Interval-valued Intuitionistic Fuzzy Sets Research Articles

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.

Multi-attribute three-way decision making based on interval-valued intuitionistic fuzzy sets

In the interval-valued intuitionistic fuzzy environment, a new multi-attribute three-way decision-making model is proposed to address the problems that the relative loss function in the existing multi-attribute three-way decision-making model does not consider the degree of hesitancy, and the alternative conditional probabilities are given subjectively by the authors, which lacks objectivity. First, three types of ideal solutions are introduced, and the correlation coefficients between the evaluated values and ideal solutions are utilized to construct alternative relative loss functions. Second, the ELECTRE-I method is generalized to the interval-valued intuitionistic fuzzy environment to establish the outranking relation and a method for estimating the conditional probability of alternatives is given. Finally, the model is used to experimentally analyze examples to illustrate the effectiveness and rationality of the model.

Selecting an optimal approach to reduce energy crises under interval-valued intuitionistic fuzzy environment

The concept of interval-valued intuitionistic fuzzy sets is intellectually stimulating and holds significant utility in the representation and analysis of real-world problems. The development of similarity measures within the class of interval-valued intuitionistic fuzzy sets possesses significant importance across various academic disciplines, particularly in the fields of decision-making and pattern recognition. The utilization of similarity measures is of utmost importance in the decision-making process when implementing interval-valued intuitionistic fuzzy sets. This is due to its inherent capability to quantitatively assess the level of resemblance or similarity between two interval-valued intuitionistic fuzzy sets. In this article, the drawbacks of the existing similarity measures in the context of an interval-valued intuitionistic fuzzy environment are addressed, and a novel similarity measure is presented. Many fundamental properties of this new interval-valued intuitionistic fuzzy similarity measure are also established, and the effectiveness of this similarity measure is illustrated by presenting a useful example. Moreover, a comparison is given to demonstrate the validity of the newly proposed similarity measure within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment. In addition, an algorithm is designed to solve multi-criteria decision making problems by means of the proposed measure in the interval-valued intuitionistic fuzzy setting. Furthermore, this newly defined similarity measure is successfully applied to select an optimal renewable energy source to reduce energy crises. Finally, we conduct a comparative study to showcase the authenticity of the recently defined technique within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment.

A Proactive Decision-Making Model for Evaluating the Reliability of Infrastructure Assets of a Railway System

Railway infrastructure is generally classified as either fixed or movable infrastructure assets. Failure in any of the assets could lead to the complete shutdown and disruption of the entire system, economic loss, inconvenience to passengers and the train operating company(s), and can sometimes result in death or injury in the event of the derailment of the rolling stock. Considering the importance of the railway infrastructure assets, it is only necessary to continuously explore their behavior, reliability, and safety. In this paper, a proactive multi-criteria decision-making model that is based on an interval-valued intuitionistic fuzzy set and some reliability quantitative parameters has been proposed for the evaluation of the reliability of the infrastructure assets. Results from the evaluation show that the failure mode ‘Broken and defective rails’ has the most risk and reliability concerns. Hence, priority should be given to the failure mode to avoid a total system collapse.

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.

An integrated QFD and FMEA method under the co-opetitional relationship for product upgrading

Improving customer satisfaction is as important as reducing risk associated with product upgrades. The quality function deployment (QFD), as a customer-centric tool, is widely used for product improvement. The failure mode and effect analysis (FMEA) method is recognized as a reliability management tool. Considering the need to eliminate risks and meet customer expectations, building an integrated QFD-FMEA framework is useful for product upgrading. To enhance the performance, the QFD and FMEA methods are improved. First, the base criterion method (BCM) is used to derive the CR weights in the QFD method and RFs in the FMEA method. Second, the combined compromise solution (CoCoSo) method and interactive multi-criteria decision making (TODIM- Portuguese acronym) methods are utilized to derive the priority of TCs and FMs, respectively. Third, the interval-valued intuitionistic fuzzy set (IVIFS) is used to express the expert evaluation. Moreover, given that co-opetitional relationship exist in firms and lead to opinion interactions, the improved Hegselmann-Krause (HK) model is utilized in our improved method to stimulate opinion interaction under different competitive states in different phases. Finally, a case study is presented to validate the improved method, and its superiority is demonstrated through sensitivity and comparative analysis.

Extended EDAS Analysis for Multi-Criteria Decision-Making Based on Distributed Generation (DG) Technologies System

Recently, there has been a growing interest in distributed generation (DG) technologies, driven by various factors such as fuel price uncertainties, environmental constraints, and increasing power consumption along with transmission capacity shortages, in modern power systems. DG, which involves utilizing clean and renewable energy sources for power generation within the distribution system, has gained significant attention globally. Many developing countries, including Libya, are considering the adoption of DG technologies as part of their energy system expansion plans. Libya, located in North Africa and characterized by vast desert lands, has abundant solar radiation, making solar energy a promising and sustainable source of power. However, despite this energy potential, the southern part of Libya faces frequent power outages. In order to effectively maintain service quality, it is essential to conduct quantitative evaluation of wireless sensor networks. the evaluation of wireless sensor networks involves addressing the multiple attribute group decision-making (MAGDM) problem. To tackle the challenges of MAGDM, an extension of the classical EDAS (Evaluation based on Distance from Average Solution) method is proposed in this paper. The proposed method incorporates interval-valued intuitionistic fuzzy sets (IVIFSs), which provide a more flexible and comprehensive representation of uncertainty, to handle the complexities of MAGDM. The paper begins with a brief review of essential concepts related to IVIFSs. Then, the weights of attributes are determined using the CRITIC method. Subsequently, the IVIF-EDAS method is established by integrating the EDAS method with IVIFSs, and all the calculation procedures are described.

An interactive data-driven multiple-attribute decision-making technique via interval-valued intuitionistic fuzzy sets for teaching quality evaluation in higher education

Improving the quality of higher education teaching is a systematic project. The improvement and formulation of relevant laws, regulations, and measures at the macro level are the minimum and specific requirements for the overall private universities, and are the basic guarantee for controlling the healthy and orderly development of universities. At the micro level, school management needs to focus on two aspects: leadership level construction and teacher level construction. Only by scientifically controlling the above issues and comprehensively considering them can the persistent problem of low teaching quality be fundamentally and gradually solved. In short, the construction of the quality assurance and evaluation system for higher education teaching in China is still in the initial stage of development. Therefore, universities should start from the guarantee and evaluation system to promote the construction of teaching process monitoring and evaluation systems, and improve the level of education and teaching quality on the basis of highlighting higher education teaching reform and research. The teaching quality evaluation of higher education in the era of artificial intelligence is a MADM. In this study, in light with interval-valued intuitionistic fuzzy Hamacher interactive hybrid weighted geometric (IVIFHIHWG) technique and induced OWG (I-OWG) technique, the induced IVIFHIHWG (I-IVIFHIHWG) technique is administrated. Then, the I-IVIFHIHWG technique is exploited to manage the MADM under IVIFSs. Finally, the numerical example for teaching quality evaluation of higher education in the era of artificial intelligence is exploited to verify the I-IVIFHIHWG technique. Thus, the main research contributions are administrated: (1) the I-IVIFHIHWG technique is administrated in line with the IVIFHIHWG and I-OWG technique; (2) the I-IVIFHIHWG technique is exploited to manage the MADM under IVIFSs; (3) the numerical example for teaching quality evaluation of higher education in the era of artificial intelligence and some comparative studies were exploited to verify the I-IVIFHIHWG technique.

Interval-valued intuitionistic fuzzy AROMAN method and its application in sustainable wastewater treatment technology selection

In the theory of interval-valued intuitionistic fuzzy set (IVIFS), the rating/grade of an element is the subset of the closed interval [0, 1], therefore the IVIFS doctrine is more useful for the decision expert to present their judgments in terms of intervals rather than the crisp values. The present work develops an integrated decision-making methodology for evaluating sustainable wastewater treatment technologies within the context of IVIFS. The proposed decision-making framework is divided into three stages. First, some Yager weighted aggregation operators and their axioms are developed to combine the interval-valued intuitionistic fuzzy information. These operators can offer us a flexible way to solve the realistic multi-criteria decision-making problems under IVIFS context. Second, an extension of Symmetry Point of Criterion model is introduced to determine the criteria weights under IVIFS environment. Third, an integrated alternative ranking order model accounting for two-step normalization (AROMAN) approach is proposed from IVIF information perspective. Next, the practicability and efficacy of the developed model is proven by implementing it on a case study of sustainable wastewater treatment technologies evaluation problem with multiple criteria and decision experts. Finally, comparative analysis is discussed to illustrate the consistency and robustness of the obtained outcomes.

Aczel–Alsina T-norm based group decision-making technique for the evaluation of electric cars using generalized orthopair fuzzy aggregation information with unknown weights

Data management and finding precise outcomes from large amounts of information are among the biggest challenges for scientists. The technique of multi-attribute group decision-making (MAGDM) is a valuable tool for investigating fuzzy data precisely. The key objective of the paper is to redefine the q-rung orthopair (q-RO) fuzzy set (FS) (q-ROFS) in the term of interval-valued and proposed new aggregation operators (AOs) based on the Aczel-Alsina (AA) t-norm (TN) and t-conorm (TCN) operations. The AA operational laws are a generalized form of existing TNs and TCNs and give more reliable results because they can fluctuate in their parametric values. The concept of interval-valued enlarges the space of membership degree (MD) and non-membership degree (NMD) for decision-makers. By taking qth power, the interval-valued q-ROFS (IV-q-ROFS) structure. The IV-q-ROFS can handle the uncertainty and vagueness in data, then interval-valued intuitionistic FS (IV-IFS) and interval-valued Pythagorean FS (PyFS) (IV-PyFS) and provide accurate results. The thought of power AOs (PAOs) makes the relationship between weight vectors and reduces the chances of uncertainty in aggregated results. By taking advantage of PAOs, this article is devoted to introducing the interval-valued q-ROF Aczel-Alsina power-weighted averaging (IV-q-ROFAAPWA) and interval-valued q-ROF Aczel-Alsina power-weighted geometric (IV-q-ROFAAPWG) operators. The fundamental axioms of AOs, idempotency, boundedness, and monotonicity, are also discussed. To illustrate the importance of suggested AOs, the real-life problem of electric car selection was solved by applying the MAGDM method using the proposed IV-q-ROFAAPWA and IV-q-ROFAAPWG operators. The comparison of proposed AOs with currently present AOs is also part of the article. We finally constructed solid conclusions.

Location selection for offshore wind power station using interval-valued intuitionistic fuzzy distance measure-RANCOM-WISP method

The development opportunities and high-performance capacity of offshore wind energy project depends on the selection of the suitable offshore wind power station (OWPS) location. The present study aims to introduce a decision-making model for assessing the locations for OWPS from multiple criteria and uncertainty perspectives. In this regard, the concept of interval-valued intuitionistic fuzzy set (IVIFS) is utilized to express uncertain information. To quantify the degree of difference between IVIFSs, an improved distance measure is proposed and further utilized for deriving the objective weights of criteria. Numerical examples are discussed to illustrate the usefulness of introduced IVIF-distance measure. The RANking COMparison (RANCOM) based on interval-valued intuitionistic fuzzy information is presented to determine the subjective weights of criteria. With the combination of objective and subjective weights of criteria, an integrated weighting tool is presented to find the numeric weights of criteria under IVIFS environment. Further, a hybrid interval-valued intuitionistic fuzzy Weighted integrated Sum Product (WISP) approach is developed to prioritize the OWPS locations from multiple criteria and uncertainty perspectives. This approach combines the benefits of two normalization tools and four utility measures, which approves the effect of beneficial and non-beneficial criteria by means of weighted sum and weighted product measures. Further, the developed approach is applied to the OWPS location selection problem of Gujarat, India. Sensitivity and comparative analyses are presented to confirm the robustness and stability of the present WISP approach. This study provides an innovative decision analysis framework, which makes a significant contribution to the OWPS locations assessment problem under uncertain environment.

Enhanced LogTODIM-TOPSIS framework for interval-valued intuitionistic fuzzy MAGDM and applications to intangible assets operational management performance evaluation of commercial sporting events

The effective operation of intangible assets in commercial sports events can bring long-term, sustainable, and large-scale economic benefits to sports events. However, currently, in the operation of commercial sports events, the lack of experience in hosting events often hinders the development of intangible assets that should have created higher profits, and cannot achieve the expected value. The intangible assets operational management performance (IAOMP) evaluation of commercial sporting events is the multiple-attribute group decision-making (MAGDM). The Logarithmic TODIM (LogTODIM) and TOPSIS technique was brought forward the MAGDM. The interval-valued intuitionistic fuzzy sets (IVIFSs) are brought forward as the useful technique for coping with uncertain and fuzzy information during the IAOMP evaluation of commercial sporting events. In this study, the interval-valued intuitionistic fuzzy number Logarithmic TODIM-TOPSIS (IVIFN-LogTODIM-TOPSIS) technique is brought forward the MAGDM under IVIFSs circumstances. Finally, the numerical example for IAOMP evaluation of commercial sporting events is brought forward to verify the IVIFN-LogTODIM-TOPSIS technique. The main contribution of this study is brought forward: (1) the LogTODIM-TOPSIS was extended to IVIFSs in light with MEREC model; (2) the MEREC model is brought forward to derive weight in light with score information values under IVIFSs circumstances. (3) the IVIFN-LogTODIM-TOPSIS is brought forward for MAGDM under IVIFSs circumstances; (4) the numerical example for IAOMP evaluation of commercial sporting events and several different comparative analysis is brought forward to verify the IVIFN-LogTODIM-TOPSIS model.

Enhanced decision-making through an intelligent algorithmic approach for multiple-attribute college English teaching quality evaluation with interval-valued intuitionistic fuzzy sets

To establish a student-centered teaching quality assurance system in English teaching in universities, it is necessary to establish an educational philosophy of survival based on quality, achieve student-centered learning, optimize the allocation of English teaching resources, and reform evaluation standards; To address the problems in English teaching, we need to raise awareness of the construction of a “student-centered” teaching quality assurance system, carry out “student-centered” teacher training activities, and improve teachers’ professional skills; At the same time, we will establish a student-centered English curriculum system, promote the reform and innovation of teaching models, establish a diversified English teaching evaluation system, and ensure the high efficiency and quality of English teaching in universities. The college English teaching quality evaluation is the MAGDM. Recently, the TODIM and MABAC technique has been employed to manage MAGDM. The interval-valued intuitionistic fuzzy sets (IVIFSs) are employed as a useful tool for portraying uncertain information during the college English teaching quality evaluation. In this paper, the interval-valued intuitionistic fuzzy TODIM-MABAC (IVIF-TODIM-MABAC) technique is built to manage the MAGDM under IVIFSs. At last, the numerical example for college English teaching quality evaluation is employed to show the IVIF-TODIM-MABAC decision technique. The main contribution of this paper is outlined: (1) the TODIM technique based on MABAC has been extended to IVIFSs based on Entropy technique; (2) the Entropy technique is employed to manage weight based on score values under IVIFSs. (3) the IVIF-TODIM-MABAC technique is founded to manage the MAGDM under IVIFSs; (4) a numerical example for college English teaching quality evaluation and some comparative analysis is supplied to verify the proposed technique.

Extended technique for interval-valued intuitionistic fuzzy MAGDM and applications to performance evaluation of intangible assets operation and management in sports events

From a management perspective, performance is the desired outcome of an organization, and it is an effective output that an organization exhibits at different levels to achieve its goals. Sports event performance refers to the results and effects generated by sports events, and is a comprehensive assessment category in sports event management. It refers not only to the concept of economic level, but also to the public satisfaction of sports events and a series of social effects caemployed by them. It focuses not only on the quality and economic value of sports events themselves, but also on the achievements and effects of sports events and society, sports events and citizens, sports events and the environment. The performance evaluation of intangible assets operation and management (IAOM) in sports events is the MAGDM. Recently, the TODIM and TOPSIS technique has been employed to manage MAGDM. The interval-valued intuitionistic fuzzy sets (IVIFSs) are employed as a useful tool for depicting uncertain information during the performance evaluation of IAOM in sports events. In this paper, the interval-valued intuitionistic fuzzy TODIM-TOPSIS (IVIF-TODIM-TOPSIS) technique is built to manage the MAGDM under IVIFSs. At last, the numerical example for sports events performance evaluation of IAOM is employed to show the IVIF-TODIM-TOPSIS decision technique. The main contribution of this paper is outlined: (1) the TODIM technique based on TOPSIS has been extended to IVIFSs based on information Entropy; (2) the information Entropy technique is employed to derive weight based on core values under IVIFSs. (3) the IVIF-TODIM-TOPSIS technique is founded to manage the MAGDM under IVIFSs; (4) a numerical case study for performance evaluation of IAOM in sports events and some comparative analysis is supplied to validate the proposed 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 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.

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

Modeling uncertainties associated with multi-attribute decision-making based evaluation of cooling system using interval-valued complex intuitionistic fuzzy hypersoft settings

<abstract><p>Academics encounter a challenge regulating data-driven unpredictability in numerous complicated decision scenarios. Regulating the cyclical nature of appraisal attributes, determining lower and higher limitations, granting multi-parametric values as a means of assessing argumentation, and modeling uncertainty are a few examples of these problems. It requires the incorporation of complex plane settings, interval-valued intuitionistic fuzzy settings, and hypersoft settings. Inspired by these kinds of scenarios, the goal of this research was to articulate a new theoretical framework, the interval-valued complex intuitionistic fuzzy hypersoft set ($ \Gamma $-set), which can handle these kinds of problems as a whole under the umbrella of a single framework. First, the concepts of $ \Gamma $-set, as well as its set operations and aggregations, such as decision matrix, cardinal matrix, aggregate matrix, and cardinality set, were examined. The second phase offers an appealing algorithm that consists of nine steps that go from taking into account necessary set construction to making the best choice. A prototype case study analyzing eighteen evaluation qualities and thirty-four sub-attributes for determining an optimal cooling system ($ \mathbb{CSYS}) $ for a factory validates the provided algorithm. Informative comparison analysis and preferred study features were provided as essential components of research to assist academics in making significant advances regarding their field and gradually, but thoroughly, advancing their specialization.</p></abstract>

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

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