M3: M3 dataset
In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

Description Usage Format Details Source References Examples

M3 is a matrix of dimension 69 x 4 containing 69 trapezoidal fuzzy rating responses, each of which is characterized by its four values inf0,inf1,sup1,sup0. The data correspond to the well-known questionnaire TIMSS-PIRLS2011. This questionnaire was adapted to allow a double-type response, namely, the original Likert and a fuzzy rating scale-based (to simplify, trapezoidal). The questionnaire was conducted on 69 fourth grade students from Colegio San Ignacio (Oviedo-Asturias, Spain). Trapezoidal fuzzy rating responses to the Question M3 "Mathematics is harder for me than any other subject" are collected in this dataset.

1	data("M3")

A matrix of dimension 69 x 4 containing 69 trapezoidal fuzzy rating responses, each of which is characterized by its four values inf0,inf1,sup1,sup0.

See examples

The complete dataset can be found in http://bellman.ciencias.uniovi.es/SMIRE/FuzzyRatingScaleQuestionnaire-SanIgnacio.html

[1] Gil, M.A.; Lubiano, M.A.; De la Rosa de Saa, S.; Sinova, B.: Analyzing data from a fuzzy rating scale-based questionnaire. A case study, Psicothema 27(2), pp. 182-191 (2015)

[2] Lubiano, M.A.; De la Rosa de Saa, S.; Montenegro, M.; Sinova, B.; Gil, M.A.: Descriptive analysis of responses to items in questionnaires. Why not a fuzzy rating scale?, Information Sciences 360, pp. 131-148 (2016)

[3] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications, European Journal of Operational Research 251, pp. 918-929 (2016)

data(M3)
filterNA(M3)
F=filterNA(M3)[[1]]
Median1norm(F)

[[1]]
     inf0   inf1   sup1   sup0
1   5.200  6.000  7.000  7.000
2   0.000  0.000  0.000  2.950
3   6.000  6.425  7.350  7.875
4   0.000  0.000  0.775  1.225
5   0.000  0.000  2.150  2.150
6  10.000 10.000 10.000 10.000
7   7.900  7.950  8.700  8.700
8   9.000  9.000  9.400 10.000
9   9.000 10.000 10.000 10.000
10  4.975  4.975  5.325  5.400
11  7.600  7.600  8.350  8.650
12  2.000  2.000  4.000  4.000
13  0.000  0.000  0.000  0.450
14  9.975 10.000 10.000 10.000
15  0.000  0.000  1.575  1.575
16  2.225  2.225  3.125  3.125
17  1.900  1.950  3.000  3.150
18  4.875  5.050  5.450  5.625
19  6.150  6.150  6.750  6.750
20  3.450  3.450  4.425  4.425
21  2.500  3.200  3.300  4.450
22  3.000  3.600  4.200  5.050
23  3.000  3.000  3.000  3.000
24  0.000  0.600  1.250  1.650
25  0.000  0.500  0.500  1.000
26  2.500  3.000  3.600  3.600
27  3.000  3.200  3.600  4.200
28 10.000 10.000 10.000 10.000
29 10.000 10.000 10.000 10.000
30  6.975  6.975  7.925  7.925
31  0.000  0.000  2.575  2.575
32  6.000  6.450  7.400  8.000
33  2.350  2.800  3.250  3.500
34  3.150  3.400  3.600  4.000
35  0.000  0.625  2.725  2.750
36  0.000  0.000  1.000  2.000
37  0.000  1.125  2.025  2.625
38  4.925  5.025  5.950  6.300
39 10.000 10.000 10.000 10.000
40  0.000  0.825  2.425  2.425
41  0.000  0.325  1.475  1.475
42  5.150  5.350  6.150  6.150
43  8.550  8.850  9.625 10.000
44  0.000  0.000  0.000  0.725
45  0.000  0.000  0.000  0.000
46 10.000 10.000 10.000 10.000
47  7.000  7.400  8.200  8.400
48  4.050  4.050  4.700  4.775
49 10.000 10.000 10.000 10.000
50  0.000  0.850  1.500  1.825
51  1.600  1.825  2.425  3.075
52  3.125  3.275  3.700  4.050
53  9.900  9.900 10.000 10.000
54  0.000  0.000  1.125  1.125
55  6.000  6.000  7.000  8.000
56  1.000  1.800  2.350  3.100
57  0.000  0.075  1.000  1.350
58  0.000  0.000  0.000  0.000
59  0.000  0.400  0.950  1.750
60 10.000 10.000 10.000 10.000
61  8.800  8.800  9.500  9.575
62  4.600  6.150  6.150  6.850
63  3.600  3.925  4.575  4.575
64  3.875  3.875  5.600  5.600
65  0.000  0.250  1.025  1.025
66 10.000 10.000 10.000 10.000
67  0.300  0.450  1.150  1.500
68  5.500  6.100  6.900  7.400
69  6.325  6.925  7.175  7.650

[[2]]
[1] 69

, , 1

       [,1]   [,2]   [,3]
  [1,] 0.00 3.1500 4.4500
  [2,] 0.01 3.1525 4.4385
  [3,] 0.02 3.1550 4.4270
  [4,] 0.03 3.1575 4.4250
  [5,] 0.04 3.1600 4.4250
  [6,] 0.05 3.1625 4.4250
  [7,] 0.06 3.1650 4.4250
  [8,] 0.07 3.1675 4.4250
  [9,] 0.08 3.1700 4.4250
 [10,] 0.09 3.1725 4.4250
 [11,] 0.10 3.1750 4.4250
 [12,] 0.11 3.1775 4.4250
 [13,] 0.12 3.1800 4.4250
 [14,] 0.13 3.1825 4.4250
 [15,] 0.14 3.1850 4.4250
 [16,] 0.15 3.1875 4.4250
 [17,] 0.16 3.1900 4.4250
 [18,] 0.17 3.1925 4.4250
 [19,] 0.18 3.1950 4.4250
 [20,] 0.19 3.1975 4.4250
 [21,] 0.20 3.2000 4.4250
 [22,] 0.21 3.2025 4.4250
 [23,] 0.22 3.2050 4.4250
 [24,] 0.23 3.2075 4.4250
 [25,] 0.24 3.2100 4.4250
 [26,] 0.25 3.2125 4.4250
 [27,] 0.26 3.2150 4.4250
 [28,] 0.27 3.2175 4.4250
 [29,] 0.28 3.2200 4.4250
 [30,] 0.29 3.2225 4.4250
 [31,] 0.30 3.2250 4.4250
 [32,] 0.31 3.2275 4.4250
 [33,] 0.32 3.2300 4.4250
 [34,] 0.33 3.2325 4.4250
 [35,] 0.34 3.2350 4.4250
 [36,] 0.35 3.2375 4.4250
 [37,] 0.36 3.2400 4.4250
 [38,] 0.37 3.2425 4.4250
 [39,] 0.38 3.2450 4.4250
 [40,] 0.39 3.2475 4.4250
 [41,] 0.40 3.2500 4.4250
 [42,] 0.41 3.2525 4.4250
 [43,] 0.42 3.2550 4.4250
 [44,] 0.43 3.2580 4.4250
 [45,] 0.44 3.2640 4.4250
 [46,] 0.45 3.2700 4.4250
 [47,] 0.46 3.2760 4.4250
 [48,] 0.47 3.2820 4.4250
 [49,] 0.48 3.2880 4.4250
 [50,] 0.49 3.2940 4.4250
 [51,] 0.50 3.3000 4.4250
 [52,] 0.51 3.3060 4.4250
 [53,] 0.52 3.3120 4.4250
 [54,] 0.53 3.3180 4.4250
 [55,] 0.54 3.3240 4.4250
 [56,] 0.55 3.3300 4.4250
 [57,] 0.56 3.3360 4.4250
 [58,] 0.57 3.3420 4.4250
 [59,] 0.58 3.3480 4.4250
 [60,] 0.59 3.3540 4.4250
 [61,] 0.60 3.3600 4.4250
 [62,] 0.61 3.3660 4.4250
 [63,] 0.62 3.3720 4.4250
 [64,] 0.63 3.3780 4.4250
 [65,] 0.64 3.3840 4.4250
 [66,] 0.65 3.3900 4.4250
 [67,] 0.66 3.3960 4.4250
 [68,] 0.67 3.4020 4.4250
 [69,] 0.68 3.4080 4.4250
 [70,] 0.69 3.4140 4.4250
 [71,] 0.70 3.4200 4.4250
 [72,] 0.71 3.4260 4.4250
 [73,] 0.72 3.4320 4.4250
 [74,] 0.73 3.4380 4.4250
 [75,] 0.74 3.4440 4.4210
 [76,] 0.75 3.4500 4.4125
 [77,] 0.76 3.4500 4.4040
 [78,] 0.77 3.4500 4.3955
 [79,] 0.78 3.4500 4.3870
 [80,] 0.79 3.4500 4.3785
 [81,] 0.80 3.4500 4.3700
 [82,] 0.81 3.4500 4.3615
 [83,] 0.82 3.4500 4.3530
 [84,] 0.83 3.4500 4.3445
 [85,] 0.84 3.4500 4.3360
 [86,] 0.85 3.4500 4.3275
 [87,] 0.86 3.4500 4.3190
 [88,] 0.87 3.4500 4.3105
 [89,] 0.88 3.4500 4.3020
 [90,] 0.89 3.4500 4.2935
 [91,] 0.90 3.4500 4.2850
 [92,] 0.91 3.4500 4.2765
 [93,] 0.92 3.4500 4.2680
 [94,] 0.93 3.4500 4.2595
 [95,] 0.94 3.4500 4.2510
 [96,] 0.95 3.4500 4.2425
 [97,] 0.96 3.4500 4.2340
 [98,] 0.97 3.4500 4.2255
 [99,] 0.98 3.4500 4.2170
[100,] 0.99 3.4500 4.2085
[101,] 1.00 3.4500 4.2000