Interval-valued Intuitionistic Fuzzy Research Articles

Identifying and prioritizing the barriers to green innovation in SMEs and the strategies to counteract the barriers: An interval-valued intuitionistic fuzzy approach

Increasing environmental burdens and the importance of innovation in the presently competitive environment have encouraged small- and mid-size enterprises (SMEs) to adopt and implement green innovation practices. This process, however, is faced with many limitations and obstacles. The purpose of this study is to propose a framework to identify barriers to green innovation in SMEs and to provide solutions/strategies to overcome such barriers. Using the systematic literature review (SLR) method and the opinions of 20 experts, the study primarily identified 29 sub-categories of barriers falling under seven main categories including “management”, “organization”, “human resources”, “financial resources”, “external cooperation”, “customers, markets or competitors”, and “the external environment.” Similarly, 22 strategies were discovered that could help to counteract the barriers identified. To determine the weights of the barriers, the Intuitionistic Fuzzy Multiplicative Best-Worst Method (IFMBWM) was used. The strategies, too, were ranked through the Interval-Valued Intuitionistic Fuzzy MULTIMOORA (IVIF-MULTIMOORA) method. Then, a sensitivity analysis and a comparative analysis were applied to confirm the robustness of the proposed method and ensure the consistency of the obtained ranking of alternatives. As the results revealed, the optimal and effective solutions that could be used by policy-makers/managers to overcome the barriers to green innovation were “simplifying authorization and licensing procedures”, “effective environmental laws and regulations”, “shared responsibility throughout the supply chain”, “a supportive organizational culture”, and “merit-based selection of managers.”

Interval-valued intuitionistic fuzzy three-way conflict analysis based on cumulative prospect theory

This paper makes a significant contribution to the field of conflict analysis by introducing a novel Interval-Valued Intuitionistic Fuzzy Three-Way Conflict Analysis (IVIFTWCA) method, which is anchored in cumulative prospect theory. The method’s key innovation lies in its use of interval-valued intuitionistic fuzzy numbers to represent an agent’s stance, addressing the psychological dimensions and risk tendencies of decision-makers that have been largely overlooked in previous studies. The IVIFTWCA method categorizes conflict situations into affirmative, impartial, and adverse coalitions, leveraging the evaluation of the closeness function and predefined thresholds. It incorporates a reference point, value functions and cumulative weight functions to assess risk preferences, leading to the formulation of precise decision rules and thresholds. The method’s efficacy and applicability are demonstrated through detailed examples and comparative analysis, and its exceptional performance is confirmed through a series of experiments, offering a robust framework for real-world decision-making in conflict situations.

Decision-making for supplier selection problems based on QUALIFLEX technique using likelihood method in LIVIFS environment

The notion of linguistic interval-valued intuitionistic fuzzy set (LIVIFS) is one of the best tools in order to deal with the qualitative decision making problems. Therefore, in this paper a linguistic interval-valued intuitionistic fuzzy (LIVIF) QUALIFLEX method with a likelihood-based comparison approach is proposed. First, the notion of likelihood of fuzzy preference relation (FPRs) to compare the linguistic interval valued intuitionistic fuzzy numbers (LIVIFNs). By employing a criterion-wise preference assessment of alternatives through the comparison of likelihoods, we introduce a novel QUALIFLEX-based model. This model aims to quantify the degree of concordance in the complete preference order for effective management of decisions involving multiple criteria. We demonstrate the practicality and applicability of the proposed methods through an illustrative example, specifically focusing on the context of Supplier Selection Problems. To validate the efficacy of the proposed methodology, a comparative analysis is performed against other existing methods.

Optimizing market risk evaluation of small and medium sized enterprises through hamacher interactive power geometric technique under uncertainty

Compared with large enterprises, the development scale and organizational structure of small and medium-sized enterprises are insufficient, which brings certain limitations to the development of small and medium-sized enterprises in China. In order to promote the long-term development of small and medium-sized enterprises in the new era, it is necessary to require enterprise leaders to innovate marketing plans, strengthen risk management of enterprises, and enhance their strength in market competition. The market risk evaluation of small and medium sized enterprises (SMSEs) in the new era is a multiple-attribute decision-making (MADM). The IVIFSs are employed as the tool for portraying uncertain information during the market risk evaluation of SMSEs in the new era. In this paper, the interval-valued intuitionistic fuzzy (IVIF) Hamacher interactive power geometric (IVIFHIPG) technique is addressed based on IVIF Hamacher interactive weighted geometric (IVIFHIWG) technique and power geometric (PG) technique. Some properties of IVIFHIPG technique were addressed. Then, the IVIFHIPG technique is employed to manage MADM under IVIFSs. Finally, an example for market risk evaluation of SMSEs in the new era is employed to verify the IVIFHIPG technique. Thus, the main contributions of this paper are addressed: (1) the IVIFHIPG technique is addressed based on IVIFHIWG technique and PG technique; (2) the IVIFHIPG technique is came up with to manage the MADM under IVIFSs; (3) a numerical example for market risk evaluation of SMSEs in the new era has been came up with to show the IVIFHIPG technique; and (4) some comparative analysis is addressed to verify the I IVIFHIPG technique.

Green knowledge management capability assessment based on interval-valued intuitionistic Fuzzy EWM-TOPSIS-Sort-B

As an emerging concept in knowledge management (KM), green knowledge management plays a crucial role in the sustainable development of enterprises. A reasonable assessment of an enterprise’s green knowledge management capabilities can help the company effectively manage the embedded green knowledge within its operational processes, thereby achieving self-reinforcement of competitive advantages for the enterprise. Therefore, this paper proposes a multi-criteria classification method based on interval-valued intuitionistic fuzzy entropy weight method-TOPSIS-Sort-B (EWM-TOPSIS-Sort-B) to assess the green knowledge management capabilities of enterprises. In this method, expert assessments are expressed using interval-valued intuitionistic fuzzy sets. A new entropy weight method is introduced into TOPSIS-Sort-B to determine the weights of various evaluation indicators, and TOPSIS-Sort-B is employed to classify and rate each evaluation scheme. It is worth noting that this paper has improved the TOPSIS-Sort-B method by not converting interval-valued intuitionistic fuzzy sets into precise values throughout the entire evaluation process, thus avoiding information loss. Finally, we applied a case of knowledge management capability assessment to validate the proposed method, and conducted sensitivity analysis and comparative analysis on this approach. The analysis results indicate that variations in the parameter ϑ of the interval-valued intuitionistic fuzzy aggregation operator lead to changes in criterion weights and the comprehensive evaluation matrix, resulting in unordered changes in the final classification results. Due to the absence of transformation of interval values in this study, compared to the four classification methods of TOPSISort-L, the classification results are more detailed, and the evaluation levels are more pronounced.

Application of Interval Valued Intuitionistic Fuzzy Uncertain MCDM Methodology for Ph.D Supervisor Selection Problem

The selection of Ph.D (Doctor of Philosophy) supervisor is always a vital and interesting problem in academia and especially for students who want to carry out Ph.D. Nowadays, selecting a supervisor for Ph.D in a scientific manner becomes a challenge for any student because of the variety of options available to the scholar. In this context, the present study aims to formulate a model for Ph.D. supervisor selection from the offered alternatives in an academic institute. A hybrid multi-criteria decision making (MCDM) framework has been applied to select the suitable supervisor of the student’s preferred criteria under interval-valued intuitionistic fuzzy (IVIF) scenario. The IVIF Analytic Hierarchy Process (AHP) has been employed to prioritize the criteria, whereas IVIF Technique for order preference by similarity to ideal solution (TOPSIS) technique is engaged to rank the available supervisors based on criteria weight. A set of eight criteria and five alternatives have been considered for modeling the problem. Moreover, the potential criteria are weighted and ranked by the multiple decision makers in the present study. To examine the consistency and robustness of the proposed integrated approach, sensitivity analysis and comparative analysis have been carried out. From all the analyses, it can be conferred that the suggested approach is quite useful to apply in different decision-making scenarios.

Sustainable selection of microwave absorbing materials: A green evaluation under interval-valued intuitionistic fuzzy environment

Environmentally friendly technology is being used by industries all over the world, and engineers in the manufacturing and materials industry are embracing sustainable business models. In this paradigm, materials are processed using economically and environmentally sound methods. The use of microwave-absorbing materials (MAMs) in low-altitude observatory aircraft and the rise in electromagnetic pollution have brought them to light. The main aim of this study is to select an ideal MAM with excellent physical, electromagnetic, chemical, and thermal properties, which also fulfills sustainability aspects based on expert judgments. In this regard, we have proposed a new hybrid framework consisting of Modified Digital Logic (MDL), a subjective weighting method in combination with the measurement of alternatives and ranking according to compromise solution (MARCOS) under an interval-valued intuitionistic fuzzy (IVIF) environment to select an optimum MAM. Furthermore, this research work contributes to streamlining the selection process by consolidating the plethora of work available in the literature on the synthesis and characterization of MAMs. A database is created for 160 potential candidate materials in C, S, X, and Ku bands for carbon-based materials, including carbon nanotubes (CNT), graphene, reduced graphene oxide (rGO), carbon fibers, and biomass-derived materials. These materials are then passed through successive screening stages to shortlist 14 materials, which are ranked subsequently over a set of 15 crisp and ambiguous criteria. This comprehensive study simultaneously caters to quantitative and qualitative information extracted from experimental work, material resource packs, or expert evaluations. The findings highlight CNT/Fe (20 wt%, E) (Al1) as the most suitable candidate for MAM application with outstanding electromagnetic properties. Finally, the results are compared with extant approaches to check the reliability of the proposed framework. In addition, sensitivity analysis is carried out to establish the feasibility and robustness of the obtained results.

A hybrid heterogeneous framework for medical waste disposal evaluation by fusing group BWM and regret-rejoice MABAC

This article attempts to develop a hybrid heterogeneous framework to evaluate the disposal modes for emergency medical waste (EMW) by fusing GBWM (group best-worst method), RT (regret theory), and MABAC (multi-attributive border approximation area comparison). This hybrid framework tries to address three key challenges: (i) determining criteria weights, (ii) computing the regret-rejoice evaluation matrix, and (iii) identifying the optimal alternative. To address the first challenge, this paper innovates an innovative interval-valued intuitionistic fuzzy (IVIF) GBWM, which considers multiplicatively consistent IVIF preference relation, to efficiently determine global criteria weights (GCWs). For the second challenge, RT is incorporated to compute the regret-rejoice evaluation matrix using experts' heterogeneous evaluations which consist of intervals, triangular fuzzy numbers, hesitant fuzzy linguistic term sets and IVIF values. Regarding the third challenge, MABAC is applied to sort alternatives based on the obtained regret-rejoice evaluation matrix. Afterwards, the validity of the hybrid framework is verified by an illustrative example, and its advantages are demonstrated with some worthy sensitivity and comparative analyses. Some innovations of the proposed framework are highlighted below: (i) The IVIF GBWM streamlines calculation load, since it derives GCWs by solving the group weight assignment model only once; (ii) The introduction of RT into MABAC assists decision-makers in mitigating regret psychology, enhancing the quality of decision outcomes; (iii) The proposed framework’s practicality is enhanced by leveraging heterogeneous evaluations which capture the inherent complexities of actual decision-making problems.

An Interval-Valued Intuitionistic Fuzzy Bow-Tie Model (IVIF-BT) for the Effectiveness Evaluation of Safety Barriers in Natural Gas Storage Tank

Safety barriers (SBs) are important means of reducing failure risks of process systems. As barriers vary in type and function, their effectiveness needs to be evaluated in order to find a more reasonable configuration strategy. However, in practice, there is often a lack of accurate and complete data relating to SBs, which poses a significant challenge in quantitatively assessing their effectiveness. To address this issue, in this study, we propose a semi-quantitative approach for evaluating the effectiveness of both preventive and protective barriers in process systems by integrating expert elicitation, interval-valued intuitionistic fuzzy numbers (IVIFNs), and a bow-tie model. In this approach, the bow-tie model is first applied to describe the system failure scenarios and the action phases of the barriers, and then IVIFNs with expert judgment are introduced to obtain the failure probabilities of basic events and the effects of SBs. Subsequently, the effectiveness of each barrier is measured by comparing the relative change in failure risk due to the addition of the barrier. To verify the feasibility of this approach, a natural gas storage tank with some barriers was analyzed. The results show that the regular inspection of the deformation or damage of the storage tank has the highest effectiveness, followed by the installation and regular maintenance of safety electrical equipment. Furthermore, compared to a single barrier, multiple barriers can significantly reduce the system risk.

An advanced approach to operational quality evaluation for industry-finance integration enterprises based on integrated interval-valued intuitionistic fuzzy multi-attribute decision making

With the acceleration of economic globalization, enterprises are facing fierce competition and huge challenges, requiring deep financial management transformation. In this context, the integration of industry and finance has gradually demonstrated extremely important value. The integration of industry and finance can not only effectively improve the efficiency of financial management, prevent business risks, and improve operational efficiency, but also enhance the comprehensive ability of enterprise financial management, providing a more flexible, transparent, and efficient financial management system for enterprises. The operational quality evaluation of industry-finance integration enterprises under lean management accounting is a multiple-attribute decision-making (MADM). In this paper, some calculating laws on IVIFSs, Hamacher sum, Hamacher product are introduced, and the interval-valued intuitionistic fuzzy Hamacher interactive power averaging (IVIFHIPA) technique is proposed based on the interval-valued intuitionistic fuzzy (IVIF) Hamacher interactive weighted averaging (IVIFHIWA) technique and power average (PA) technique. Meanwhile, some ideal properties of IVIFHIPA technique are studied. Then, the IVIFHIPA technique is employed to cope with the MADM under IVIFSs. Finally, an example for operational quality evaluation of industry-finance integration enterprises under lean management accounting is employed to test the IVIFHIPA technique. Thus, the main research aim of this paper is concluded as follows: (1) the IVIFHIPA technique is constructed based on IVIFHIWA technique and classical power average (PA) technique; (2) the IVIFHIPA technique is put forward to cope with the MADM under IVIFSs; (3) an empirical example for operational quality evaluation of industry-finance integration enterprises under lean management accounting has been put forward to show the IVIFHIPA technique.

Extension of Interaction Geometric Aggregation Operator for Material Selection Using Interval-Valued Intuitionistic Fuzzy Hypersoft Set

A recently emerged area of research named intuitionistic fuzzy hypersoft set (IFHSS) attempts to describe the internal limitations of intuitionistic fuzzy soft sets on multiparameter functions. A computation of such a type connects a power set of the universe with a tuple of sub-parameters. The strategy shows the allocation of attributes to their respective sub-attribute values in distinct groupings. The above features make it a unique methodical tool for handling obstacles of hesitation. The aggregation operators have an important role in the assessment of both types of potential and in identifying problems from their assessment. This research extends the use of the interaction aggregation operator to the interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS), which is an entirely new structure generated through the interval-valued intuitionistic fuzzy soft set (IVIFSS). The IVIFHSS significantly condenses information that is inaccurate and imprecise compared to the frequently utilized IFSS and IVIFSS. Fuzzy reasoning is recognized as the prevalent strategy for improving imperfect data in decision-making processes. The core objective of the research is to develop operational rules for interval-valued intuitionistic fuzzy hypersoft numbers (IVIFHSNs), which promote interactions. This research is designed to broaden the utilization of the interaction geometric aggregation operator in the framework of IVIFHSS. In particular, we propose a novel operator known as the Interval-Valued Intuitionistic Fuzzy Hypersoft Interactive Weighted Geometric (IVIFHSIWG) operator. The aggregation operator indicates industry professional support for the implementation of a robust MCGDM material selection technique in order to address this need. The practical application of the intended MCGDM technique has been introduced in selecting materials (MS) for cryogenic storage containers. The influence advocates that the anticipated model is more operational and stable in demonstrating anxious facts based on IVIFHSS.

From Ambiguity to Clarity: Unraveling the Power of Similarity Measures in Multi-Polar Interval-Valued Intuitionistic Fuzzy Soft Sets

The utilization of similarity measures in the context of multi-polar interval-valued intuitionistic fuzzy soft sets (mPIVIFSS) is a significant theoretical approach that offers a valuable structure for tackling intricate situations that are characterized by imprecise information and uncertainty. Nevertheless, these issues frequently entail conditions that are not limited in scope and exhibit a considerable level of uncertainty in scenarios involving multiple dimensions, hence presenting substantial difficulties. The objective of this research study is to provide a comprehensive understanding of similarity measures in the context of mPIVIFSS. Additionally, we will examine several operations, such as complement, subset, union, intersection, AND, OR, and De-Morgan’s Laws, as they relate to mPIVIFSS. This study not only includes theoretical debates but also explores practical applications. These efforts contribute to the improvement of decision-making, pattern recognition, and data analysis in settings characterized by ambiguous and uncertain information, hence emphasizing the importance of similarity measures in efficiently addressing multi-dimensional problems.

An Interval-Valued Intuitionistic Fuzzy VIKOR Approach for R&D Project Selection in Defense Industry Investment Decisions

Defense Industry projects are high-budget projects that take many years, required infrastructure, and go through serious research and development processes. When making investment decisions, solutions obtained with models based on expert opinions and analytical techniques are required. At this point, interval-valued intuitionistic fuzzy (IVIF) methods are a good alternative to eliminate uncertainty, especially in order to evaluate all preference information provided by decision makers. In this study, multi-criteria decision making in the IVIF environment in the defense industry is extended with the VIKOR method. For the application, the literature was examined and 8 different criteria were determined. 4 different alternative projects were evaluated based on these criteria by 3 different decision makers. The results show that the analyzes performed with the VIKOR method in the IVIF environment are similar to the literature. Additionally, there is no study in the literature examining this methodology on the defense industry.

An Extended EDAS Approach Based on Cumulative Prospect Theory for Multiple Attributes Group Decision Making with Interval-Valued Intuitionistic Fuzzy Information

The interval-valued intuitionistic fuzzy sets (IVIFSs), based on the intuitionistic fuzzy sets (IFSs), combine the classical decision method and its research and application is attracting attention. After a comparative analysis, it becomes clear that multiple classical methods with IVIFSs’ information have been applied to many practical issues. In this paper, we extended the classical EDAS method based on the Cumulative Prospect Theory (CPT) considering the decision experts (DEs)’ psychological factors under IVIFSs. Taking the fuzzy and uncertain character of the IVIFSs and the psychological preference into consideration, an original EDAS method, based on the CPT under IVIFSs (IVIF-CPT-EDAS) method, is created for multiple-attribute group decision making (MAGDM) issues. Meanwhile, the information entropy method is used to evaluate the attribute weight. Finally, a numerical example for Green Technology Venture Capital (GTVC) project selection is given, some comparisons are used to illustrate the advantages of the IVIF-CPT-EDAS method and a sensitivity analysis is applied to prove the effectiveness and stability of this new method.

Decision Algorithm With Interval-Valued Intuitionistic Fuzzy Hamy Mean Aggregation Operators for Assessment of Agricultural Education Practice

Decision Algorithm With Interval-Valued Intuitionistic Fuzzy Hamy Mean Aggregation Operators for Assessment of Agricultural Education Practice

Improving Similarity Measures for Modeling Real-World Issues With Interval-Valued Intuitionistic Fuzzy Sets

Improving Similarity Measures for Modeling Real-World Issues With Interval-Valued Intuitionistic Fuzzy Sets

Similarity Measure for Interval-Valued Intuitionistic Fuzzy Set and Its Applications

Similarity Measure for Interval-Valued Intuitionistic Fuzzy Set and Its Applications

Interactively iterative group decision-making method with interval-valued intuitionistic fuzzy preference relations based on a new additively consistent concept

Interval-valued intuitionistic fuzzy preference relation (IVIFPR) is a powerful instrument for describing uncertain judgement of expert in preference group decision making (PGDM). Nevertheless, the extant additive consistency definitions for IVIFPRs violate the invariance regarding arrangement of objectives. In addition, the modification for comparative judgments in the consensus reaching process (CRP) of existing PGDMs with IVIFPRs do not involve the interaction or communication with experts. Therefore, we propose an PGDM to avoid these situations. First, a new additive consistency definition for IVIFPRs is given satisfying the invariance regarding arrangement of objectives. Then, an interactively iterative algorithm considering minimum information loss is developed to enhance the consistency of IVIFPRs. Next, as to group decision making (GDM) with IVIFPRs, a bi-objective optimization model is constructed to determine the experts’ weights, and an interactively iterative algorithm considering minimum information loss is developed to enhance the consensus level among experts. Furthermore, a fuzzy optimization model is constructed to derive the interval priority weights of objectives from an IVIFPR. Finally, the feasibility and superiority of the proposed GDM method are verified by application examples and analyses. The proposed GDM method has obtained an average of 0.0432 for information deviations and 22/72 for modified judgments on two datasets, respectively, which is one of the best results compared to state-of-art.

Protecting Infrastructure Networks: Solving the Stackelberg Game with Interval-Valued Intuitionistic Fuzzy Number Payoffs

Critical infrastructure is essential for the stability and development of modern society, and a combination of complex network theory and game theory has become a new research direction in the field of infrastructure protection. However, existing studies do not consider the fuzziness and subjective factors of human judgment, leading to challenges when analyzing strategic interactions between decision makers. This paper employs interval-valued intuitionistic fuzzy numbers (IVIFN) to depict the uncertain payoffs in a Stackelberg game of infrastructure networks and then proposes an algorithm to solve it. First, we construct IVIFN payoffs by considering the different complex network metrics and subjective preferences of decision makers. Next, we propose a lexicographic algorithm to solve this game based on the concept of a strong Stackelberg equilibrium (SSE). Finally, we conduct experiments on target scale-free networks. Our results illustrate that in an SSE, for the defender in a weak position, it is better to defend nodes with high degrees. The experiments also indicate that taking fuzziness into account leads to higher SSE payoffs for the defender. Our work aims to solve a Stackelberg game with IVIFN payoffs and apply it to enhance the protection of infrastructure networks, thereby improving their overall security.

Some Connectivity Parameters of Interval-Valued Intuitionistic Fuzzy Graphs with Applications

Connectivity in graphs is useful in describing different types of communication systems like neural networks, computer networks, etc. In the design of any network, it is essential to evaluate the connections based on their strengths. In this manuscript, we comprehensively describe various connectivity parameters related to interval-valued intuitionistic fuzzy graphs (IVIFGs). These are the generalizations of the parameters defined for fuzzy graphs, interval-valued fuzzy graphs, and intuitionistic fuzzy graphs. First, we introduce interval-valued intuitionistic fuzzy bridges (IVIF bridges) and interval-valued intuitionistic fuzzy cut-nodes (IVIF cut-nodes). We discuss the many characteristics of these terms as well as establish the necessary and sufficient conditions for an arc to become an IVIF-bridge and a vertex to be an IVIF-cutnode. Furthermore, we initiate the concepts of interval-valued intuitionistic fuzzy cycles (IVIFCs) and interval-valued intuitionistic fuzzy trees (IVIFTs) and explore few relationships among them. In addition, we introduce the notions of fuzzy blocks and fuzzy block graphs and extend these terms as interval-valued fuzzy blocks (IVF-blocks) and interval-valued intuitionistic fuzzy block graphs (IVIF-block graphs). Finally, we provide the application of interval-valued intuitionistic fuzzy trees (IVIFTs) in a road transport network.