Interval-valued Intuitionistic Fuzzy Environment Research Articles

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.

Two-sided matching decision method and application based on subject differences in interval intuitionistic fuzzy environment

In this paper, a two-sided matching decision model based on interval-valued intuitionistic fuzzy environment is proposed to maximize the demand of individual differences. Firstly, the attribute feature table and weight matrix of both agents are constructed, and a formula for calculating the comprehensive advantage in the interval-valued intuitionistic fuzzy environment is given, namely the interval-valued intuitionistic fuzzy comprehensive advantage aggregation operator (IIFCAAO); Secondly, the interval-valued intuitionistic fuzzy decision matrix of both agents is calculated by using the comprehensive advantage aggregation operator, and the interval-valued intuitionistic fuzzy decision matrix is transformed into a score function matrix by using a score function formula; Thirdly, the two-sided matching model is established to maximize the score; Finally, the scientificity and practicability of the model are verified by an example of college students changing their majors.

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.

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.

Multi-attribute decision-making based on dual probabilistic interval-valued intuitionistic hesitant fuzzy weighted heronian mean aggregation operator

Probabilistic interval-valued intuitionistic hesitant fuzzy sets (PIVIHFSs) can well describe the evaluation information of decision-makers (DMs) in multi-attribute decision-making (MADM) problems. However, PIVIHFSs only depict the situation where both membership and non-membership information occur with equal probability while ignoring the situations of non-equal possibility due to DMs’ subjective preferences. In this paper, we develop dual probabilistic interval-valued intuitionistic hesitant fuzzy sets (DPIVIHFSs) concept based on the truncated normal distribution. The DPIVIHFSs overcome the shortcomings of PIVIHFSs and are more interpretable. Then, the operations and ranking method of DPIVIHFSs are introduced. Furthermore, we study MADM methods in dual probabilistic interval-valued intuitionistic hesitant fuzzy environments by aggregation operators (AOs). We propose a series of AOs including the DPIVIHF heronian mean (DPIVIHFHM) operator and the DPIVIHF weighted heronian mean (DPIVIHFWHM) operator. The basic properties of the presented are discussed and proved. Finally, a novel method for solving the MADM problem is proposed based on the DPIVIHFWHM operator and a numerical example of express company selection strategy is used to illustrate the effectiveness of the method. The proposed method in this article can capture more fuzzy and uncertain information when solving MADM problems and have a wider application range.

Novel evaluation model of teaching quality based on the improved IVIF-BWM and IVIFWMSM

The evaluation of teaching quality plays a crucial role in promoting the improvement of education quality and ensuring the healthy development of education. This study presents a novel teaching quality evaluation model based on improved interval-valued intuitionistic fuzzy Best-Worst method (IVIF-BWM) and interval-valued intuitionistic fuzzy weighted Maclaurin symmetric mean operators (IVIFWMSM). The study is divided into three parts. Firstly, to derive the optimal interval-valued intuitionistic fuzzy weights of criteria, we develop an improved IVIF-BWM by establishing a goal programming model based on the multiplicative consistent interval-valued intuitionistic fuzzy preference relation(IVIFPR), and then we propose the new consistency index (CI) and the consistency ratio (CR) under interval-valued intuitionistic fuzzy environment to verify the reliability of the derived results. Secondly, with regard to the importance and interaction relationships among criteria, IVIFWMSM is used to aggregate evaluation values of alternatives on each evaluation criteria in multi-criteria decision making process. Finally, the proposed teaching quality evaluation model is applied to a case of teaching quality evaluation in higher education and a comparison study with other existing methods are performed. The results demonstrate that the proposed teaching quality evaluation model not only overcomes the shortcomings of previous methods, but also is more accuracy, effective and reasonable for dealing with the teaching quality evaluation under the intuitionistic fuzzy environments.

A Novel Weighted Averaging Operator of Linguistic Interval-Valued Intuitionistic Fuzzy Numbers for Cognitively Inspired Decision-Making

An aggregation operator of linguistic interval-valued intuitionistic fuzzy numbers (LIVIFNs) is an important tool for solving cognitively inspired decision-making problems with LIVIFNs. So far, many aggregation operators of LIVIFNs have been presented. Each of these operators works well in its specific context. But they are not always monotone because their operational rules are not always invariant and persistent. Dempster-Shafer evidence theory, a general framework for modelling epistemic uncertainty, was found to provide the capability for operational rules of fuzzy numbers to overcome these limitations. In this paper, a weighted averaging operator of LIVIFNs based on Dempster-Shafer evidence theory for cognitively inspired decision-making is proposed. Firstly, Dempster-Shafer evidence theory is introduced into linguistic interval-valued intuitionistic fuzzy environment and a definition of LIVIFNs under this theory is given. Based on this, four novel operational rules of LIVIFNs are developed and proved to be always invariant and persistent. Using the developed operational rules, a new weighted averaging operator of LIVIFNs is constructed and proved to be always monotone. Based on the constructed operator, a method for solving cognitively inspired decision-making problems with LIVIFNs is presented. The application of the presented method is illustrated via a numerical example. The effectiveness and advantage of the method are demonstrated via quantitative comparisons with several existing methods. For the numerical example, the best alternative determined by the presented method is exactly the same as that determined by other comparison methods. For some specific problems, only the presented method can generate intuitive ranking results. The demonstration results suggest that the presented method is effective in solving cognitively inspired decision-making problems with LIVIFNs. Furthermore, the method will not produce counterintuitive ranking results since its operational rules are always invariant and persistent and its aggregation operator is always monotone.

Multiattribute decision making based on nonlinear programming model, the Gini coefficient, and novel score function of interval-valued intuitionistic fuzzy values

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming (NLP) model, the Gini coefficient, and the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a novel SF of IVIFVs to overcome the shortcomings of the existing SFs of IVIFVs. Then, we construct a score matrix (SMX) based on the proposed SF of IVIFVs and the decision matrix given by the decision maker (DMK). Then, we construct a NLP model based on the constructed SMX, the Gini coefficient, and the interval-valued intuitionistic fuzzy (IVIF) weights of the attributes given by the DMK. After solving the constructed NLP model, we obtain the optimal weight (OW) of each attribute. Then, we compute the weighted score (WS) of each alternative based on the constructed SMX and the obtained OWs of the attributes. Finally, we rank the alternatives based on the obtained WSs of the alternatives. The proposed MADM method can overcome the shortcomings of the existing MADM methods in IVIF environments.

Multiattribute group decision making based on novel score function considering both the angle and fuzzy information under interval-valued intuitionistic fuzzy environment

The interval-valued intuitionistic fuzzy values (IVIFVs) have been widely employed for multiattribute group decision making (MAGDM). However, the existing decision making method using IVIFVs has some drawbacks. The recognition degree and information utilization suffer from a gap in the evaluation of alternatives. Therefore, the need for a reliable and effective decision method is obvious. In this paper, a novel score function considering both the angle and fuzzy information of IVIFVs is proposed, which ensures the effective fusion of the fuzzy information measure and angle measure and overcomes the shortcomings of the existing methods. Then, the weights of decision makers (DMs) are set as IVIFVs and subjective values are determined by the optimization model to ensure the objectivity and authenticity of the weights of DMs. Furthermore, a novel MAGDM method based on the proposed score function is proposed. Finally, the proposed method is implemented on the regional innovation resource allocation efficiency evaluation. The results show that our method possesses a higher recognition degree than the other methods, and it ensures relatively high ranking accuracy. The ideology and results of this research will help the DMs to evaluate the alternatives effectively.

Optimization-Based Three-Way Decisions With Interval-Valued Intuitionistic Fuzzy Information.

Due to the effectiveness and advantages of interval-valued intuitionistic fuzzy sets (IVIFSs) in evaluating uncertainty and risk, we introduce IVIFSs into loss functions of decision-theoretic rough sets (DTRSs) and propose an optimization-based approach to interval-valued intuitionistic fuzzy three-way decisions. First, based on the classical DTRSs and two previous optimization models, we construct a new concise linear programming model for simultaneously determining the threshold pair. Our model is mathematically equivalent to the DTRSs and the previous models under the Karush-Kuhn-Tucker (KKT) condition. Second, we extend the constructed model via the IVIFSs of loss functions and we discuss the relations between these loss functions based on a similarity measure function-based ranking method and a multiple score function-based ranking method for IVIFSs. Third, we develop our extended models via two ranking methods and we prove the existence and uniqueness of the optimal solution of the model. The optimization-based method, along with its algorithm for three-way decisions, is designed in an interval-valued intuitionistic fuzzy environment. Compared to the latest existing methods, our method has three advantages (see Advantages 1-3). Finally, an illustrative example is considered, and the advantages of our approach are demonstrated by this example.

A data-driven group emergency decision-making method based on interval-valued intuitionistic hesitant fuzzy sets and its application in COVID-19 pandemic

The outbreak of Corona Virus Disease 2019 (COVID-19) makes people more concerned about the validity and timeliness of emergency decision making. When an emergency occurs, it is difficult for decision makers (DMs) to give accurate assessment information in the early stage due to the urgency of time, the incompleteness of information, and the limitations of DMs’ cognition and knowledge. Hence, we use interval-valued intuitionistic hesitant fuzzy sets rather than exact numbers to better characterize the fuzziness and uncertainty of emergencies. In addition, the Internet has become a major platform for the public to express their opinions or concerns, so we can collect the user-generated content on social media to help DMs determine appropriate emergency decision-making criteria which are the premise and basis of scientific decisions. However, there is likely to be some correlation between the obtained criteria. To this end, we first extend the Bonferroni mean (BM) operator to the interval-valued intuitionistic hesitant fuzzy environment, and propose three interval-valued intuitionistic hesitant fuzzy BM operators to capture the interrelation of fuzzy input variables, including an interval-valued intuitionistic hesitant fuzzy BM operator, a simplified interval-valued intuitionistic hesitant fuzzy BM operator, and a simplified interval-valued intuitionistic hesitant fuzzy weighted BM (SIVIHFWBM) operator. Then, a new group emergency decision-making method based on the SIVIHFWBM operator and social media data is proposed, and the specific steps of ranking all emergency plans are put forward. Moreover, our method is applied to evaluate emergency plans for the prevention and control of COVID-19. Finally, the effectiveness and feasibility of the method are verified by the sensitivity analysis, validity test, and comparative analysis.

A multiattribute group decision-making method based on a new aggregation operator and the means and variances of interval-valued intuitionistic fuzzy values

The development of information measures associated with interval-valued intuitionistic fuzzy values (IVIFVs) has been an important research area over the past few decades. In the literature, the existing decision -making method using IVIFVs has some drawbacks, and the identification degree and information utilization suffer from a gap in the evaluation of alternatives. Therefore, the need for a reliable, useful, and comprehensive decision method is obvious. To obtain more accurate and reliable evaluation results, multiattribute group decision-making (MAGDM) problems, where the same attribute weights given by different decision-makers are different, are studied in this paper. First, the novel operational laws of IVIFVs and a new interval-valued intuitionistic fuzzy weighted arithmetic aggregation operator are defined to overcome the drawbacks of the IIFWA aggregation operator and avoid losing or distorting the original decision information in the process of aggregation. Second, the mean and variance of the possibility degrees of IVIFVs are defined based on the concept of a definite integral. Third, a novel MAGDM method based on the new aggregation operator and the mean and variance of the possibility degrees of IVIFVs is proposed to improve the identification of the evaluation results and ensure the effectiveness of the ranking order. Finally, the effectiveness and practicability of the proposed method are verified by an air combat training accuracy assessment example. This example can be used to assist decision-makers in evaluating air combat training hits in a timely and efficient manner, providing an objective, scientific basis for the realization and application of air combat training hit assessment and a new method and idea for MAGDM problems in an interval-valued intuitionistic fuzzy environment.

A distance measure for optimistic viewpoint of the information in interval-valued intuitionistic fuzzy sets and its applications

Distance measures in interval-valued intuitionistic fuzzy sets are useful tools for a wide range of decision-making, pattern recognition, and clustering problems. However, so far, only a few distance measures have been developed. Furthermore, the developed distance measure takes a moderate view of the information held in the interval-valued intuitionistic fuzzy sets. It is frequently necessary to be optimistic about the information contained in interval-valued intuitionistic fuzzy sets. Furthermore, in decision-making problems, cross-time information is an important parameter. As a result, a new distance measure has been developed to fill this gap in the literature. The developed distance measure takes into account the optimistic viewpoint of the information held in the interval-valued intuitionistic fuzzy sets as well as the cross-time information via the difference between the maximum and minimum cross-information factors. Numerical and comparative studies are being conducted to demonstrate the superiority of the proposed distance measure. Furthermore, to establish the validity and applicability of the proposed distance measure, it is being used to solve multi-attribute decision making problems, pattern recognition problems, and clustering problems in an interval-valued intuitionistic fuzzy environment. The results of the multi-attribute decision making problem of recruiting a marketing expert have been found to be equivalent to the majority of existing methods. Furthermore, the pattern recognition and clustering problems of building material classification are based on the same data set, with the pattern recognition problem determining that polyvinyl chloride flooring belongs to carpet, and the clustering problem determining that polyvinyl chloride flooring and carpet belong to the same class with a very high confidence interval. These demonstrate the proposed distance measure’s validity and applicability. In general, this work highlights on decision making, pattern recognition, and clustering of engineering problems under interval-valued intuitionistic fuzzy environment from an optimistic point of view.

Multi-objective multi-item four dimensional green transportation problem in interval-valued intuitionistic fuzzy environment

Multi-objective multi-item four dimensional green transportation problem in interval-valued intuitionistic fuzzy environment

The algorithm of correction of the unconscientious experts’ evaluations in the interval-valued intuitionistic fuzzy sets case

In the interval-valued intuitionistic fuzzy environment unconscientious opinions may cause problems in the data processing. The problem is similar to those arising in the case of intuitionistic fuzzy sets. In this paper the previous ways of correction of the unconscientious experts’ evaluations in the interval-valued intuitionistic fuzzy sets environment are presented and some new algorithms are proposed.

A multi-criterion three-way decision-making method under linguistic interval-valued intuitionistic fuzzy environment

How to solve a multi-criterion decision-making (MCDM) problem with linguistic interval-valued intuitionistic fuzzy numbers (LIVIFNs) effectively is an important research topic. So far, a number of methods for solving this problem have been presented within the academia. Each of these methods can work well in specific situation. But they could produce undesirable decision-making results when the information for decision-making is insufficient or acquisition of the information needs a certain cost, since all of them are based on conventional two-way decision model. In this paper, three-way decision model is introduced into linguistic interval-valued intuitionistic fuzzy environment and a multi-criterion three-way decision-making method under this environment is presented. A specific relative loss function derived from an LIVIFN is established and corresponding three-way decision rules are developed. Based on the established function and developed rules, a three-way decision method for solving an MCDM problem with LIVIFNs is proposed. The application of the proposed method is illustrated via a practical example. The effectiveness and advantage of the method are demonstrated via an experimental comparison with some existing methods. The comparison results suggest that the proposed method is as effective as the existing methods and is more flexible than the existing methods in solving an MCDM problem with LIVIFNs.

Aralık-Değerli Sezgisel Bulanık Ortamda ÇKKV Yöntemleri Kullanılarak Tekstil Endüstrisinde Yeşil Tedarikçi Seçimi

The importance of protecting the environment is increasing day by day due to environmental concerns such as global warming, human toxicity, eutrophication, and water scarcity. For this reason, companies have started to change their production processes to be enviromentally friendly. One of the necessary changes is to supply raw materials and/or products that are less harmful to the environment. Therefore, companies have to procure raw materials and/or products from green suppliers. This study, it is aimed to evaluate green suppliers for a textile industry under the interval-valued intuitionistic fuzzy (IVIF) environment, considering various environmental and economic criteria. AHP and TOPSIS methods are integrated under the IVIF environment to be used in the evaluation process of green suppliers. In the integrated method, the IVIF-AHP method is used to calculate criterion weights and the IVIF-TOPSIS method is used to rank green suppliers. At the end of the study, a sensitivity analysis is conducted to observe the effects of changes in the weights of the criteria in the selection of green suppliers for the textile industry.

A Novel Risk Assessment Approach Using a Hybrid Method Based On Fine–Kinney and Extended MCDM Methods Under Interval-Valued Intuitionistic Fuzzy Environment

Subway construction is one of the most dangerous industries due to the highest number of occupational accidents. Risk assessment is an effective tool to evaluate risk factors and reduce the number of accidents in such industries. In this study, a novel risk assessment method is proposed using three-stage hybrid method based on Fine–Kinney risk assessment method to evaluate the risk factors encountered in subway constructions and take necessary precautions against possible accidents. Accordingly, in order to deal with the drawbacks of the Fine–Kinney risk assessment method, a novel hybrid approach, which includes Fine–Kinney, analytic hierarchy process (AHP), and multiple multi-objective optimization by ratio analysis (MULTIMOORA) methods, is suggested under interval-valued intuitionistic fuzzy (IVIF) environment to handle uncertainty in the risk evaluation. To demonstrate the applicability and benefits of the proposed hybrid risk assessment method, a real-life case study in subway construction is presented. To determine the weights of three risk parameters in Fine–Kinney method and the risk priority of occupational risk factors in subway construction, IVIF-AHP and IVIF-MULTIMOORA methods are performed, respectively. Then, a sensitivity analysis is applied to confirm the robustness of the proposed method. Finally, a comparative analysis is carried out to check the consistency of the ranking of risk factors obtained in proposed method. The results prove that the proposed risk assessment method generates consistent and reliable results.

Multiattribute decision making based on novel score function and the power operator of interval-valued intuitionistic fuzzy values

In this paper, we propose a novel multiattribute decision making (MADM) method on the basis of the proposed novel score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs) and the power operator of IVIFVs. The proposed SF of IVIFVs can conquer the shortcomings of the existing SFs of IVIFVs. Based on the proposed SF of IVIFVs and the power operator of IVIFVs, we propose a new MADM method in the interval-valued intuitionistic fuzzy context. The proposed MADM method can conquer the shortcoming of the existing MADM methods. It provides us a very useful approach for MADM in interval-valued intuitionistic fuzzy environments.