Intuitionistic Fuzzy Environment Research Articles

The intuitionistic fuzzy concept-oriented three-way decision model

Recently, some researchers have explored three-way decision models in the fuzzy multi-criteria environments from the perspective of criterion fuzzy concept. The main characteristics of these models include the subjective preference of decision-maker for criteria and the evaluation value information system provided by decision-maker. However, the criterion fuzzy concept only considers the decision-maker’s membership preference to each criterion, and ignores the decision-maker’s non-membership preference to each criterion. In view of this, this paper further proposes a new criterion fuzzy concept, namely the intuitionistic fuzzy concept, to express decision-maker’s preference for each criterion. At the same time, we build an intuitionistic fuzzy concept-oriented three-way decision model to solve the ranking and classification problem in the intuitionistic fuzzy multi-criteria environments with decision-maker’s preference. Firstly, based on the defined intuitionistic fuzzy concept, we construct a new intuitionistic fuzzy loss function model. Meanwhile, using intuitionistic fuzzy similarity, we propose a new conditional probability calculation method to express the correlation degree between the intuitionistic fuzzy concept and alternative’s evaluation values. Secondly, we introduce three decision-making perspectives from the membership degree and non-membership degree of expected loss to obtain the final three-way classification scheme. Moreover, by combining the thresholds of the positive and negative perspectives, we obtain the comprehensive thresholds of the comprehensive perspective, which can be used to rank all alternatives. Finally, a supplier selection problem is used to verify the feasibility and superiority of the model, and six data sets are used to verify the applicability of the model.

Response to a Note on “A New Ranking Approach for Solving Fully Fuzzy Transportation Problem in Intuitionistic Fuzzy Environment”

Response to a Note on “A New Ranking Approach for Solving Fully Fuzzy Transportation Problem in Intuitionistic Fuzzy Environment”

A Note on “A New Ranking Approach for Solving Fully Fuzzy Transportation Problem in Intuitionistic Fuzzy Environment”

A Note on “A New Ranking Approach for Solving Fully Fuzzy Transportation Problem in Intuitionistic Fuzzy Environment”

Selection of Optimal E-Learning Tool with Type-2 Intuitionistic Fuzzy Einstein Interactive Weighted Aggregation Operator

Not only are daily life activities being disrupted by the COVID-19 pandemic, but so are educational systems. To some extent, encouraging the use of e-learning technology has helped to stabilize the situation. The suitable selection of the appropriate e-learning platform for the institution depends upon different criteria with uncertain information. As type 2 intuitionistic fuzzy (T2IF) sets are conceptually intriguing and they provide a lot of expressive potential for dealing with uncertainty in expert knowledge, this work investigates the best e-learning tool for higher education in a type 2 intuitionistic fuzzy environment. A type-2 intuitionistic fuzzy einstein interactive weighted averaging (T2IFEIWA) operator is proposed for this purpose. The desirable properties of the proposed aggregation operator are validated, and the operator is used to choose the best e-learning tool.

Trapezoidal Intuitionistic Fuzzy Power Heronian Aggregation Operator and Its Applications to Multiple-Attribute Group Decision-Making

Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used. It is mainly because of the flexibility in capturing the incompleteness that occurs in the data. Aggregation operators play a vital role in real-life decision-making problems (modelled under an intuitionistic fuzzy environment). Different aggregation operators are available in the literature for better decision-making. Various aggregation operators are introduced in the literature as a generalization to the conventional aggregation functions defined on the set of real numbers. Each aggregation operator has a specific purpose in solving the problems effectively. In recent years, the power average (PA) operator has been used to reduce the effect of biased data provided by decision-makers. Similarly, the Heronian mean (HM) operator has a property that considers the inter-relationship among various criteria available in the decision-making problem. In this paper, we have considered both the operators (HM, PA) to introduce a new aggregation operator (on the set of TrIFNs), which takes advantage of both properties of these operators. In this study, firstly, we propose the idea of a trapezoidal intuitionistic fuzzy power Heronian aggregation (TrIFPHA) operator and a trapezoidal intuitionistic fuzzy power weighted Heronian aggregation (TrIFPWHA) operator by combining the idea of the Heronian mean operator and power average operator in real numbers. Secondly, we study different mathematical properties of the proposed aggregation operators by establishing a few essential theorems. Thirdly, we discuss a group decision-making algorithm for solving problems modelled under a trapezoidal intuitionistic fuzzy environment. Finally, we show the applicability of the group decision-making algorithm by solving a numerical case problem, and we compare the proposed method’s results with existing methods.

Complex intuitionistic fuzzy ordered weighted distance measure

Compared with the complex fuzzy set (CFS) and the intuitionistic fuzzy set (IFS), the complex intuitionistic fuzzy set (CIFS) can handle the two-dimensional and uncertain information simultaneously, and thus strengthen the capability of capturing useful information. In this paper, we consider the situation with complex intuitionistic fuzzy environment, where the importance of certain information is also taken into consideration. To deal with these situations, we develop the complex intuitionistic fuzzy ordered weighted distance (CIFOWD) measure and investigate its main properties. We find that the CIFOWD measure provides a parameterized family of aggregation distance measures, which includes, for example, complex intuitionistic fuzzy ordered weighted geometric distance (CIFOWGD) measure, complex intuitionistic fuzzy ordered weighted Hamming distance (CIFOWHD) measure, and complex intuitionistic fuzzy ordered weighted Euclidean distance (CIFOWED) measure as special types. The CIFOWD measure is capable of alleviating the influence of excessively large or excessively small deviations on the aggregation results via weight vector. Based on these distance measures, a multiple criteria group decision-making approach is presented under the CIFSs environment. An illustrative example regarding coronavirus vaccine selection on COVID-19 is taken for demonstrating the effectiveness of the proposed approach. Finally, the proposed results are compared with the results obtained from the existing methods.

A closed-loop supply chain model with carbon emission and pricing decisions under an intuitionistic fuzzy environment

A closed-loop supply chain model with carbon emission and pricing decisions under an intuitionistic fuzzy environment

TOPSIS Model for evaluating the corporate environmental performance under intuitionistic fuzzy environment

With global resource waste and environmental pollution becoming increasingly serious, corporate environmental performance (CEP) has received much attention from researchers over the past decade. As an important part of economic development, enterprises also pay increasingly attention to environmental protection and pollution control. CEP is regarded as the result of corporate environmental management. Assessing CEP can not only make enterprises focus on the environmental protection and management, but also promote sustainable social development. And it is frequently viewed as a multi-attribute group decision-making (MAGDM) issue. Thus, a novel MAGDM method is needed to tackle it. Depending on the conventional TOPSIS (Technique for Order Preferenceby Similarity to Ideal Solution) method and intuitionistic fuzzy sets (IFSs), this essay design a novel intuitive distance based IF-TOPSIS method to assess CEP. First of all, a related literature review is conducted. What’s more, some necessary theories related to IFSs are briefly reviewed. In addition, since subjective randomness frequently exists in determining criteria weights, the weights of criteria is decided objectively by utilizing CRITIC method. Afterwards, relying on novel distance measures between IFNs, the conventional TOPSIS method is extended to the intuitionistic fuzzy environment to calculate assessment score of each enterprise. Eventually, an application about CEP evaluation and some comparative analysis have been given to demonstrate the superiority of the designed method. The results illustrate that the designed framework is useful for assessing CEP.

Risk Priority Evaluation for Power Transformer Parts Based on Intuitionistic Fuzzy Preference Selection Index Method

The risk assessment of power transformer equipment can not only improve the safety and management level of transformer operation, but also reduce the operation and maintenance costs of the equipment on the basis of ensuring the overall reliable operation of the power system. As a result, it can enhance the rewards of assets investment. The quantitative analysis of power equipment risk often contains qualitative indicators that are difficult to quantify. These indicators have the characteristics of fuzziness. In order to improve the accuracy and reliability of risk assessment results, this paper proposed a new risk evaluation method based on intuitionistic fuzzy set. Firstly, language variables are transformed into corresponding intuitionistic fuzzy numbers. Secondly, a novel entropy of intuitionistic fuzzy set is established. Thirdly, a weighting method for determining each expert’s importance is proposed based on the new propose entropy. Furthermore, an extended preference selection index is put forward under intuitionistic fuzzy environment. Finally, an example of the risk assessment of power transformer components is discussed to illustrate the effectiveness of the new risk evaluation method.

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.

An Application of Fully Intuitionistic Fuzzy Multi-objective Linear Fractional Programming Problem in E-education System

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.

On Intuitionistic Fuzzy Primary Ideal of a Ring

The purpose of this paper is to introduce and investigate primary ideal and P-primary ideal in the intuitionistic fuzzy environment and lay down the foundation for the primary decomposition theorem in the intuitionistic fuzzy setting. Also a suitable characterization of intuitionistic fuzzy P-primary ideal will be discussed.

2DLIF-PROMETHEE methods for multiple attribute decision making under 2-dimension linguistic intuitionistic fuzzy environments

<h2>Abstract</h2> In this paper, how to run 2DLIF-PROMETHEE methods are introduced to deal with the multiple attribute decision making (MADM) problems evaluated by 2-dimension linguistic intuitionistic fuzzy variables (2DLIFVs). Firstly, the Euclidean distance and the cosine similarity measures for 2DLIFSs are introduced respectively. Then a hybrid distance for 2DLIFSs is introduced by integrating these two measures. Based on the hybrid distances for 2DLIFSs, six improved preference functions are designed to form the kernel part of 2DLIF-PROMETHEE methods. Finally, the partial ranking order of alternatives or the total ranking order of alternatives may be obtained by 2DLIF-PROMETHEE methods.

Two flexibility degrees-driven consensus model in group decision making with intuitionistic fuzzy preference relations

A group of experts are commonly invited to find an optimal solution to a complex decision making problem. When the bipolarity of decision information should be considered in group decision making (GDM), intuitionistic fuzzy values (IFVs) have the capability to model such opinions of decision makers (DMs). This paper develops a consensus model in GDM under intuitionistic fuzzy environments with flexibility. First, it is assumed that the initial opinions of DMs are expressed as intuitionistic fuzzy preference relations (IFPRs). A novel additive consistency index is constructed to measure the deviation degree of IFPRs from fuzzy preference relations (FPRs) with additive consistency, where the non-determinacy degree of IFPRs is incorporated. The thresholds of the proposed index corresponding to IFPRs with acceptable additive consistency are discussed and computed. Second, the consensus level of DMs is defined using the similarity degree between two IFVs. An optimization problem is established by maximizing the fitness function, which is constructed by linearly combining the proposed additive consistency index and consensus level. Two flexibility degrees are offered to each DM such that the initial opinions with the bipolarity can be adjusted correspondingly. Third, individual IFPRs in GDM are optimized using the particle swarm optimization (PSO) algorithm. Numerical examples are carried out to illustrate the proposed consensus model by comparing with the existing ones. The obtained results reveal that the proposed additive consistency index can reflect the inherent property of IFPRs. Different with the previous studies, two original flexibility degrees are proposed to characterize the multi-granularity of decision information in GDM.

Solving Multi-Objective Multilevel Programming problems using two-phase Intuitionistic Fuzzy Goal Programming method

This paper presents a two-phase intuitionistic fuzzy goal programming (two-phase IFGP) algorithm to solve Multi-Objective Multilevel Programming (MO-MLP) problems. The coefficient of each objective and constraint function is assumed to be triangular intuitionistic fuzzy parameters and the crisp MO-MLP problems are obtained using the accuracy function method. To avoid decision lock, the top levels set tolerance limits for decision variables to control the lower levels. The problem is modeled in the intuitionistic fuzzy environment using membership and non-membership functions for each objective function at all levels and decision variables controlled by the top levels. Then, we proposed an IFGP algorithm to achieve the highest degree of each membership and non-membership goal by minimizing unwanted deviational variables and generating compensatory solutions for all decision-makers at all levels. Moreover, in the proposed approach, two-phase IFGP is modeled to yield a compromise solution that satisfies both the MN-Pareto optimal solution and the Pareto optimal solution at each level. Also, verification of the proposed method is discussed with numerical examples.

A hybrid decision-making framework for photovoltaic poverty alleviation project site selection under intuitionistic fuzzy environment

The photovoltaic poverty alleviation project (PPAP), with functions of clean generation and poverty assistance, is regarded as an effective way to promote energy structure transformation and social coordinated development. Improper site selection poses a threat to stable profits, which hinders PPAP development. However, existing index systems fail to reflect PPAPs’ characteristics, and traditional decision-making techniques are faced with some problems such as information loss and evaluation bias. Therefore, a hybrid decision-making framework for PPAP site selection is proposed: First, based on 4-dimension searching loop, a comprehensive index system which includes veto indexes and sorting indexes is established; Second, a combined weight determining method is adopted to balance logic importance and decision-making contribution; Third, an extended ranking method is proposed for optimal alternative determination with consideration of intuitionistic fuzzy environment and bounded rationality; Finally, a case of Anhui, China is employed to verify the practicability and the robustness of the proposed framework. Results show that number of households assisted, initial capital and local villager support play a vital role in PPAP site selection. Judging from contributions, this paper can not only provide effective decision-making guidance for project investors, but also enriches the theoretical system of multi-criteria decision-making methods.

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.

An [formula omitted]-cut interval based IF-importance measure for intuitionistic fuzzy fault tree analysis of subsea oil and gas production system

The subsea production system is very important for having deep water oil and gas production. The leakage of the oil and gas in the subsea production system may result in enormous adverse consequences on marine lives, high production loss, and serious deadly disasters to humans. For the safety analysis of subsea production system, importance measures play an important role to rank the components of the system according to their contribution to the leakage of oil and gas for preventive and corrective purposes. In conventional fault tree analysis and fuzzy fault tree analysis, various importance measures are developed for criticality analysis of the system. The objective of the present study is to develop a novel IF-importance measure by employing the concept of α-cut interval under intuitionistic fuzzy environment. The failure possibilities of basic events in fault tree analysis are quantified by triangular and trapezoidal intuitionistic fuzzy numbers. The presented research study applies α-cut intervals of intuitionistic fuzzy numbers, intuitionistic fuzzy fault tree analysis and interval arithmetic operations. The validation is carried out by comparing the developed importance measure with some pre-existing importance measures.

Multiple Attribute Group Decision-Making Based on Intuitionistic Fuzzy Schweizer-Sklar Generalized Power Aggregation Operators

An intuitionistic fuzzy set (IFS) is a valuable tool to execute uncertain and indeterminate information. IFSs are more suitable to identify decision-maker’s evaluation data in decision-making problems. Intuitionistic fuzzy aggregation operators (AOs) are of enormous consequences in multiple attribute group decision-making (MAGDM) problems with an intuitionistic fuzzy environment. Consequently, the main impacts of this article are: firstly, to instigate various new novel generalized power AOs based on Schweizer-Sklar operational rules for IFS. Secondly, the study aims to discuss characteristics and particular cases of AOs. The core edge of proposed AOs is that they can eradicate the influence of uncomfortable data which could be too high or too low, making them more admirable for efficiently solving more and more complex MAGDM problems. Thirdly, we instigate two new algorithms to deal with MAGDM established on the generalized Schweizer-Sklar power AOs. Lastly, we appertain the anticipated method and algorithms to health care waste treatment technology selection (HCW-TT) to show the competence of the anticipated method and algorithms. The prevailing novelties of these items are duplex. Firstly, new generalized AOs established on Schweizer-Sklar operational rules are initiated for IFNs. Secondly, two new approaches for IF MAGDM are initiated, one for known decision-makers (DMs) and attributes weights, while the other for unknown DMs and attributes weights.