems, and we analyzed their acquired consequences. There is a development of novel work in which many situations are evaluated, and from this perspective, the suggested work is changed into already prevailing work. This study also examines the merits of novel DSMs and the limitations for DSMs of IFSs and PyFSs. The comparison between established measures with existing measures is explored and their graphical interpretations are also discussed to show the reliability and effectiveness of the explored measures. Keywords Pythagorean fuzzy sets · q-Rung orthopair fuzzy sets · Dice similarity measures · Generalized dice similarity measures
Introduction Multi-attribute decision-making (MADM) problem is a useful technique and important part of modern decision theory. In real decision situation, because the decision-making problems are fuzzy and uncertain, the attribute values are not always shown as real numbers, and some of them are more suitable to be denoted by fuzzy numbers. So, Zadeh [1] established the framework of fuzzy set (FS) for modelling the
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Naeem Jan [email protected]; [email protected]
1
Department of Mathematics and Statistic, International Islamic University Islamabad, Islamabad, Pakistan
2
Department of Data Analysis and Mathematical Modeling, Faculty of Bioscience Engineering, Ghent University, Ghent, Belgium
3
Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of Mesila, Mesila, Algeria
4
Faculty of Mathematics and Natural Sciences, University of Rzeszów, Rzeszów, Poland
ambiguous dealings of real life. A fuzzy set allocates a membership grade of an element of a set in the real unit interval [0, 1]. The theory of a FS is extensively utilized in the field of aggregation operators [2], medical diagnosis [3] and M
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