Manufacturing companies contribute significantly to the economic evolution of any country. Due to rapid globalization, scarcity of resources and variations in demand patterns, manufacturing companies are gradually focusing toward innovative strategies for meeting the customer demands in today’s competitive and resource-constrained global landscape (Saha et al., 2025), while minimizing waste generation and maximizing resource efficiency (Sakib et al., 2025). In this context, Lean Six Sigma (LSS) has garnered increasing attention as a strategic methodology for improving quality, efficiency, responsiveness and environmental performance of a manufacturing organization (Ngouono et al., 2025; Widiwati et al., 2025). It combines Lean and Six Sigma principles to improve employee and company performance by eliminating resource waste and process/product flaws. The successful implementation of LSS enables organizations to enhance their performance by improving quality, reducing cycle time, minimizing wastes, along with creating value for customers (Cabeça et al., 2025; Corredor-Rojas et al., 2025).

In the recent past, Sustainable Lean Six Sigma (SLSS) comes to stand out as an innovative strategy for managing organizational sustainability performance, while optimizing their operations and reducing the waste materials and product defects (Utama and Abirfatin, 2023). The integration of sustainability and LSS results in SLSS, which has emerged as an effective methodology that focuses on economic, environmental and social aspects of a company together with the waste minimization and defects reduction in the business processes. Despite its importance, manufacturing companies encounter challenges when adopting SLSS into their business operations (Parmar and Desai, 2021). In this regard, manufacturers need to identify and prioritize the enablers for the effective operation of SLSS into business operations. Consequently, there is a need to assess and rank the enablers influencing SLSS adoption within a manufacturing organization.

Evaluating enablers requires an effective method to help the manufacturing organizations in implementing SLSS. Moreover, uncertainty significantly impacts the decision-making process, which necessitates the embracing of more advanced models able to managing such imprecise data. Zadeh (1965) offered a conceptual framework, namely Fuzzy Set (FS), for handling uncertainty in decision-making applications. It is characterized by the membership function that ranges from ‘0’ to ‘1’, signifying the degree of membership of an element in a set. The emergence of FS theory provided a potent tool for addressing ambiguity and uncertainty in practical issues (Alaoui et al., 2024; Adali and Tuş, 2025). Later, the theory of intuitionistic fuzzy set (IFS) has been introduced by Atanassov (1986). In IFS, an element is portrayed by the membership and non-membership degrees with their sum restricted to 1. As a generalization of FS theory, an IFS is regarded as a more effective way to confront uncertainty and ambiguity of real-world applications (Miliauskaitė and Kalibatiene, 2025).

Existing studies have documented the efforts to the development of theories and applications of IFS theory. Li et al. (2023) suggested a combined intuitionistic fuzzy (IF) decision-making model to distinguish and rank the key challenges for collaborative innovation projects. For the purpose, they incorporated the entropy model, Stepwise Weight Assessment Ratio Analysis (SWARA) and Measurement of Alternatives and Ranking according to the Compromise Solution (MARCOS) models under the context of IFSs. Deb et al. (2023) integrated the Weighted Aggregated Sum Product Assessment (WASPAS) and consensus reaching with IFSs, along with its application in open-source software learning management systems evaluation. Rani and Kumar (2023) presented new measures for finding the degree of discrimination and similarity between IFSs with their applicability in online shopping websites assessment. Salimian et al. (2023) introduced a collective IF-based decision-making model for assessing the sustainable construction projects under uncertain background. Hezam et al. (2023) identified the sustainability indicators using IFSs-based Symmetry Point of Criterion (SPC) and Rank-Sum (RS) models for the evaluation of biomass resources for biofuel formation. Kumar and Kumar (2024) presented new score and distance formulae in the setting of IFSs. Based on these measures, they proposed a combined IF-decision framework and utilized to deal with uncertainty of sustainable biomass crop selection problem. Within the framework of IFSs, Rani et al. (2025) developed a new distance based decision-making framework by combining MEthod based on the Removal Effects of Criteria (MEREC) and RS models with its relevance in the embracing of blockchain technology within the logistics sector. Ziquan et al. (2025) integrated the SWARA and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) approaches within the IF environment and further used to rank the risk factors of e-commerce supply chain. Mishra et al. (2025) developed an intuitionistic fuzzy extension of multi-attribute multi-objective optimisation based on the ratio analysis model considering score and distance measures, along with its application in solar power plant location selection problem.

Considering the advantages of IFS theory, this paper proposes an integrated IF-decision support model for estimating and ranking the enablers of SLSS adoption in Indian electric manufacturing companies. To this aim, we integrate the Weights by ENvelope and SLOpe (WENSLO) and Modified Preference Selection Index (MPSI) models under the context of IFSs, and develop a combined ranking framework, which has not yet been presented in the literature. Pamucar et al. (2023) proposed the idea of WENSLO method to determine the objective weighting, while Gligorić et al. (2022) developed the concept of MPSI model to derive the subjective weighting. A WENSLO is mainly effective for finding weight of attributes as it combines slope and envelope axioms of the decision-matrix. By uniting these two dimensions, the approach alleviates subjective bias and gives a more stable illustration of the relative significance of criteria. Contrasting purely judgment-based approaches, WENSLO originates weights directly from the decision-matrix, improving both robustness and transparency. This mixture of objectivity and sensitivity purifies WENSLO particularly appropriate for complex decision-making perspectives concerning multiple interdependent attributes. Further, MPSI method is based on the degree of the oscillation, i.e. variation in the preference value for each criterion. That variation actually presents the distance between normalized value and mean value per criterion and is expressed by using the Euclidean distance. MPSI method is characterized as a very simple and easy to understand approach for defining the objective weights of criteria. In this work, we consider the advantages of both the models by integrating them into a hybrid framework, named as IF-WENSLO-MPSI. In the following, the major contributions of this work in terms of methodology are listed below:

Other sections are settled in the following manner. In Section 2, we present the related studies. In Section 3, we firstly present the basic concepts related to this work. Secondly, we propose a modified IF-score formula for ranking intuitionistic fuzzy numbers. Lastly, we develop a new IF-distance formula for estimating the variation degree between IFSs. In Section 4, we present the stepwise procedure of an integrated IF-WENSLO-MPSI method. In Section 5, we implement the proposed IF-WENSLO-MPSI model on a case study of enablers analysis for SLSS adoption, validated through sensitivity and comparative discussions. Section 6 showcases the concluding remarks and suggested some insights for further study.

Enablers are defined as the critical and fundamental factors that can drive the smooth and efficient implementation of SLSS in business processes (Hussain et al., 2025). Existing literature attests the efforts on the evaluation of enablers for LSS adoption. Pandey et al. (2018) utilized Analytic Hierarchy Process (AHP) model for investigating the ranks of enablers influencing green LSS implementation. Kaswan and Rathi (2019) analysed the enablers persuading green LSS adoption in business operations. In addition, they investigated the interactions among these enablers by using an integrated interpretive structural modelling and Impact Matrix Cross-Reference Multiplication Applied to a Classification (MICMAC) based technique. Parmar and Desai (2020) used fuzzy Decision-Making Trial and Evaluation Laboratory (DEMATEL) technique for evaluating the enablers of SLSS in a manufacturing firm. Swarnakar et al. (2020) examined and evaluated the twenty-nine enablers for SLSS adoption using fuzzy MICMAC model within the manufacturing organization. With the use of best worst method, Singh et al. (2021) analysed and ordered the enablers of environmental LSS in Indian micro-small and medium organizations. Letchumanan et al. (2022) identified the main factors enabling the green LSS adoption and further provided a systematic methodology to conceptualise and set up the green LSS into the Malaysian electronics manufacturing sector. In a study, Singh and Rathi (2022) identified twenty-five enablers influencing LSS operation in Indian micro-small and medium firms, together with their prioritization through AHP model. Perez-Burgoin et al. (2024) acknowledged the enablers of green LSS and further investigated the associations between the considered enablers in the execution of green LSS in the Mexican manufacturing organization. As per author’s knowledge, there is no such literature available including WENSLO-MPSI in intuitionistic fuzzy environment to evaluate the enablers for SLSS adoption in manufacturing sector. Thus, it motivates us to employ the idea of intuitionistic fuzzy based WENSLO-MPSI in the assessment and prioritization of SLSS adoption enablers.

On the basis of existing studies, we acknowledge some research challenges, given as below: –

Existing works are unable to handle the intuitionistic fuzzy information-based SLSS enablers assessment problem, while IFS, as an extension of FS, is a more powerful tool to manage the uncertainty of a real-life application.

This section proposes a new IF-score formula together with score-induced IF-distance measure. Before these developments, we present the basic notions related to this study.

The present section introduces a hybrid framework combining the DEs’ weighting model, IF-aggregation operators, and integrated criteria weight-estimating model on IFSs. In the model, we present score function-based structure to obtain the weights of DEs and further aggregate an individual decision opinion of DE into an aggregated decision-matrix. Later, we integrate weight-estimating approach of attributes with WENSLO and MPSI methods on IFSs and obtain an integrated weight of each criterion. For this aim, let us consider an IF-information-based MCDM problem assuming a set of options M = { M 1 , M 2 , … , M r }, which has to be evaluated over criteria set F = { F 1 , F 2 , … , F s }. To choose an optimal alternative, a committee of ‘n’ DEs L = { L 1 , L 2 , … , L n } is created and asked them to use linguistic value (LV) for rating the performance of alternatives and criteria. Table 3 presents the LVs and their corresponding IFNs, adopted from Mishra et al. (2025).

Step 1: Derive the weights of experts.

In this step, we introduce a procedure to determine weights of DEs. First, consider that ϑ i = ( μ i , ν i ), i = 1 , 2 , … , n be an IFV associated to the LV defined as rating of significance of ith expert. Considering the following Eqs. (8)–(10), the numeric weight of ith DE is determined, where i = 1 , 2 , … , n.

Substep 1.1: Taking into account the proposed IF-score function in Eq. (6), the normalized assessment rating of ith DE is calculated, where i = 1 , 2 , … , n. (8) ϖ i o = ( Y ( ϑ i ) · { a b s ( μ − ν ) + ( μ + ν ) } + 1 ) ∑ i = 1 n ( Y ( ϑ i ) · { a b s ( μ − ν ) + ( μ + ν ) } + 1 ) , i = 1 , 2 , … , n , where Y ( ϑ i ) = sgn ( μ i − ν i ) , sgn ( . ) and a b s ( · ) represent the sign function and the absolute value function, respectively.

Substep 1.2: In virtue of Eq. (8), acquire the rank ( r a i ) of ith expert. Next, compute performance score of ith experts by means of the rank reciprocal formula (9). (9) ϖ i s = 1 / r a i ∑ i = 1 n ( 1 / r a i ) , i = 1 , 2 , … , n .

Substep 1.3: With the combination of Eqs. (8) and (9), compute the collective significance degree/weight of ith expert, given by Eq. (10). (10) ϖ i = α ( ϖ i o ) + ( 1 − α ) ( ϖ i s ) , i = 1 , 2 , … , n , wherein α ∈ [ 0 , 1 ] signifies the strategic parameter to derive the numeric weight of ith expert. Moreover, ϖ = ( ϖ 1 , ϖ 2 , … , ϖ n ) T represents the weight vector of DEs with ϖ i ∈ [ 0 , 1 ] and ∑ i = 1 n ϖ i = 1.

Step 2: Create the linguistic performance matrix (LPM).

In this step, a LPM Z = ( z j k ( i ) ) is created on the basis of experts’ linguistic opinions, in which each element z i k ( i ) denotes LV of an alternative M j over diverse criterion F k presented by ith DE.

Step 3: Aggregate the experts’ opinions.

To make a group decision, we require to combine diverse opinions of DEs related to each option over each criterion. To this aim, an IFWA operator (Xu, 2007) is applied to construct an intuitionistic fuzzy aggregated decision-matrix (IFADM) Z ¯ = ( z ¯ j k ) r × s , where (11) z ¯ j k = ( μ ¯ j k , ν ¯ j k ) = I F W A ϖ i ( z j k ( 1 ) , z j k ( 2 ) , … , z j k ( n ) ) = ( 1 − ∏ i = 1 n ( 1 − μ j k ( i ) ) ϖ i , ∏ i = 1 n ( ν j k ( i ) ) ϖ i ) .

Step 4: Determine the objective weights by IF-WENSLO model.

Substep 4.1: Normalize the input information.

Construct the normalized decision-matrix Z ⌢ = ( z ⌢ j k ) r × s , where (12) z ⌢ j k = S ( z ¯ j k ) ∑ j = 1 r S ( z ¯ j k ) , and S ( z ¯ j k ) ( j = 1 , 2 , … , r, k = 1 , 2 , … , s) can be calculated through Eq. (6).

Substep 4.2: Compute the criterion class interval.

Taking into account Sturges’ rule, find the criterion class interval ( Δ z ⌢ k ) using Eq. (13). (13) Δ z ˜ k = max j = 1 , 2 , … , r z ⌢ j k − min j = 1 , 2 , … , r z ⌢ j k 1 + 3.332 log ( r ) .

Substep 4.3: Compute the slope of criterion.

Considering the criterion class interval, the slope of each criterion is computed through Eq. (14). (14) tan θ k = ∑ j = 1 r z ⌢ j k ( r − 1 ) Δ z ⌢ k , k = 1 , 2 , … , s .

Substep 4.4: Derive the envelope of criterion.

On the basis of criterion class interval, the envelope of each criterion is computed by Eq. (15). (15) ρ k = ∑ j = 1 r − 1 ( z ⌢ ( j + 1 ) k − z ⌢ j k ) 2 + ( Δ z ⌢ j k ) 2 , k = 1 , 2 , … , s .

Substep 4.5: Determine the envelope-slope ratio.

In accordance with previous steps, the ratio of envelope-slope of kth criterion is estimated using Eq. (16). (16) α k = ρ k tan θ k , k = 1 , 2 , … , s .

Substep 4.6: Derive the objective weight of criterion.

Considering the envelope-slope ratio of each criterion, the objective assessment degree ‘ w k o ’ of kth criterion is determined via Eq. (17). (17) w k o = α k ∑ k = 1 s α k , k = 1 , 2 , … , s .

Step 5: Derive the subjective weights by IF-MPSI model.

Substep 5.1: In this step, each expert gives the linguistic assessment rating of each criterion using Table 3. Then, find the IF-score of each IF-assessment rating of criterion by means of Eq. (6) and build the IF-score matrix A = ( A i k ) n × s . Here, A i k signifies the attained IF-score value of each entry of IFADM, wherein i = 1 , 2 , … , n and k = 1 , 2 , … , s.