Evaluating readiness degree for Industrial Internet of Things adoption in manufacturing enterprises under interval-valued Pythagorean fuzzy approach

Figures & data

Table 1. Linguistic term and the corresponding interval-valued pythagorean fuzzy numbers (IVPFN)

Linguistic terms	IVPFN
Very good (VG)	([0.80, 0.95],[0.00, 0.15])
Good (G)	([0.70, 0.80],[0.15, 0.25])
Medium good (MG)	([0.55, 0.70],[0.25, 0.40])
Medium (M)	([0.45, 0.55],[0.40, 0.55])
Medium poor (MP)	([0.30, 0.45],[0.55, 0.70])
Poor (P)	([0.20, 0.30],[0.70, 0.80])
Very poor (VP)	([0.00, 0.20],[0.80, 0.95])

Table 2. Weighting scale for IVPF-AHP (IIbahar et al., 2018)

Linguistic terms	IVPFN equivalents numbers
	${\mu }_L$	${\mu }_U$	${\nu }_L$	${\nu }_U$
Certainly Low Importance – CLI	0.00	0.00	0.90	1.00
Very Low Importance – VLI	0.10	0.20	0.80	0.90
Low Importance – LI	0.20	0.35	0.65	0.80
Below Average Importance – BAI	0.35	0.45	0.55	0.65
Average Importance – AI	0.45	0.55	0.45	0.55
Above Average Importance – AAI	0.55	0.65	0.35	0.45
High Importance – HI	0.65	0.80	0.20	0.35
Very High Importance – VHI	0.80	0.90	0.10	0.20
Certainly High Importance – CHI	0.90	1.00	0.00	0.00
Exactly Equal – EE	0.1965	0.1965	0.1965	0.1965

Table 3. Pairwise comparison matrix X = ${\left(x_{jj}\right)}_{n\times n}$

	$C_1$	$\dots$	$C_n$
$C_1$	$⟨\left[0.1965,0.1965\right],\left[0.1965,0.1965\right]⟩$	$\dots$	$⟨\left[{\mu }_{L_{1m}},{\mu }_{U_{1m}}\right],\left[{\nu }_{L_{1m}},{\nu }_{U_{1m}}\right]⟩$
$⋮$	$⋮$	$\ddots$	$⋮$
$C_n$	$⟨\left[{\mu }_{L_{m1}},{\mu }_{U_{m1}}\right],\left[{\nu }_{L_{m1}},{\nu }_{U_{m1}}\right]⟩$	$\dots$	$⟨\left[0.1965,0.1965\right],\left[0.1965,0.1965\right]⟩$

Figure 1. The proposed framework for evaluating the readiness degree for IIoT adoption

Table 4. Experts’ experience and qualification

Expert (E)	Experience (years)	Position	Organization	Area of expertise
E1	18	Factory manager	Automotive company	Production management
E2	11	Production engineering director	Precision machining company	Advance manufacturing technology
E3	9	Chief technology officer	Food processing company	Technology management
E4	12	Academician	Engineering department of a research university	Additive manufacturing
E5	21	Industrial expert	Industrial promotion department of a government agency	Industrial technology development

Figure 2. Decision model for evaluating the readiness degree for IIoT adoption.

Table 5. The significant weight of each expert

Expert	Linguistic terms	${\mu }_L$	${\mu }_U$	${\nu }_L$	${\nu }_U$	${\pi }_L$	${\pi }_U$	$\lambda$	${\lambda }_k$
E1	G	0.700	0.800	0.15	0.250	0.698	0.545	0.385	0.186
E2	G	0.700	0.800	0.15	0.250	0.698	0.545	0.385	0.186
E3	VG	0.800	0.950	0.00	0.150	0.600	0.273	0.586	0.283
E4	M	0.550	0.700	0.250	0.400	0.796	0.591	0.322	0.156
E5	G	0.700	0.800	0.150	0.250	0.698	0.545	0.385	0.186

Table 6. The aggregated pairwise comparison of experts

	C1				C2					C12
	${\mu }_L$	${\mu }_U$	${\nu }_L$	${\nu }_U$	${\mu }_L$	${\mu }_U$	${\nu }_L$	${\nu }_U$		${\mu }_L$	${\mu }_U$	${\nu }_L$	${\nu }_U$
C1	0.196	0.196	0.197	0.197	0.785	0.902	0.123	0.226	…	0.771	0.893	0.134	0.242
C2	0.187	0.309	0.696	0.817	0.196	0.196	0.197	0.197	…	0.395	0.547	0.480	0.626
C3	0.200	0.350	0.650	0.800	0.482	0.582	0.420	0.520	…	0.450	0.550	0.450	0.550
C4	0.450	0.550	0.450	0.550	0.650	0.800	0.200	0.350	…	0.703	0.805	0.224	0.315
C5	0.200	0.350	0.650	0.800	0.200	0.350	0.650	0.800	…	0.450	0.550	0.450	0.550
C6	0.000	0.000	0.822	1.000	0.702	0.836	0.170	0.304	…	0.650	0.800	0.200	0.350
C7	0.200	0.350	0.650	0.800	0.516	0.632	0.381	0.490	…	0.516	0.632	0.381	0.490
C8	0.284	0.409	0.592	0.719	0.384	0.485	0.517	0.617	…	0.510	0.610	0.392	0.492
C9	0.450	0.550	0.450	0.550	0.740	0.861	0.146	0.268	…	0.740	0.861	0.146	0.268
C10	0.200	0.350	0.650	0.800	0.270	0.414	0.591	0.734	…	0.566	0.695	0.323	0.441
C11	0.450	0.550	0.450	0.550	0.650	0.800	0.200	0.350	…	0.650	0.800	0.200	0.350
C12	0.100	0.200	0.800	0.900	0.264	0.408	0.596	0.741	…	0.196	0.196	0.197	0.197

Table 7. The differences between lower ($d_{j{k}_L})$ and upper ($d_{j{k}_U})$ values of membership and nonmembership functions

	C1		C2		C3			C11		C12
	$d_{1_L}$	$d_{1_U}$	$d_{2_L}$	$d_{2_U}$	$d_{3_L}$	$d_{3_U}$		$d_{{11}_L}$	$d_{{11}_U}$	$d_{{12}_L}$	$d_{{12}_U}$
C1	0.000	0.000	0.565	0.799	0.300	0.000	…	0.394	0.597	0.535	0.779
C2	−0.632	−0.388	0.000	0.000	0.165	0.163	…	−0.574	−0.299	−0.236	0.069
C3	−0.600	−0.301	−0.038	0.163	0.000	0.600	…	−0.673	−0.406	−0.101	0.099
C4	−0.101	0.099	0.300	0.600	0.300	−0.301	…	−0.479	−0.189	0.396	0.598
C5	−0.600	−0.301	−0.600	−0.301	0.018	0.670	…	−1.000	−0.759	−0.101	0.099
C6	−1.000	−0.676	0.400	0.670	0.300	0.254	…	−0.466	−0.177	0.300	0.600
C7	−0.600	−0.301	0.026	0.254	0.018	−0.032	…	−0.661	−0.431	0.026	0.254
C8	−0.436	−0.183	−0.233	−0.032	−0.101	0.720	…	−0.369	−0.046	0.018	0.219
C9	−0.101	0.099	0.476	0.720	0.300	−0.177	…	0.126	0.379	0.476	0.720
C10	−0.600	−0.301	−0.466	−0.177	−0.345	0.600	…	−0.800	−0.600	0.126	0.379
C11	−0.101	0.099	0.300	0.600	0.300	−0.189	…	0.000	0.000	0.300	0.600
C12	−0.800	−0.600	−0.479	−0.189	−0.479	0.000	…	−0.479	−0.189	0.000	0.000

Table 8. The interval multiplicative matrix S = ${\left(S_{jk}\right)}_{n\times n}$

	C1		C2		C3			C11		C12
	$S_{1_L}$	$S_{1_U}$	$S_{2_L}$	$S_{2_U}$	$S_{3_L}$	$S_{3_U}$		$S_{{11}_L}$	$S_{{11}_U}$	$S_{{12}_L}$	$S_{{12}_U}$
C1	0.999	0.999	7.048	15.792	2.814	0.999	…	3.900	7.860	6.348	14.748
C2	0.113	0.261	0.999	0.999	1.765	1.754	…	0.138	0.356	0.443	1.267
C3	0.126	0.354	0.877	1.754	0.999	7.934	…	0.098	0.246	0.707	1.410
C4	0.707	1.410	2.814	7.934	2.814	0.354	…	0.191	0.521	3.920	7.880
C5	0.126	0.354	0.126	0.354	1.066	10.105	…	0.032	0.073	0.707	1.410
C6	0.032	0.097	3.987	10.105	2.814	2.408	…	0.200	0.542	2.814	7.934
C7	0.126	0.354	1.094	2.408	1.066	0.895	…	0.102	0.226	1.094	2.408
C8	0.222	0.532	0.447	0.895	0.707	12.031	…	0.280	0.853	1.066	2.131
C9	0.707	1.410	5.175	12.031	2.814	0.542	…	1.544	3.702	5.175	12.031
C10	0.126	0.354	0.200	0.542	0.303	7.934	…	0.063	0.126	1.544	3.702
C11	0.707	1.410	2.814	7.934	2.814	0.521	…	0.999	0.999	2.814	7.934
C12	0.063	0.126	0.191	0.521	0.191	1.000	…	0.191	0.521	0.999	0.999

Table 9. The determinacy value $\tau ={\left({\tau }_{jk}\right)}_{n\times n}$ of $x_{jk}$

	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12
C1	0.923	0.736	0.620	0.536	0.726	0.666	0.668	0.620	0.801	0.713	0.666	0.720
C2	−0.212	0.923	0.558	−0.146	0.780	−0.290	−0.048	0.620	−0.401	0.278	−0.148	0.235
C3	−0.146	0.447	0.923	−0.146	0.447	−0.146	0.474	0.322	−0.374	0.164	−0.257	0.395
C4	0.395	0.620	0.620	0.923	0.620	−0.001	0.620	0.668	0.067	0.620	−0.001	0.698
C5	−0.146	−0.146	0.492	−0.290	0.923	−0.290	−0.374	0.090	−0.759	−0.146	−0.759	0.395
C6	−0.676	0.673	0.620	0.395	0.673	0.923	0.620	0.583	0.395	0.620	0.014	0.620
C7	−0.146	0.481	0.492	−0.374	0.538	−0.146	0.923	0.092	0.090	0.583	−0.262	0.481
C8	0.046	0.265	0.395	−0.146	0.492	−0.137	0.395	0.923	−0.290	0.492	0.090	0.492
C9	0.395	0.713	0.620	0.583	0.673	0.538	0.713	0.673	0.923	0.713	0.538	0.713
C10	−0.146	0.014	0.146	−0.146	0.492	−0.481	0.265	0.265	−0.290	0.923	−0.481	0.538
C11	0.395	0.620	0.620	0.447	0.780	0.447	0.602	0.620	0.395	0.620	0.923	0.620
C12	−0.481	−0.001	−0.001	−0.259	0.474	−0.001	0.395	0.474	0.022	0.474	−0.001	0.923

Table 10. The normalized priority weights ($w_j$)

	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	$\sum _{k=1}^m{t}_{ik}$	$w_i$	Ranking
C1	0.922	8.404	1.182	2.504	8.023	3.917	4.599	3.331	15.529	6.134	3.917	7.595	66.058	0.280	1
C2	−0.040	0.922	0.982	−0.328	9.270	−0.045	−0.015	3.331	−0.046	0.328	−0.036	0.201	14.523	0.062	6
C3	−0.035	0.588	4.122	−0.082	0.588	−0.035	0.792	0.263	−0.046	0.092	−0.044	0.418	6.620	0.028	7
C4	0.418	3.331	0.982	4.122	3.331	0.000	3.331	4.599	0.035	3.331	0.000	4.115	27.592	0.117	4
C5	−0.035	−0.035	2.750	−0.322	0.922	−0.045	−0.046	0.051	−0.040	−0.035	−0.040	0.418	3.543	0.015	12
C6	−0.043	4.741	1.618	1.705	4.741	0.922	3.331	1.684	0.418	3.331	0.005	3.331	25.783	0.109	5
C7	−0.035	0.842	0.483	−0.413	1.412	−0.035	0.922	0.054	0.051	1.684	−0.043	0.842	5.763	0.024	9
C8	0.017	0.178	2.513	−0.112	0.787	−0.030	0.418	0.922	−0.045	0.787	0.051	0.787	6.273	0.027	8
C9	0.418	6.134	1.040	2.835	4.741	1.412	6.134	4.741	0.922	6.134	1.412	6.134	42.057	0.178	2
C10	−0.035	0.005	0.601	−0.065	0.787	−0.045	0.178	0.178	−0.045	0.922	−0.045	1.412	3.847	0.016	10
C11	0.418	3.331	1.033	1.970	9.270	0.588	2.265	3.331	0.418	3.331	0.922	3.331	30.206	0.128	3
C12	−0.045	0.000	−0.001	−0.081	0.792	0.000	0.418	0.792	0.006	0.792	0.000	0.922	3.594	0.015	11

Table 11. The aggregation of rating values and defuzzified values

	DM1	DM2	DM3	DM4	DM5	Aggregated values	Defuzzified value
C1	([0.80,0.95], [0.00,0.15])	([0.70,0.80], [0.15,0.25])	([0.70,0.80], [0.15,0.25])	([0.70,0.80], [0.15,0.25])	([0.55,0.70], [0.25,0.40])	([0.685,0.805], [0.161,0.272])	0.687
C2	([0.70,0.80], [0.15,0.25])	([0.70,0.80], [0.15,0.25])	([0.55,0.70], [0.25,0.40])	([0.55,0.70], [0.25,0.40])	([0.70,0.80], [0.15,0.25])	([0.629,0.754], [0.200,0.326])	0.462
C3	([0.45,0.55], [0.40,0.55])	([0.30,0.45], [0.55,0.70])	([0.30,0.45], [0.55,0.70])	([0.20,0.30], [0.70,0.80])	([0.45,0.55], [0.40,0.55])	([0.327,0.454], [0.536,0.676])	0.233
C4	([0.45,0.55], [0.40,0.55])	([0.45,0.55], [0.40,0.55])	([0.30,0.45], [0.55,0.70])	([0.45,0.55], [0.40,0.55])	([0.55,0.70], [0.25,0.40])	([0.416,0.543], [0.432,0.582])	0.300
C5	([0.70,0.80], [0.15,0.25])	([0.70,0.80], [0.15,0.25])	([0.55,0.70], [0.25,0.40])	([0.70,0.80], [0.15,0.25])	([0.55,0.70], [0.25,0.40])	([0.624,0.751], [0.203,0.331])	0.336
C6	([0.30,0.45], [0.55,0.70])	([0.20,0.30], [0.70,0.80])	([0.30,0.45], [0.55,0.70])	([0.20,0.30], [0.70,0.80])	([0.20,0.30], [0.70,0.80])	([0.241,0.362], [0.639,0.759])	0.361
C7	([0.70,0.80], [0.15,0.25])	([0.70,0.80], [0.15,0.25])	([0.55,0.70], [0.25,0.40])	([0.70,0.80], [0.15,0.25])	([0.70,0.80], [0.15,0.25])	([0.653,0.770], [0.184,0.302])	0.617
C8	([0.45,0.55], [0.40,0.55])	([0.55,0.70], [0.25,0.40])	([0.45,0.55], [0.40,0.55])	([0.45,0.55], [0.40,0.55])	([0.30,0.45], [0.55,0.70])	([0.653,0.770], [0.184,0.302])	0.490
C9	([0.20,0.30], [0.70,0.80])	([0.20,0.30], [0.70,0.80])	([0.20,0.30], [0.70,0.80])	([0.45,0.55], [0.40,0.55])	([0.45,0.55], [0.40,0.55])	([0.263,0.368], [0.628,0.740])	0.376
C10	([0.55,0.70], [0.25,0.40])	([0.45,0.55], [0.40,0.55])	([0.55,0.70], [0.25,0.40])	([0.30,0.45], [0.55,0.70])	([0.30,0.45], [0.55,0.70])	([0.430,0.574], [0.412,0.562])	0.450
C11	([0.20,0.30], [0.70,0.80])	([0.45,0.55], [0.40,0.55])	([0.30,0.45], [0.55,0.70])	([0.20,0.30], [0.70,0.80])	([0.30,0.45], [0.55,0.70])	([0.281,0.406], [0.592,0.721])	0.372
C12	([0.70,0.80], [0.15,0.25])	([0.70,0.80], [0.15,0.25])	([0.70,0.80], [0.15,0.25])	([0.55,0.70], [0.25,0.40])	([0.70,0.80], [0.15,0.25])	([0.673,0.783], [0.169,0.280])	0.262

Table 12. The overall readiness degree of IIoT adoption

		ABC Company			Success Company			% Gap values of readiness Degree*
Readiness criteria	Weight$\left(w_j\right)$	Rating score $(r_{ABC}^j$)		Readiness degree $Z_{ABC}^{read}$ = $r_{ABC}^j\times w_j$	Rating score $(r_{success}^j$)		Readiness degree ($Z_{success}^{read}$ = $r_{success}^j\times w_j$)
Top management commitment and support (C1)	0.280	0.687		0.192	0.850		0.238	19.32
Financial capability (C2)	0.062	0.462		0.028	0.638		0.039	28.20
Managing cyber security and privacy (C3)	0.028	0.233		0.006	0.692		0.019	68.42
Digital business model development capability (C4)	0.116	0.300		0.035	0.587		0.068	48.53
Technology infrastructure capability (C5)	0.015	0.336		0.005	0.638		0.009	44.44
Change management capability (C6)	0.109	0.361		0.039	0.554		0.060	35.00
Data management and analytics capabilities (C7)	0.024	0.617		0.015	0.660		0.016	6.25
Seamless value-chain integration capability (C8)	0.027	0.490		0.013	0.589		0.015	13.33
Strategic technology roadmap for digitalization (C9)	0.178	0.376		0.067	0.532		0.094	28.72
Employees digital knowledge capabilities (C10)	0.016	0.450		0.007	0.673		0.010	30.00
Digital culture readiness (C11)	0.128	0.372		0.047	0.533		0.068	30.88
Lean practice implementation (C12)	0.015	0.262		0.003	0.448		0.006	50.00
Overall readiness degree			0.461 (46.10%) ($Z_{ABC}^{read}$)			0.648 (64.8%) ($Z_{success}^{read}$)
Overall unreadiness degree			0.539 (53.9%) (1- $Z_{ABC}^{read}$)			0.352 (35.2%) (1-$Z_{success}^{read}$)

*Note: % Gap values of readiness Degree = $\frac{\left|Z_{success}^{read}-Z_{ABC}^{read}\right|\times 100}{Z_{success}^{read}}$

Table 13. Summary of result comparisons

		C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11		C12	Overall readiness degree value
ABC company	Weight	0.28	0.062	0.028	0.116	0.015	0.109	0.024	0.027	0.178	0.016	0.128		0.015	-
	Rating score	0.687	0.462	0.233	0.300	0.336	0.361	0.617	0.490	0.376	0.450	0.372		0.262	-
	Readiness degree	0.192	0.028	0.006	0.035	0.005	0.039	0.015	0.013	0.067	0.007	0.047		0.003	0.461 (46.1%)
Success company	Rating score	0.850	0.638	0.692	0.587	0.638	0.554	0.660	0.589	0.532	0.673	0.533		0.448
	Readiness degree	0.238	0.039	0.019	0.068	0.009	0.060	0.016	0.015	0.094	0.010	0.068		0.006	0.648 (64.8%)
% Gap values of reading degree		19.32	28.20	68.42	48.53	44.44	36.00	6.25	13.33	28.72	30.00	30.88	50.00
	Ranking	10	9	1	3	4	5	12	11	8	7	6	2

Figure 3. Readiness factor degree between the success company and ABC company.

Table

Abbreviation	Definition/ Explanation
AHP	Analytic Hierarchy Process
AI	Artificial Intelligence
AIFDA	Aggregated Intuitionistic Fuzzy Dimensional Analysis
AIFIS	Aggregated Intuitionistic Fuzzy Index of Similarity
CPS	Cyber-Physical Systems
DM	Decision Maker
FMCDM	Fuzzy Multi Criteria Decision Making
GDP	Gross Domestic Product
IFN	Intuitionistic Fuzzy Numbers
IFS	Intuitionistic Fuzzy Sets
IIoT	Industrial Internet of Things
IoT	Internet of Things
IT	Information Technology
IT2FS	Interval Two-Type Fuzzy Sets
IVPFS	Interval-valued Pythagorean Fuzzy Set
IVPF-AHP	Interval-valued Pythagorean Fuzzy AHP
IVPFN	Interval-valued Pythagorean Fuzzy Number
IVPFWG	Interval-valued Pythagorean Fuzzy Weighted Geometric
IVPFLWA	interval-valued Pythagorean Fuzzy Weighted Geometric
MCDM	Multi Criteria Decision Making
M2M	Machine-to-Machine
PFS	Pythagorean Fuzzy Set
PFAHP	Pythagorean Fuzzy Analytical Hierarchy Process
TFS	Triangular Fuzzy Set

IIbahar, E., Karasan, A., Cebi, S., & Kahraman, C. (2018). A novel approach to risk assessment for occupational health and safety using pythagorean fuzzy AHP & fuzzy inference system. Safety Science, 103(March), 124–136. https://doi.org/10.1016/j.ssci.2017.10.025

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