Interval valued Pythagorean fuzzy aggregation operators based Malcolm Baldrige National Quality Award assessment

Abstract

Malcolm Baldrige National Quality Award (MBNQA) is a quality assessment and rewarding system that aims to increase the awareness of quality management. Although the award is launched in the USA in 1989 and only given to the U.S based companies, it is recognized internationally. There are 7 types of categories in the award system (Leadership, Strategic planning, Customer focus, Measurement, analysis, and knowledge management, Workforce focus, Process management, and Results) where the evaluation is made over 1000 points and each category has its own weight. Since almost all the publications in the literature are based on crisp measurements and evaluations of the system performances, we proposed a multi attribute decision making (MADM) method using interval valued Pythagorean fuzzy weighted averaging (IVPFWA) and interval valued Pythagorean fuzzy weighted geometric (IVPFWG) aggregation operators for MBNQA assessment to represent the decision makers’ subjective evaluations better. A comparison of the results with Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method and an illustrative example are presented in the study.

Keywords

Malcolm Baldrige National Quality Award interval-valued Pythagorean fuzzy sets multi attribute decision making interval-valued Pythagorean fuzzy aggregation operators

1 Introduction

Total quality management (TQM) is a well-known approach being applied by organizations to improve their process quality, process efficiency, and customer satisfaction by intending to achieve impeccable outcomes in order to survive in today’s extremely competitive business world. MBNQA, European Foundation for Quality Management (EFQM) Excellence Award, and Deming Prize are the most frequently considered quality award models by the companies as a guide of TQM implementation.

MBNQA was introduced by U.S congress in 1987 and being presented in six categories: manufacturing, service, small business, education, health care, and nonprofit. The assessments depend on seven criteria groups as listed below with their explanations.

Leadership: How the organization is led by the upper management and how it leads within the community.

Strategy: How the strategic goals are determined and planned to be performed by the organization.

Customers: How relationships with customers are constituted and sustained by the organization.

Measurement, analysis, and knowledge management: How the knowledge and information are used to support key operations and manage the performance of the organization.

Workforce: How the workforce of the organization is authorized and comprised.

Operations: How the key operations of the organization are planned, maintained, and developed.

Results: How the organization performs and compares to its competitors.

These seven criteria groups are divided into 18 criteria where their total scores are equal to 1,000. In the literature their evaluations mostly depend on crisp values. However, fuzzy representations of their assessments can be more accurate to develop a better evaluation method due to their enhanced ability to represent the vagueness and impreciseness in real-life scenarios.

The most frequently used fuzzy sets are shown in Fig. 1 in a chronological order with their developers.

Fig. 1

Most frequently used fuzzy sets.

Fuzzy set theory was introduced to the literature by Zadeh [25]. The first type of fuzzy sets is ordinary fuzzy sets, which are represented by only a membership degree for an x value as given in Equation (1).

$\tilde{A} = {(x, μ (x)) | x \in X}$ (1) where X represents the universe, 0 ≤ μ (x) ≤ 1 and the non-membership degree equals to 1-μ (x).

Zadeh [26] developed type-2 fuzzy sets since ordinary fuzzy sets were criticized by some researchers. A type-2 fuzzy set $\tilde{\tilde{A}}$ in the universe of discourse X which can be represented by a type-2 membership function $μ_{\tilde{\tilde{A}}}$ is given as $\tilde{\tilde{A}} = {\begin{matrix} ((x, u), μ_{\tilde{\tilde{A}}} (x, u)) | \forall x \in X, \\ \forall u \in J_{x} \subseteq [0, 1], 0 \leq μ_{\tilde{\tilde{A}}} (x, u) \leq 1 \end{matrix}}$ (2) where J_x denotes an interval [0, 1]. Moreover, $\tilde{\tilde{A}}$ represented by: $\tilde{\tilde{A}} = \int_{x \in X} \int_{u \in J_{x}} μ_{\tilde{\tilde{A}}} (x, u) / (x, u)$ where ∬ denotes union over all admissible x and u.

Intuitionistic fuzzy sets (IFSs) are developed as a generalization of Zadeh’s ordinary fuzzy sets by Atanassov [24]. These sets involve the degrees of membership and non-membership together with experts’ hesitancies.

Let U be a universe of discourse. An IFS $\tilde{A}$ is an object having the form, $\tilde{A} = {〈 u, (μ_{\tilde{A}} (u), ν_{\tilde{A}} (u)) | u \in U}$ (3) where the function $μ_{\tilde{A}} : U \to [0, 1], ν_{\tilde{A}} : U \to [0, 1]$ and $0 \leq μ_{\tilde{A}} (u) + v_{\tilde{A}} (u) \leq 1$ are the degree of membership, non-membership of u to $\tilde{A}$ , respectively. For any IFS $\tilde{A}$ and u ∈ U, $π_{\tilde{A}} = 1 - μ_{\tilde{A}} (u) - ν_{\tilde{A}} (u)$ is called degree of hesitancy of u to $\tilde{A}$ .

Neutrosophic sets are introduced by Smarandache [12] to the literature. Let U be a universe of discourse. Neutrosophic set $\tilde{A}$ in U is an object having the form, $\tilde{A} = {〈 u, (T_{\tilde{A}} (u), I_{\tilde{A}} (u), F_{\tilde{A}} (u)) | u \in U}$ (4) where, $T_{\tilde{A}}$ is the truth-membership function, $I_{\tilde{A}}$ is the indeterminacy-membership function and $F_{\tilde{A}}$ is the falsity-membership function. There is no restriction on their sum and so $0 \leq T_{\tilde{A}} (u) + I_{\tilde{A}} (u) + F_{\tilde{A}} (u) \leq 3$ .

Hesitant fuzzy sets are developed by Torra [44] and defined as follows: $E = {〈 x, h_{E} (x) : x \in X 〉}$ (5) where h_E (x) shows that possible membership degrees of the element x ∈ X to the set E.

Pythagorean fuzzy sets (PFSs) are developed by Yager [36]. Let U be a universe of discourse. A PFS $\tilde{P}$ is an object having the form, $\tilde{P} = {〈 u, (μ_{\tilde{p}} (u), ν_{\tilde{p}} (u)) | u \in U}$ (6) where the function $μ_{\tilde{p}} : U \to [0, 1], ν_{\tilde{p}} : U \to [0, 1]$ and $0 \leq μ_{\tilde{p}}^{2} (u) + v_{\tilde{p}}^{2} (u) \leq 1$ are the degree of membership, non-membership of u to P, respectively. For any PFS $\tilde{A}$ and u ∈ U, $π_{\tilde{p}} = (1 - μ_{\tilde{p}}^{2} (u) - ν_{\tilde{p}}^{2} (u))^{1 / 2}$ is called degree of hesitancy of u to $\tilde{P}$ .

Kutlu Gündoğdu and Kahraman [11] developed the spherical fuzzy sets. Spherical fuzzy sets ${\tilde{A}}_{S}$ of the universe of discourse U is given by ${\tilde{A}}_{S} = {〈 u, μ_{{\tilde{A}}_{S}} (u), ν_{{\tilde{A}}_{S}} (u), π_{{\tilde{A}}_{S}} (u) | u \in U 〉}$ (7) where $μ_{{\tilde{A}}_{S}} : U \to [0, 1], ν_{{\tilde{A}}_{S}} : U \to [0, 1], π_{{\tilde{A}}_{S}} : U \to [0, 1]$ and $0 \leq μ_{{\tilde{A}}_{S}}^{2} (u) + ν_{{\tilde{A}}_{S}}^{2} (u) + π_{{\tilde{A}}_{S}}^{2} (u) \leq 1$ . For each u, the numbers $μ_{{\tilde{A}}_{S}} (u), ν_{{\tilde{A}}_{S}} (u)$ and $π_{{\tilde{A}}_{S}} (u)$ are the degree of membership, non-membership and hesitancy of u to ${\tilde{A}}_{S}$ , respectively.

Since PFSs extend the set of possible values that membership and non-membership degrees can take, they provide higher flexibility for dealing with uncertainty. It is geometrically shown in Fig. 2 that PFSs gives a wider coverage for information span than IFSs.

Fig. 2

IFSs and PFSs comparison.

Therefore, we presented a MADM method using IVPFWA and IVPFWG aggregation operators for MBNQA assessment. We compared the results with IVPF TOPSIS method.

The rest of this study is organized as follows. Section 2 presents a literature review on MBNQA assessment. Section 3 gives the preliminaries for IVPFSs. Section 4 develops MADM methods using IVPF aggregation operators for MBNQA assessment. Section 5 illustrates the application of the proposed model. Section 6 presents a comparative analysis for the results with TOPSIS method. Section 7 concludes the paper with future directions.

2 MBNQA assessment under fuzziness: A literature review

A literature review on MBNQA based on Scopus database gave a list of 341 publications when the MBNQA keyword search is limited into article titles, abstracts, and keywords. Figure 3 shows the distribution of the MBNQA publications with respect to years.

Fig. 3

Distribution of the MBNQA publications with respect to years.

After the first study about MBNQA was published in 1989, the highest publication rate was attained in 1994 and 2004 with 19 studies each.

As it is given in Fig. 4, most of the MBNQA studies are in article form which is followed by conference papers and reviews.

Fig. 4

Document types distributions of MBNQA publications.

MBNQA assessment has been applied to many subject areas and Fig. 5 shows their frequencies. Business, management and accounting (BMA) and engineering are the most frequently applied subjects respectively.

Fig. 5

Document types distributions of MBNQA publications.

Some representative MBNQA studies are given below considering their development over the years.

Amsden and Amsden [37] aimed to search whether the MBNQA can serve as similar national quality prizes for quality improvement by American organizations by analyzing the requirements, scope and purpose of both quality awards. Dooley et al. [18] discussed the goals, criteria, and administration of the MBNQA and compared with the Deming Prize. Reimann and Haines [5] discussed the scoring criteria and the evaluation process of the four elements of MBNQA (leadership, system, quality results, customer satisfaction) which are further divided into seven categories. Wever and Vorhauer [13] described a matrix based on categories adapted from MBNQA process and developed an assessment tool to measure the progress toward environmental management excellence. Yarborough [4] evaluated the value of the MBNQA on occupational health services. Jordan [9] described how the Baldrige criteria can be used to improve an organization’s overall operational performance and competitiveness. Matta et al. [20] presented several propositions that derived from a study of MBNWQA winners regarding the implementation of TQM. Bantham and Bobrowski [16] developed an organizing framework for exploring buyer-supplier partnerships using the MBNQA criteria. Wilson and Collier [7] presented an empirical study to test the impact of the criteria weights implied in the MBNQA on firm performance and customer satisfaction. Wu et al. [15] designed a questionnaire based on the seven categories of the MBNQA criteria to assist organizations in conducting self-evaluations of their TQM programs. Puay et al. [39] compared the nine major national quality awards (three European, two North American, three Asia Pacific and one South American) including MBNQA. Prybutok and Spink [43] developed a survey for the health care industry based on the MBNQA criteria to assess the executives’ perceptions of current Baylor health care system quality practices. Wilson and Collier [6] tested the theory and causal performance linkages implied by the MBNQA. Angell [27] explored whether the best-practice quality firms leverage their quality programs for environmental management by comparing the implementation of successful and unsuccessful quality and environmental initiatives in five manufacturing- and five service-sector MBNQA winners. Khoo and Tan [14] compared the distinctive differences and overlapping concepts between the US and Japanese approach to TQM, regarding the countries’ quality award (MBNQA, Japanese Deming Prize, and the Japan Quality Award) frameworks and criteria. Prybutok and Cutshall [42] used a MBNQA criteria-based survey to assess the quality status of organizations that employ quality professionals. Badri et al. [29] empirically tested the causal relationships in the MBNQA Education Performance Excellence Criteria. Sohn et al. [40] adopted MBNQA criteria to assess the R&D environmental factors of recipient companies. Tai [28] examined the synchronous and lagged relationships between CEOs’ pay and the performance of a group of public companies that had won MBNQA. Kuo et al. [41] utilized a survey instrument tied to MBNQA criteria to examine the effectiveness of ISO 9000 implementations towards TQM practices and operational performance from employees’ perspective. Chen [3] established a total quality improvement framework based on quality function deployment by integrating the MBNQA and a balanced scorecard. Lee and Lee [8] compared six best-known quality awards including MBNQA to identify common quality award criteria. Jones [34] identified the critical factors that predict quality management program success using the MBNQA Criteria for Performance Excellence framework as a measurement proxy. Mellat-Parast [32] investigated the relationships among the MBNQA criteria using a unique data set: the independent reviewers’ scores. Ismail et al. [35] evaluated the interrelationships between the EFQM excellence model and information systems criterion of MBNQA model in the higher education institutions of Malaysia. Sudheer Muhammed et al. [21] utilized MBNQA criteria to measure and evaluate performance in the healthcare system. Miller and Parast [17] examined whether organizations improve their quality performance after applying for the MBNQA. Shokri [1] investigated the gap between the current vision and knowledge of future early career operations leaders and common strategic TQM frameworks such as MBNQA and competing value framework. Parast and Golmohammadi [33] investigated the determinants of customer satisfaction and quality results using the Baldrige data in the healthcare industry. Asif [30] investigated the relationships between participative leadership, administrative quality, medical quality, and patient satisfaction using the MBNQA healthcare criteria.

There is a limited number of publications in the literature that studies MBNQA assessment under fuzziness. Lam et al. [19] proposed a MBNQA-oriented self-assessment quality management system based on the seven criteria group of MBNQA to constitute contractors to benchmark and applied fuzzy analytical hierarchy (AHP) process method to calculate the weights of criteria by conducting a questionnaire survey. They compared the fuzzy method results with the original weights of MBNQA. Zohrabi and Manteghi [2] used fuzzy screening technique based on MBNQA education criteria group for selecting competitive strategies for education-al organizations. Jaeger et al. [31] used fuzzy AHP to calculate the weights and sub-sequent ranking of seven quality criteria group of MBNQA. Aydın and Kahraman [38] developed a new AHP-based fuzzy multi-criteria decision-making approach to measure the performance excellence of firms applying for MBNQA.

3 Interval-valued Pythagorean fuzzy sets: Preliminaries

This section reviews some basic definitions related to IVPSs on the set X.

Definition 1. Peng and Yang [45] introduced IVPFSs. Let Int([0,1]) denote the set of all closed subintervals of [0,1], and X be a universe of discourse. An IVPFS $\tilde{P}$ in X is given by $\tilde{P} = {〈 x, μ_{p} (x), v_{p} (x) 〉 | x \in X}$ (8) where the functions μ_p: X ⟶ Int([0, 1])(x ∈ X ⟶ μ_p(x) ⊆ [0, 1]) and v_p: X ⟶ Int([0, 1])(x ∈ X ⟶ v_p(x) ⊆ [0, 1]) denote the membership degree and non-membership degree of the element x ∈ X to the set $\tilde{P}$ , respectively, and for every x ∈ X, 0≤sup{ (μ_p (x)) ²} + sup{ (v_p (x)) ²}≤1. Also, for each x ∈ X,μ_p(x) and v_p(x) are closed intervals and their lower and upper bounds are denoted by $μ_{p}^{L} (x)$ , $μ_{p}^{U} (x)$ , $v_{p}^{L} (x)$ , $v_{p}^{U} (x)$ , respectively. Therefore, $\tilde{P}$ can also be expressed in another style as follows: $\tilde{P} = {〈 \begin{matrix} x, [μ_{p}^{L} (x), μ_{p}^{U} (x)], \\ [v_{p}^{L} (x), v_{p}^{U} (x)] \end{matrix} 〉 | x \in X}$ (9)

The degree of indeterminacy is given by Equation (10): $π_{P} (x) = (\begin{matrix} \sqrt{1 - {(μ_{p}^{U} (x))}^{2} - {(v_{p}^{U} (x))}^{2}}, \\ \sqrt{1 - {(μ_{p}^{L} (x))}^{2} - {(v_{p}^{L} (x))}^{2}} \end{matrix})$ (10)

Definition 2. Let $\tilde{A} = [μ_{A}^{L}, μ_{A}^{U}], [v_{A}^{L}, v_{A}^{U}]$ , $\tilde{B} = [μ_{B}^{L}, μ_{B}^{U}], [v_{B}^{L}, v_{B}^{U}]$ be two IVPF numbers, and λ > 0, then some operations of IVPF numbers are defined as follows [45]: $\tilde{A} \oplus \tilde{B} = (\begin{matrix} [\begin{matrix} \sqrt{(μ_{A}^{L})^{2} + {(μ_{B}^{L})}^{2} - {(μ_{A}^{L})}^{2} {(μ_{B}^{L})}^{2}}, \\ \sqrt{(μ_{A}^{U})^{2} + {(μ_{B}^{U})}^{2} - {(μ_{A}^{U})}^{2} {(μ_{B}^{U})}^{2}} \end{matrix}], \\ [v_{A}^{L} v_{B}^{L}, v_{A}^{U} v_{B}^{U}] \end{matrix})$ (11) $\tilde{A} \otimes \tilde{B} = (\begin{matrix} [μ_{A}^{L} μ_{B}^{L}, μ_{A}^{U} μ_{B}^{U}], \\ [\begin{matrix} \sqrt{(v_{A}^{L})^{2} + (v_{B}^{L})^{2} - (v_{A}^{L})^{2} (v_{B}^{L})^{2}}, \\ \sqrt{(v_{A}^{U})^{2} + (v_{B}^{U})^{2} - (v_{A}^{U})^{2} (v_{B}^{U})^{2}} \end{matrix}] \end{matrix})$ (12) $λ \tilde{A} = (\begin{matrix} [\begin{matrix} \sqrt{1 - {(1 - {(μ_{A}^{L})}^{2})}^{λ}}, \\ \sqrt{1 - {(1 - {(μ_{A}^{U})}^{2})}^{λ}} \end{matrix}], \\ [{(v_{A}^{L})}^{λ}, {(v_{A}^{U})}^{λ}] \end{matrix})$ (13) ${(\tilde{A})}^{λ} = (\begin{matrix} [{(μ_{A}^{L})}^{λ}, {(μ_{A}^{U})}^{λ}], \\ [\begin{matrix} \sqrt{1 - {(1 - {(ν_{A}^{L})}^{2})}^{λ}}, \\ \sqrt{1 - {(1 - {(ν_{A}^{U})}^{2})}^{λ}} \end{matrix}] \end{matrix})$ (14)

Definition 2. Let ${\tilde{A}}_{i}$ be a collection of IVPF numbers. Then, IVPFWA [22] and IVPFWG [23] aggregation operators can be defined as in Equations (15) and (16) respectively.

$\begin{matrix} {IVPFWA}_{λ} ({\tilde{A}}_{1}, {\tilde{A}}_{2}, {\tilde{A}}_{3}, \dots, {\tilde{A}}_{k}) \\ = (\begin{matrix} [\begin{matrix} \sqrt{1 - \prod_{i = 1}^{k} {(1 - {(μ_{A_{i}}^{L})}^{2})}^{λ_{i}}}, \\ \sqrt{1 - \prod_{i = 1}^{k} {(1 - {(μ_{A_{i}}^{U})}^{2})}^{λ_{i}}} \end{matrix}], \\ [\prod_{i = 1}^{k} {(ν_{A_{i}}^{L})}^{λ_{i}}, \prod_{i = 1}^{k} {(ν_{A_{i}}^{U})}^{λ_{i}}] \end{matrix}) \end{matrix}$ (15)

$\begin{matrix} {IVPFWG}_{λ} ({\tilde{A}}_{1}, {\tilde{A}}_{2}, {\tilde{A}}_{3}, \dots, {\tilde{A}}_{k}) \\ = (\begin{matrix} [\prod_{i = 1}^{k} (μ_{A_{i}}^{L})^{λ_{i}}, \prod_{i = 1}^{k} (μ_{A_{i}}^{U})^{λ_{i}}], \\ [\begin{matrix} \sqrt{1 - \prod_{i = 1}^{k} {(1 - {(ν_{A_{i}}^{L})}^{2})}^{λ_{i}}}, \\ \sqrt{1 - \prod_{i = 1}^{k} {(1 - {(ν_{A_{i}}^{U})}^{2})}^{λ_{i}}} \end{matrix}] \end{matrix}) \end{matrix}$ (16) where λ = (λ₁, λ₂, …, λ_k) ^T is the weighted vector of ${\tilde{A}}_{i}$ (i = 1,2, ... ,k) with λ_iɛ [0, 1] and $\sum_{i = 1}^{k} λ_{i} = 1$ .

Definition 3. For any IVPF number $\tilde{p} = ([μ_{p}^{L} (x), μ_{p}^{U} (x)], [v_{p}^{L} (x), v_{p}^{U} (x)])$ , score and accuracy functions of $\tilde{p}$ is defined respectively as follows [31]: $s (\tilde{p}) = \frac{1}{2} [{(μ_{p}^{L})}^{2} + {(μ_{p}^{U})}^{2} - {(v_{p}^{L})}^{2} - {(v_{p}^{U})}^{2}]$ (17) $a (\tilde{p}) = \frac{1}{2} [{(μ_{p}^{L})}^{2} + {(μ_{p}^{U})}^{2} + {(v_{p}^{L})}^{2} + {(v_{p}^{U})}^{2}]$ (18)

4 MADM using IVPF operators for MBNQA assessment

MADM methods are one of the most studied and applied fields of the decision science. Various methods have been proposed to deal with choosing, ranking, or classifying available alternatives. Since traditional MADM methods mostly fail to represent uncertainty and the vagueness in the parameters, fuzzy MADM techniques have developed. Based on IVPFWA and IVPFWG aggregation operators, we proposed an approach for MADM under the environment of IVPFSs to rank the alternatives and select the best MBNQA candidate as shown below in 4 steps:

Let A ={ A₁, A₂, …, A_n } be a set of n alternatives, C ={ C₁, C₂, …, C_m } be the set of m criteria, and λ = (λ₁, λ₂, …, λ_m) ^T be the weighted vector of the criteria, C_i(i = 1,2, ... ,m) with λ_iɛ [0, 1] and $\sum_{i = 1}^{m} λ_{i} = 1$ .

Step 1. Collect the information from the decision maker to construct the decision matrix.

Step 2. Compute $a_{j} = ([μ_{a_{j}}^{L} (x), μ_{a_{j}}^{U} (x)]$ , $[v_{a_{j}}^{L} (x)$ , $v_{a_{j}}^{U} (x)])$ (j = 1, 2, …, n) by using the IVPFWA and IVPFWG aggregation operators given in Equations (15) and (16).

Step 3. Compute the scores of a_j by using the score function given in Equation (17).

Step 4. Rank the scores of the alternatives with respect to each aggregation operator and select the company with the highest value.

5 IVPF-MBNQA assessment system application

Suppose that 4 car manufacturers A₁, A₂, A₃ and A₄ are being evaluated according to MBNQA criteria C_m(m = 1, ... , 18) for performance excellence. The weight vector of C_m is λ = (0.07, 0.05, 0.04, 0.045, 0.04, 0.045, 0.045, 0.045, 0.045, 0.04, 0.035, 0.05, 0.1, 0.07, 0.07, 0.07, 0.07, 0.07)^T where λ values are normalized point values since $\sum_{i = 1}^{m} λ_{i}$ should be equal to 1.

Step 1. The decision-maker gave his/her decision as given in Table 2 by using Table 1.

Table 1
Criteria for performance excellence [38]

Criteria groups Criteria Point values

Leadership Senior Leadership (C₁) 70

Governance and Social Responsibilities (C₂) 50

Strategic Planning Strategy Development (C₃) 40

Strategy Deployment (C₄) 45

Customer Focus Customer Engagement (C₅) 40

Voice of the Customer (C₆) 45

Measurement, Analysis, and Knowledge Management Measurement, Analysis, and Improvement of Organizational Performance (C₇) 45

Management of Information, Knowledge, and Information Technology (C₈) 45

Workforce Focus Workforce Systems (C₉) 45

Workforce Environment (C₁₀) 40

Process Management Work Systems (C₁₁) 35

Work Processes (C₁₂) 50

Results Product Outcomes (C₁₃) 100

Customer-Focused Outcomes (C₁₄) 70

Financial and Market Outcomes (C₁₅) 70

Workforce-Focused Outcomes (C₁₆) 70

Process Effectiveness Outcomes (C₁₇) 70

Leadership Outcomes (C₁₈) 70

TOTAL POINTS 1000

Criteria groups	Criteria	Point values
Leadership	Senior Leadership (C₁)	70
	Governance and Social Responsibilities (C₂)	50
Strategic Planning	Strategy Development (C₃)	40
	Strategy Deployment (C₄)	45
Customer Focus	Customer Engagement (C₅)	40
	Voice of the Customer (C₆)	45
Measurement, Analysis, and Knowledge Management	Measurement, Analysis, and Improvement of Organizational Performance (C₇)	45
	Management of Information, Knowledge, and Information Technology (C₈)	45
Workforce Focus	Workforce Systems (C₉)	45
	Workforce Environment (C₁₀)	40
Process Management	Work Systems (C₁₁)	35
	Work Processes (C₁₂)	50
Results	Product Outcomes (C₁₃)	100
	Customer-Focused Outcomes (C₁₄)	70
	Financial and Market Outcomes (C₁₅)	70
	Workforce-Focused Outcomes (C₁₆)	70
	Process Effectiveness Outcomes (C₁₇)	70
	Leadership Outcomes (C₁₈)	70
	TOTAL POINTS	1000

Table 2

IVPF decision matrix

	A₁	A₂	A₃	A₄
C₁	([0.65, 0.80], [0.25, 0.40])	([0.30, 0.45], [0.60, 0.70])	([0.50, 0.65], [0.35, 0.40])	([0.45, 0.50], [0.25, 0.35])
C₂	([0.60, 0.80], [0.50, 0.60])	([0.40, 0.55], [0.30, 0.50])	([0.65, 0.75], [0.55, 0.65])	([0.60, 0.75], [0.50, 0.55])
C₃	([0.80, 0.85], [0.30, 0.45])	([0.35, 0.50], [0.55, 0.80])	([0.85, 0.95], [0.25, 0.30])	([0.55, 0.65], [0.30, 0.60])
C₄	([0.60, 0.70], [0.25, 0.50])	([0.55, 0.60], [0.25, 0.50])	([0.55, 0.70], [0.30, 0.60])	([0.25, 0.50], [0.30, 0.75])
C₅	([0.70, 0.75], [0.40, 0.65])	([0.30, 0.45], [0.60, 0.70])	([0.35, 0.45], [0.55, 0.80])	([0.85, 0.90], [0.35, 0.40])
C₆	([0.30, 0.50], [0.55, 0.80])	([0.65, 0.70], [0.30, 0.65])	([0.85, 0.90], [0.30, 0.35])	([0.65, 0.70], [0.30, 0.60])
C₇	([0.90, 0.95], [0.20, 0.25])	([0.75, 0.85], [0.40, 0.45])	([0.50, 0.55], [0.55, 0.80])	([0.20, 0.45], [0.60, 0.75])
C₈	([0.20, 0.45], [0.60, 0.70])	([0.40, 0.50], [0.60, 0.70])	([0.40, 0.60], [0.70, 0.80])	([0.55, 0.70], [0.35, 0.60])
C₉	([0.45, 0.50], [0.65, 0.70])	([0.35, 0.40], [0.75, 0.80])	([0.45, 0.50], [0.65, 0.70])	([0.70, 0.75], [0.30, 0.55])
C₁₀	([0.50, 0.60], [0.20, 0.50])	([0.45, 0.50], [0.30, 0.70])	([0.45, 0.60], [0.45, 0.50])	([0.35, 0.50], [0.50, 0.80])
C₁₁	([0.50, 0.65], [0.30, 0.55])	([0.55, 0.75], [0.30,0.60])	([0.25, 0.40], [0.60, 0.70])	([0.60, 0.65], [0.25, 0.50])
C₁₂	([0.35, 0.50], [0.50, 0.85])	([0.45, 0.50], [0.35, 0.55])	([0.65, 0.75], [0.30, 0.60])	([0.55, 0.60], [0.30, 0.40])
C₁₃	([0.60, 0.75], [0.20, 0.60])	([0.75, 0.85], [0.30, 0.35])	([0.65, 0.80], [0.40, 0.55])	([0.65, 0.70], [0.35, 0.60])
C₁₄	([0.90, 0.95], [0.15, 0.20])	([0.45, 0.60], [0.75, 0.80])	([0.45, 0.50], [0.50, 0.85])	([0.45, 0.50], [0.60, 0.75])
C₁₅	([0.65, 0.70], [0.35, 0.60])	([0.75, 0.80], [0.20, 0.25])	([0.60, 0.80], [0.50, 0.55])	([0.55, 0.65], [0.50, 0.70])
C₁₆	([0.70, 0.80], [0.20, 0.25])	([0.65,0.80], [0.20, 0.60])	([0.45, 0.50], [0.60, 0.70])	([0.90, 0.95], [0.20, 0.30])
C₁₇	([0.45, 0.65], [0.40, 0.50])	([0.70, 0.75], [0.35, 0.60])	([0.90, 0.95], [0.10, 0.15])	([0.45, 0.60], [0.75, 0.80])
C₁₈	([0.60, 0.75], [0.40, 0.45])	([0.65,0.70], [0.30, 0.60])	([0.30, 0.50], [0.55, 0.80])	([0.45, 0.55], [0.70, 0.80])

Step 2. We computed a_j (j = 1, 2, 3, 4) values with respect to IVPFWA and IVPFWG aggregation operators as given in Table 3.

Table 3

a_j values with respect to aggregation operators

a_j values	IVPFWA	IVPFWG
a ₁	$(\begin{matrix} [0.6308, 0.7479], \\ [0.3394, 0.5076] \end{matrix})$	$(\begin{matrix} [0.5605, 0.5997], \\ [0.3810, 0.5715] \end{matrix})$
a ₂	$(\begin{matrix} [0.5909, 0.6897], \\ [0.3677, 0.5586] \end{matrix})$	$(\begin{matrix} [0.5216, 0.6281], \\ [0.4644, 0.6257] \end{matrix})$
a ₃	$(\begin{matrix} [0.6216, 0.7416], \\ [0.4103, 0.5481] \end{matrix})$	$(\begin{matrix} [0.5244, 0.6477], \\ [0.4850, 0.6553] \end{matrix})$
a ₄	$(\begin{matrix} [0.6085, 0.6985], \\ [0.3914, 0.5770] \end{matrix})$	$(\begin{matrix} [0.5175, 0.6310], \\ [0.4764, 0.6467] \end{matrix})$

Step 3. We found the scores of a_j (j = 1, 2, 3, 4) values as given in Table 4 with respect to IVPFWA and IVPFWG aggregation operators.

Table 4

a_j values with respect to aggregation operators

Scores of a_j values	IVPFWA	IVPFWG
s _{a ₁}	0.2923	0.1011
s _{a ₂}	0.1888	0.0297
s _{a ₃}	0.2338	0.0150
s _{a ₄}	0.1860	0.0104

Step 4. We ranked the MBNQA candidate companies (A₁, A₂, A₃, A₄) according to their scores with respect to the aggregation operators as shown in Table 5.

Table 5

Rankings of the MBNQA candidate companies

Rank	IVPFWA	IVPFWG
A ₁	1	1
A ₂	3	4
A ₃	2	2
A ₄	4	3

The first two companies are determined as A₁ and A₃ regardless the aggregation operators. On the contrary, rankings for the companies A₂ and A₄ are affected from the operators.

6 A comparative analysis with IVPF TOPSIS

TOPSIS method bases on the idea that the best alternative should have the shortest distance from the ideal solution and the farthest from the negative-ideal solution. Based on TOPSIS under the environment of IVPFSs, we compared the results of the MADM method using IVPFWA and IVPFWG aggregation operators. Steps of TOPSIS are shown below where:

C_i : i^thcriterion i = 1, 2, …, m

A_j : j^thalternative j = 1, 2, …, n

$[μ_{ij}^{L}, μ_{ij}^{U}], [v_{ij}^{L}, v_{ij}^{U}]$ : IVPF assessment value of j^th alternative with respect to i^th criterion

w_i is the weight of the i^th criterion or attribute and $\sum_{i = 1}^{m} = 1$ .

Step 1. Set the initial IVPF decision matrix ${\tilde{X}}_{ij}$ as in Equation (19). ${\tilde{X}}_{ij} = {[([μ_{ij}^{L}, μ_{ij}^{U}], [v_{ij}^{L}, v_{ij}^{U}])]}_{m \times n}$ (19)

Step 2. Determine the IVPF weighted decision matrix ${\tilde{X}}_{ij}^{'}$ , by using Equation (20). ${\tilde{X}}_{ij}^{'} = ([μ_{ij}^{L}, μ_{ij}^{U}], [v_{ij}^{L}, v_{ij}^{U}]) \otimes (w_{i})$ (20)

Step 3. Determine the ideal (A^*) and negative ideal (A^-) solutions as shown in Equations (21) and (22). $A^{*} = {\underset{j}{(\max} {\tilde{X}}_{ij}^{'} | i \in I), (\min_{j} {\tilde{X}}_{ij}^{'} | i \in I^{'}}$ (21) $A^{-} = {\underset{j}{(\min} {\tilde{X}}_{ij}^{'} | j \in J), (\max_{j} {\tilde{X}}_{ij}^{'} | i \in I^{'}}$ (22)

Step 4. Calculate the separation measures using the m-dimensional Euclidean distance. The separation measures of each alternative from the positive ideal solution and the negative ideal solution are given in Equations (23) and (24), respectively. $S_{j}^{*} = \sqrt{\sum_{i = 1}^{m} (\tilde{x}'_{ij} - \tilde{x}'_{i}^{*})^{2}}$ (23) $S_{j}^{-} = \sqrt{\sum_{i = 1}^{m} (\tilde{x}'_{ij} - \tilde{x}'_{i}^{-})^{2}}$ (24)

Step 5. Calculate the relative closeness to the ideal solution. The relative closeness of the alternative A_j with respect to A^* is defined in Equation (25). Finally, rank the preference order. ${RC}_{j}^{*} = \frac{S_{j}^{-}}{S_{j}^{-} + S_{j}^{*}}$ (25)

Application of the given IVPF TOPSIS method on the illustrative example is presented below in steps.

Step 1. Initial IVPF decision matrix ${\tilde{X}}_{ij}$ is formed as given in Table 2.

Step 2. IVPF weighted decision matrix ${\tilde{X}}_{ij}^{'}$ is determined by using Equation (20) as shown in Table 6.

Table 6

IVPF weighted decision matrix

	A₁	A₂	A₃	A₄
C₁	([0.194, 0.263], [0.908, 0.938])	([0.081, 0.125], [0.965, 0.975])	([0.141, 0.194], [0.929, 0.938])	([0.125, 0.141], [0.908, 0.929])
C₂	([0.149, 0.223], [0.966, 0.975])	([0.093, 0.134], [0.942, 0.966])	([0.165, 0.201], [0.971, 0.979])	([0.149, 0.201], [0.966, 0.971])
C₃	([0.200, 0.224], [0.953, 0.969])	([0.072, 0.107], [0.976, 0.991])	([0.224, 0.298], [0.946, 0.953])	([0.120, 0.147], [0.953, 0.980])
C₄	([0.141, 0.173], [0.940, 0.969])	([0.127, 0.141], [0.940, 0.969])	([0.127, 0.173], [0.947, 0.977])	([0.054, 0.113], [0.947, 0.987])
C₅	([0.163, 0.180], [0.964, 0.983])	([0.061, 0.095], [0.980, 0.986])	([0.072, 0.095], [0.976, 0.991])	([0.224, 0.254], [0.959, 0.964])
C₆	([0.065, 0.113], [0.973, 0.990])	([0.156, 0.173], [0.947, 0.981])	([0.237, 0.268], [0.947, 0.954])	([0.156, 0.173], [0.947, 0.977])
C₇	([0.268, 0.315], [0.930, 0.940])	([0.191, 0.237], [0.960, 0.965])	([0.113, 0.127], [0.973, 0.990])	([0.043, 0.101], [0.977, 0.987])
C₈	([0.043, 0.101], [0.977, 0.984])	([0.088, 0.113], [0.977, 0.984])	([0.088, 0.141], [0.984, 0.990])	([0.127, 0.173], [0.954, 0.977])
C₉	([0.101, 0.113], [0.981, 0.984])	([0.077, 0.088], [0.987, 0.990])	([0.101, 0.113], [0.981, 0.984])	([0.173, 0.191], [0.947, 0.973])
C₁₀	([0.107, 0.133], [0.938, 0.973])	([0.095, 0.107], [0.953, 0.986])	([0.095, 0.133], [0.969, 0.973])	([0.072, 0.107], [0.973, 0.991])
C₁₁	([0.100, 0.138], [0.959, 0.979])	([0.112, 0.169], [0.959,0.982])	([0.048, 0.078], [0.982, 0.988])	([0.124, 0.138], [0.953, 0.976])
C₁₂	([0.081, 0.120], [0.966, 0.992])	([0.106, 0.120], [0.949, 0.971])	([0.165, 0.201], [0.942, 0.975])	([0.134, 0.149], [0.942, 0.955])
C₁₃	([0.209, 0.282], [0.851, 0.950])	([0.282, 0.347], [0.887, 0.900])	([0.231, 0.312], [0.912, 0.942])	([0.231, 0.255], [0.900, 0.950])
C₁₄	([0.331, 0.388], [0.876, 0.893])	([0.125, 0.175], [0.980, 0.985])	([0.125, 0.141], [0.953, 0.989])	([0.125, 0.141], [0.965, 0.980])
C₁₅	([0.194, 0.215], [0.929, 0.965])	([0.237, 0.263], [0.893, 0.908])	([0.175, 0.263], [0.953, 0.959])	([0.158, 0.194], [0.953, 0.975])
C₁₆	([0.215, 0.263], [0.893, 0.908])	([0.194,0.263], [0.893, 0.965])	([0.125, 0.141], [0.965, 0.975])	([0.331, 0.388], [0.893, 0.919])
C₁₇	([0.125, 0.194], [0.938, 0.953])	([0.215, 0.237], [0.929, 0.965])	([0.331, 0.388], [0.851, 0.876])	([0.125, 0.175], [0.980, 0.985])
C₁₈	([0.175, 0.237], [0.938, 0.946])	([0.194,0.215], [0.919, 0.965])	([0.081, 0.141], [0.959, 0.985])	([0.125, 0.158], [0.975, 0.985])

Step 3. Ideal (A^*) and negative ideal (A^-) solutions are determined by using Equations (21) and (22) as given in Table 7. In this step, first the scores of the values in the IVPF weighted decision matrix are calculated by using Equation (17) in order to be able to rank the IVPF values.

Table 7

Ideal (A^*) and negative ideal (A^-) solutions

	(A^*)	(A^-)
C₁	–0.279	0.420
C₂	0.061	0.195
C₃	–0.285	0.736
C₄	–0.170	0.269
C₅	–0.309	0.625
C₆	–0.301	0.660
C₇	–0.340	0.805
C₈	–0.305	0.155
C₉	–0.460	0.330
C₁₀	–0.259	0.160
C₁₁	–0.314	0.235
C₁₂	–0.300	0.268
C₁₃	0.215	0.536
C₁₄	–0.320	0.825
C₁₅	–0.007	0.550
C₁₆	–0.199	0.791
C₁₇	–0.320	0.840
C₁₈	–0.313	0.280

Step 4. The separation measures of each alternative from the positive ideal solution $(S_{j}^{*})$ and the negative ideal solution $(S_{j}^{-})$ are calculated by using Equations (23) and (24), respectively as in Table 8.

Table 8

Separation measures of each alternative from positive and negative ideal solutions

	$(S_{j}^{*})$	$(S_{j}^{-})$
A₁	1.6653	2.4116
A₂	2.3275	1.6689
A₃	2.3305	2.0535
A₄	2.3540	1.9748

Step 5. The relative closeness to the ideal solution is calculated by using Equation (25) as shown in Table 9. Finally, the alternatives are ranked.

Table 9

Relative closeness to the ideal solution

	${RC}_{j}^{*}$
A₁	0.5915
A₂	0.4176
A₃	0.4684
A₄	0.4562

Since the alternative with the higher relative closeness to the ideal solution has the higher rank and the alternative closest to the ideal solution is the best one, the ranking should be as A₁ > A₃ > A₄ > A₂.

Table 10 shows the comparison between three MADM methods’ results we used in this paper.

Table 10

Rankings of the MBNQA candidate companies regarding the MADM methods

Rank	IVPFWA	IVPFWG	IVPF TOPSIS
A ₁	1	1	1
A ₂	3	4	4
A ₃	2	2	2
A ₄	4	3	3

As can be seen in Table 10 that MADM method using IWPFWG aggregation operator and IVPF TOPSIS gave the same rankings. Only for MADM method using IWPFWA aggregation operator, the rankings of alternatives A₂ and A₄ are opposite according to the two other methods. By the results of the MADM methods we used, it can be concluded that the best MBNQA candidate is A₁ among the other companies.

7 Conclusion

MBNQA is a widely known excellence model that was established by the US congress in 1987 to raise awareness about quality and its importance for organizations. Up to 18 awards are given annually across seven categories ant the assessment is based on a scale of 0–1000 points. However, decision makers tend to use linguistic assessments rather than exact numerical values. Fuzzy set theory has been successfully applied to handle the vagueness and impreciseness in such evaluations since its introduction to the literature. Although, there are various publications on TQM assessments based on MBNQA in the literature, there was a large gap for its applications under fuzziness. In this paper (which is an extension of the conference paper [10]), to describe the fuzziness and ambiguity, the concept of IVPF sets is applied according to the degrees of membership and non-membership that are represented by flexible interval values that reflect the degree of hesitation and MADM methods using IVPFWA and IVPFWG aggregation operators for MBNQA assessment are proposed where the decision matrix is constructed by IVPFSs. A stepwise method is presented with an illustrative example for selecting the best candidate for MBNQA considering eighteen performance excellence criteria. A comparative analysis is performed using IVPF TOPSIS method. The results of the two MADM methods using IWPFWA and IWPFWG aggregation operators and the IVPF TOPSIS gave similar rankings. Only for MADM method using IWPFWA aggregation operator, the rankings of the last two alternatives are reverse of the two other methods.

For further research, we suggest a comparative analysis through q-rung orthopair fuzzy sets (q-ROFSs). A q-ROFS is represented by means of two membership degrees as truth and falsity where the summation of the q^th power of truth-membership and the q^th power of falsity-membership should be less than or equal to one. Since, q-ROFSs extend the concepts of IFSs and PFSs, it provides a wider range to deal with the uncertain information. Also, the results of the proposed methods can be compared with other IVPF aggregation operators such as IVPF ordered weighted geometric operator or IVPF hybrid geometric operator.

References

Shokri

, Investigating the view of quality management success factors amongst future early career operations leaders, International Journal of Quality and Service Sciences 11(4) (2019), 487–503.

Zohrabi

and Manteghi

, A proposed model for strategic planning in educational organizations, Procedia - Social and Behavioral Sciences 28 (2011), 205–210.

Chen

, Improvement of QFD-based total quality for local cultural industries: Procedural and empirical investigation, Journal of the Chinese Institute of Industrial Engineers 28(2) (2011), 124–133.

Yarborough

C.M.

, Baldrige value to occupational health services, Journal of Occupational Medicine 36(3) (1994), 334–337.

Reimann

C.W.

and Haines

R.A.

, Malcolm Baldrige national quality award, U.S.Woman Engineer 37(6) (1991), 11–14.

Wilson

D.D.

and Collier

D.A.

, An empirical investigation of the Malcolm Baldrige national quality award causal model, Decision Sciences 31(2) (2000), 361–383.

Wilson

and Collier

, Empirical study to test the impact of the criteria weights implied in the Malcolm Baldridge national quality award on firm performance and customer satisfaction, Proceedings - Annual Meeting of the Decision Sciences Institute 3 (1996), 1784–1786.

Lee

D.H.

and Lee

D.H.

, A comparative study of quality awards: Evolving criteria and research, Service Business 7(3) (2013), 347–362.

Jordan

D.W.

, Using the Baldrige criteria for self assessment, Engineering Management Journal 6(2) (1994), 16–19.

10.

Haktanır

and Kahraman

, Malcolm Baldrige National Quality Award Assessment Using Interval Valued Pythagorean Fuzzy Sets, in: Intelligent and Fuzzy Techniques in Big Data Analytics and Decision Making, C. Kahraman, S. Cebi, S. Cevik Onar, B. Oztaysi, A. Tolga, I. Sari, ed., Springer, 2020, pp. 1097–1103.

11.

Kutlu Gündoğdu

and Kahraman

, Spherical Fuzzy Sets and Spherical Fuzzy TOPSIS Method, Journal of Intelligent and Fuzzy Systems 36(1) (2019), 337–352.

12.

Smarandache

, Neutrosophy. Neutrosophic Probability, Set, And Logic, Proquest Information and Learning. Ann Arbor, Michigan, USA, 105 (1998).

13.

Wever

G.H.

and Vorhauer

G.F.

, Kodak’s framework and assessment tool for implementing TQEM, Environmental Quality Management 3(1) (1993), 19–30.

14.

Khoo

H.H.

and Tan

K.C.

, Managing for quality in the USA and japan: Differences between the MBNQA, DP and JQA, TQM Magazine 15(1) (2003), 14–24.

15.

, Wiebe

H.A.

and Politi

, Self-assessment of total quality management programs, Engineering Management Journal 9(1) (1997), 25–32.

16.

Bantham

J.H.

and Bobrowski

P.M.

, Using the Baldridge award criteria as an organizing framework for exploring buyer-supplier partnerships: A case study, Proceedings - Annual Meeting of the Decision Sciences Institute 3 (1996), 1232–1234.

17.

Miller

and Parast

M.M.

, Learning by applying: The case of the Malcolm Baldrige national quality award, IEEE Transactions on Engineering Management 66(3) (2019), 337–353.

18.

Dooley

K.J.

, Bush

, Anderson

J.C.

and Rungtusanatham

, The United States’ Baldrige award and Japan’s Deming prize: Two guidelines for total quality control, Engineering Management Journal 2(3) (1990), 9–16.

19.

Lam

, Lam

M.C.

and Wang

, MBNQA-oriented self-assessment quality management system for contractors: Fuzzy AHP approach, Construction Management and Economics 26(5) (2008), 447–461.

20.

Matta

, Davis

, Mayer

and Conlon

, Research questions on the implementation of total quality management, Total Quality Management 7(1) (1996), 39–50.

21.

Sudheer Muhammed

K.M.

, D’Souza

and Sheena

, Effective governance through quality in healthcare organizations: An empirical study, International Journal of Economic Research 14(18) (2017), 271–278.

22.

Rahman

, Ali

and Khan

M.S.A.

, Some Interval-Valued Pythagorean Fuzzy Weighted Averaging Aggregation Operators and Their Application to Multiple Attribute Decision Making, Journal of Mathematics 50(2) (2018), 113–129.

23.

Rahman

, Abdullah

, Shakeel

, Khan

M.S.

and Ullah

, Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem, Cogent Mathematics 4(1) (2017).

24.

Atanassov

K.T.

, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20(1) (1986), 87–96.

25.

Zadeh

L.A.

, Fuzzy Sets, Information and Control (1965), 338–353.

26.

Zadeh

L.A.

, The concept of a linguistic variable and its application to approximate reasoning, Information Sciences 8 (1975), 199–249.

27.

Angell

L.C.

, Comparing the environmental and quality initiatives of Baldrige award winners, Production and Operations Management 10(3) (2001), 306–326.

28.

Tai

L.S.

, Synchronous and lagged relationships between CEO pay and performance of quality companies, Managerial Finance 34(8) (2008), 555–561.

29.

Badri

M.A.

, Selim

, Alshare

, Grandon

E.E.

, Younis

and Abdulla

, The Baldrige education criteria for performance excellence framework: Empirical test and validation, International Journal of Quality and Reliability Management 23(9) (2006), 1118–1157.

30.

Asif

, Jameel

, Sahito

, Hwang

, Hussain

and Manzoor

, Can leadership enhance patient satisfaction? Assessing the role of administrative and medical quality, International Journal of Environmental Research and Public Health 16(17) (2019), 3212.

31.

Jaeger

, Adair

and Al-Qudah

, MBNQA criteria used in the GCC countries, The TQM Journal 25(2) (2013), 110–123.

32.

Mellat-Parast

, A longitudinal assessment of the linkages among the Baldrige criteria using independent reviewers’ scores, International Journal of Production Economics 164 (2015), 24–34.

33.

Parast

M.M.

and Golmohammadi

, Quality management in healthcare organizations: Empirical evidence from the Baldrige data, International Journal of Production Economics 216 (2019), 133–144.

34.

Jones

M.R.

, Identifying critical factors that predict quality management program success: Data mining analysis of Baldrige award data, Quality Management Journal 21(3) (2014), 49–61.

35.

Ismail

, Murad

M.A.A.

, Jabar

M.A.

, Nor

R.N.H.

and Mustapha

, Integration of EFQM excellence model and information systems criterion, Journal of Theoretical and Applied Information Technology 94(1) (2016), 18–30.

36.

Yager

R.R.

, Pythagorean fuzzy subsets, Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, (2013), 57–61.

37.

Amsden

R.T.

and Amsden

D.M.

, National quality prizes. drivers for total quality, Annual Quality Congress Transactions 44 (1990), 776–781.

38.

Aydın

and Kahraman

, Evaluation of firms applying to Malcolm Baldrige National Quality Award: a modified fuzzy AHP method, Complex & Intelligent Systems 5(1) (2019), 53–63.

39.

Puay

S.H.

, Tan

K.C.

, Xie

and Goh

T.N.

, A comparative study of nine national quality awards, TQM Magazine 10(1) (1998), 30–39.

40.

Sohn

S.Y.

, Gyu Joo

and Kyu Han

, Structural equation model for the evaluation of national funding on R&D project of SMEs in consideration with MBNQA criteria, Evaluation and Program Planning 30(1) (2007), 10–20.

41.

Kuo

, Chang

, Hung

and Lin

, Employees’ perspective on the effectiveness of ISO 9000 certification: A total quality management framework, Total Quality Management and Business Excellence 20(12) (2009), 1321–1335.

42.

Prybutok

and Cutshall

, Malcolm Baldrige national quality award leadership model, Industrial Management and Data Systems 104(7) (2004), 558–566.

43.

Prybutok

V.R.

and Spink

, Transformation of a health care information system: A self-assessment survey, IEEE Transactions on Engineering Management 46(3) (1999), 299–310.

44.

Torra

, Hesitant fuzzy sets, International Journal of Intelligent Systems (2010), 529–539.

45.

Peng

and Yang

, Fundamental Properties of Interval-Valued Pythagorean Fuzzy Aggregation Operators, International Journal of Intelligent Systems 31(5) (2016), 444–487.