Interval-valued Intuitionistic Fuzzy Aggregation Operators Research Articles

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.

Target Damage Assessment Method Based on Interval‐Valued Intuitionistic Fuzzy Aggregation Operator under Dynamic Multi‐Expert

This study aims to solve the problem that the current target damage assessment method does not fully take into account the time series characteristics of the target and the dynamic changes in the battlefield situation, thus leading to insufficient accuracy of the assessment results. Target damage assessment method based on interval‐valued intuitionistic fuzzy aggregation operator (IVIFAO) under dynamic multi‐experts is a combination of interval‐valued intuitionistic fuzzy set (IVIFS) theory and dynamic multi‐attribute swarm decision‐making theory. Firstly, we extracted the effective factors that cause damage to the target and established the damage assessment index system. Secondly, in order to take into account the subjective weights and objective weights, we proposed a comprehensive weight model of damage factors based on interval‐valued intuitionistic fuzzy entropy (IVIFE) based on a cosine function (IVIFECF). The spatio‐temporal weights for each moment are determined using the Poisson distribution method. Then, given the inherent ambiguity and complexity of the decision‐making process, the decision‐making information is represented by interval‐valued intuitionistic fuzzy numbers (IVIFNs). We constructed a weighted interval‐valued intuitionistic fuzzy (WIVIF) decision matrix. Here, the interval‐valued intuitionistic fuzzy weighted geometric average (IVIFPWGA) operator is used to synthesize decision‐making information related to damage factors. We further introduce the dynamic interval‐valued intuitionistic fuzzy power‐weighted geometric average (DIVIFPWGA) operator, which combines instantaneous decision information with time series weights to generate a dynamic multi‐expert fusion WIVIF decision matrix. Finally, the improved TOPSIS method is used to rank the IVIFNs, resulting in a comprehensive damage assessment of the targets, which is analysed for superiority with the novel method, comparing both real‐time and scalability. The stability and validity of the method were verified.

The Linguistic Interval-Valued Intuitionistic Fuzzy Aggregation Operators Based on Extended Hamacher T-Norm and S-Norm and Their Application

Linguistic interval-valued intuitionistic fuzzy sets, as an extension of interval-valued intuitionistic fuzzy sets, have strong practical value in the management of complex uncertainty system with qualitative evaluation information. This study focuses on the development of several linguistic interval-valued intuitionistic fuzzy Hamacher (LIVIFH) aggregation operators based on the extended Hamacher t-norm and s-norm. First, the extended Hamacher t-norm and s-norm, which are applicable to linguistic information environment, are applied to define the linguistic interval-valued intuitionistic fuzzy Hamacher operational laws. Second, based on the proposed operational laws, this study defines the linguistic interval-valued intuitionistic fuzzy Hamacher weighted average (LIVIFHWA) operator and the linguistic interval-valued intuitionistic fuzzy Hamacher weighted geometric (LIVIFHWG) operator, and then investigates their properties. Furthermore, the degeneracy and monotonicity of the proposed operators with respect to the adjustable parameter are explored. Finally, a multiple attribute group decision-making (MAGDM) approach is developed based on the proposed LIVIFH aggregation operators, and then this approach is applied to a supplier selection problem. Parameter analysis indicates that the adjustable parameter in the proposed LIVIFH aggregation operators could reflect the attitudes of decision makers. The LIVIFHWA operator would be more appropriate to optimistic decision makers, and the LIVIFHWG operator to pessimistic decision makers. In addition, as the adjustable parameter increasing, both attitudes tend to be neutral. The proposed method is also compared with two other approaches to show its feasibility and efficiency.

Multi-attribute group decision making based on extended TOPSIS method under interval-valued intuitionistic fuzzy environment

In this paper, we propose a novel multi-attribute group decision making (MAGDM) method under interval-valued intuitionistic fuzzy environment by integrating extended TOPSIS and linear programming methods. We assume that multiple decision makers provide the input information, namely the assessment values and attribute weights using interval-valued intuitionistic fuzzy (IVIF) values for incorporating inherent uncertainty in the MAGDM process. Furthermore, the weights of decision makers given by experts to describe their importance in group decision making are assumed as IVIF values. The advantage and disadvantage scores are employed to determine the individual measure of importance for each decision maker. Aggregation of the assessment values and attributes weights are performed using two different IVIF aggregation operators. A weighted similarity measure, based upon the optimal attributes weights obtained through linear programming method, is defined for determining relative closeness coefficients for selection of the most preferred alternative. A real-world case study is provided to illustrate the working of the proposed methodology. Moreover, a thorough comparison has been done with related existing works in order to show the advantages of the methodology.

Note on continuous interval-valued intuitionistic fuzzy aggregation operator

Recently, Zhou et al. proposed the C-IVIFOWA operator for aggregating interval-valued intuitionistic fuzzy numbers. The flaws of the C-IVIFOWA operator are illustrated by two counter-examples. The aim of this short communication is to show how the existing aggregation operator can be improved to increase accuracy. Some desirable properties of the revised C-IVIFOWA operator are studied in detail.

Multiple attribute group decision making based on interval-valued intuitionistic fuzzy aggregation operators and transformation techniques of interval-valued intuitionistic fuzzy values

In this paper, we propose a new method for multiple attribute group decision making (MAGDM) based on the proposed interval-valued intuitionistic fuzzy aggregation (IVIFA) operators (including the interval-valued intuitionistic fuzzy weighted averaging (IVIFWA) operator, the interval-valued intuitionistic fuzzy ordered weighted averaging (IVIFOWA) operator and the interval-valued intuitionistic fuzzy hybrid weighted averaging (IVIFHWA) operator) of interval-valued intuitionistic fuzzy values (IVIFVs). First, we propose transformation techniques between IVIFVs and right-angled triangular fuzzy numbers based on the proposed addition operator of IVIFVs. We also prove some properties of the proposed addition operator of IVIFVs. Then, we propose the IVIFWA operator, the IVIFOWA operator and the IVIFHWA operator for aggregating IVIFVs. Finally, we propose a new MAGDM method based on the proposed IVIFA operators. The experimental results show that the proposed MAGDM method can overcome the drawbacks of the existing methods. It provides us with a useful way for MAGDM in interval-valued intuitionistic fuzzy environments.

Several New Interval-Valued Intuitionistic Fuzzy Hamacher Hybrid Operators and Their Application to Multi-Criteria Group Decision Making

Interval-valued intuitionistic fuzzy sets (IVIFSs) contain three ranges, namely the membership degree range, the non-membership degree range, and the hesitancy degree range, and they are very suitable for depicting uncertain or fuzzy information. In the course of decision making with IVIFSs, interval-valued intuitionistic fuzzy aggregation operators play a very important role and have received considerable attention in recent years. In this paper, we note the drawbacks of existing aggregation operators for IVIFNs. Some new interval-valued intuitionistic fuzzy Hamacher hybrid aggregation operators, such as the interval-valued intuitionistic fuzzy Hamacher hybrid arithmetical averaging operator and the interval-valued intuitionistic fuzzy Hamacher hybrid arithmetical geometric operator, are introduced to overcome the drawbacks of the existing operators. All of these newly developed operators can weigh both the interval-valued intuitionistic fuzzy arguments and their ordered positions simultaneously, and they have several desirable properties, such as idempotency, boundedness, and monotonicity. To show the applications of our proposed hybrid aggregation operators, we propose a simple procedure for multi-criteria group decision making with interval-valued intuitionistic fuzzy information and then use a numerical example to illustrate the validity and applicability of the proposed procedure and operators.

INTERVAL-VALUED INTUITIONISTIC FUZZY ORDERED PRECISE WEIGHTED AGGREGATION OPERATOR AND ITS APPLICATION IN GROUP DECISION MAKING

An important research topic related to the theory and application of the interval-valued intuitionistic fuzzy weighted aggregation operators is how to determine their associated weights. In this paper, we propose a precise weight-determined (PWD) method of the monotonicity and scale-invariance, just based on the new score and accuracy functions of interval-valued intuitionistic fuzzy number (IIFN). Since the monotonicity and scale-invariance, the PWD method may be a precise and objective approach to calculate the weights of IIFN and interval-valued intuitionistic fuzzy aggregation operator, and a more suitable approach to distinguish different decision makers (DMs) and experts in group decision making. Based on the PWD method, we develop two new interval-valued intuitionistic fuzzy aggregation operators, i.e. interval-valued intuitionistic fuzzy ordered precise weighted averaging (IIFOPWA) operator and interval-valued intuitionistic fuzzy ordered precise weighted geometric (IIFOPWG) operator, and study their desirable properties in detail. Finally, we provide an illustrative example.

Hydrogen Production Technologies Evaluation Based on Interval-Valued Intuitionistic Fuzzy Multiattribute Decision Making Method

We establish a decision making model for evaluating hydrogen production technologies in China, based on interval-valued intuitionistic fuzzy set theory. First of all, we propose a series of interaction interval-valued intuitionistic fuzzy aggregation operators comparing them with some widely used and cited aggregation operators. In particular, we focus on the key issue of the relationships between the proposed operators and existing operators for clear understanding of the motivation for proposing these interaction operators. This research then studies a group decision making method for determining the best hydrogen production technologies using interval-valued intuitionistic fuzzy approach. The research results of this paper are more scientific for two reasons. First, the interval-valued intuitionistic fuzzy approach applied in this paper is more suitable than other approaches regarding the expression of the decision maker’s preference information. Second, the results are obtained by the interaction between the membership degree interval and the nonmembership degree interval. Additionally, we apply this approach to evaluate the hydrogen production technologies in China and compare it with other methods.

Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making

In this paper, we introduce a new operator called the continuous interval-valued intuitionistic fuzzy ordered weighted averaging (C-IVIFOWA) operator for aggregating the interval-valued intuitionistic fuzzy values. It combines the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator and the continuous ordered weighted averaging (C-OWA) operator by a controlling parameter, which can be employed to diminish fuzziness and improve the accuracy of decision making. We further apply the C-IVIFOWA operator to the aggregation of multiple interval-valued intuitionistic fuzzy values and obtain a wide range of aggregation operators including the weighted C-IVIFOWA (WC-IVIFOWA) operator, the ordered weighted (OWC-IVIFOWA) operator and the combined C-IVIFOWA (CC-IVIFOWA) operator. Some desirable properties of these operators are investigated. And finally, we give a numerical example to illustrate the applications of these operators to group decision making under interval-valued intuitionistic fuzzy environment.

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov's intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the Łukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.

Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making

This study investigates the group decision making under interval-valued intuitionistic fuzzy environment in which the attributes and experts are in different priority level. We first propose some interval-valued intuitionistic fuzzy aggregation operators such as the interval-valued intuitionistic fuzzy prioritized weighted average (IVIFPWA) operator, the interval-valued intuitionistic fuzzy prioritized weighted geometric (IVIFPWG) operator. These proposed operators can capture the prioritization phenomenon among the aggregated arguments. Then, some of their desirable properties are investigated in detail. Furthermore, an approach to multi-criteria group decision making based on the proposed operators is given under interval-valued intuitionistic fuzzy environment. Finally, a practical example about talent introduction is provided to illustrate the developed method.