Intuitionistic Trapezoidal Fuzzy Research Articles

A Novel Ranking Approach to Rank Interval-Valued Trapezoidal Intuitionistic Fuzzy Sets by Using the Concept of Centroids

A Novel Ranking Approach to Rank Interval-Valued Trapezoidal Intuitionistic Fuzzy Sets by Using the Concept of Centroids

Correction to: An Interval‑Valued Trapezoidal Intuitionistic Fuzzy TOPSIS Approach for Decision‑Making Problems

Correction to: An Interval‑Valued Trapezoidal Intuitionistic Fuzzy TOPSIS Approach for Decision‑Making Problems

Evaluating and Ranking Metaverse Platforms Using Intuitionistic Trapezoidal Fuzzy VIKOR MCDM: Incorporating Score and Accuracy Functions for Comprehensive Assessment

The purpose of this study is to develop a new approach for decision-making for addressing multi-attribute decision-making problems within a trapezoidal intuitionistic fuzzy environment, while taking into account decision makers' psychological behavior. As a starting point, we propose and apply a distance metric model for trapezoidal intuitionistic fuzzy numbers. Then, by incorporating the expected value, score function, and accuracy value, we create a novel approach by comparing it with the results obtained from the VIKOR multi-criteria decision-making technique, allowing us to account for decision makers' risk tolerance. Through correlation analysis, we assess the similarities and deviations in the resulting rankings. Finally, we illustrate the practical utility and feasibility of our proposed approach by evaluating the digital marketing capabilities of a few metaverse platforms using standards set in line with marketing mix criteria.

Multi-Attribute Decision-Making with Independent Trapezoidal Intuitionistic Fuzzy Information Based on Risk Orientation and Similarity Measure

The strategy production in intuitionistic fuzzy multi-attribute decision-making is influenced by various factors. More realistic data representations are needed to portray ambiguity under increasingly complex decision-making contexts. Firstly, this study proposes a new approach for ranking independent trapezoidal intuitionistic fuzzy numbers based on the risk attitudes of decision-makers. The proposed ranking approach incorporates the decision-makers’ risk preferences and considers all possible values in the feasible domain. After that, a novel similarity measure between two independent trapezoidal intuitionistic fuzzy numbers is presented based on the three-segment projection. The constructed similarity measure uses the image structure of the data to reflect the variation of vagueness and then also combines deviation to achieve optimization. Moreover, this study improves the VIKOR method under the independent trapezoidal intuitionistic fuzzy environment (V-ITIFE) to solve the multi-attribute decision-making problems. Finally, a numerical example is presented to illustrate the applicability and efficiency of the V-ITIFE method.

Techniques for Finding Analytical Solution of Generalized Fuzzy Differential Equations with Applications

Engineering and applied mathematics disciplines that involve differential equations include classical mechanics, thermodynamics, electrodynamics, and general relativity. Modelling a wide range of real-world situations sometimes comprises ambiguous, imprecise, or insufficient situational information, as well as multiindex, uncertainty, or restriction dynamics. As a result, intuitionistic fuzzy set models are significantly more useful and versatile in dealing with this type of data than fuzzy set models, triangular, or trapezoidal fuzzy set models. In this research, we looked at differential equations in a generalized intuitionistic fuzzy environment. We used the modified Adomian decomposition technique to solve generalized intuitionistic fuzzy initial value problems. The generalized modified Adomian decomposition technique is used to solve various higher-order generalized trapezoidal intuitionistic fuzzy initial value problems, circuit analysis problems, mass-spring systems, steam supply control sliding value problems, and some other problems in physical science. The outcomes of numerical test applications were compared to exact technique solutions, and it was shown that our generalized modified Adomian decomposition method is efficient, robotic, and reliable, as well as simple to implement.

Intuitionistic Trapezoidal Fuzzy based Aggregation Operator: Applications in Medical Diagnosis

Since the inception of fuzzy sets given by Zadeh, uncertainty arises due to partial information or imprecise information has been measured. The generalized version of fuzzy sets has been introduced by Atanassov, known as intuitionistic fuzzy sets (IFSs), which have wide applications in decision making processes and consider both membership and non-membership functions. A generalized fuzzy based decision making method with aggregation operator has been discussed with application in medical diagnosis. In this paper, IF based method have been discussed for the application of the diagnosis of the type of child cancer.

SHORTEST PATH ON INTERVAL-VALUED INTUITIONISTIC TRAPEZOIDAL NEUTROSOPHIC FUZZY GRAPHS WITH APPLICATION

In this article, stretch esteemed Interval Valued Intuitionistic Trapezoidal Neutrosophic Fuzzy Graph (IVITrNFG) of SPP, which is drew on trapezoidal numbers and IVITrNFG. Hear a genuine application is given an illustrative model for IVITrNFG. Additionally Shortest way is determined for this model. This present Dijkstra’s Algorithm briefest way was checked.

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.

Failure Risk Assessment of Coal Gasifier Based on the Integration of Bayesian Network and Trapezoidal Intuitionistic Fuzzy Number-Based Similarity Aggregation Method (TpIFN-SAM)

The coal gasifier is the core unit of the coal gasification system. Due to its exposure to high temperatures, high pressures, and aggressive media, it is highly susceptible to serious accidents in the event of failure. Therefore, it is important for the gasifier to perform failure-risk assessment to understand its safety status and provide safety measures. Bayesian networks (BNs) for risk analysis of process systems has received a lot of attention due to its powerful inference capability and its ability to reflect complex relationships between risk factors. However, the acquisition of basic probability data in a Bayesian network is always a great challenge. In this study, an improved Bayesian network integrated with a trapezoidal intuitionistic fuzzy number-based similarity aggregation method (TpIFN-SAM) is proposed for the failure-risk assessment of process systems. This approach used the TpIFN-SAM to collect and aggregate experts’ opinions for obtaining the prior probabilities of the root events in the BN. In the TpIFN-SAM, the intuitionistic fuzzy analytic-hierarchy-process method (IF-AHP) was adopted to assign the expert weights for reducing subjectivity or the bias caused by individual differences. To clarify the suitability of the proposed method, a case study of a coal gasifier was demonstrated, and both prediction and diagnosis analyses of the BN were performed; finally, the weak links of the gasifier were identified.

Multicriteria group decision making via generalized trapezoidal intuitionistic fuzzy number-based novel similarity measure and its application to diverse COVID-19 scenarios.

Havoc, brutality, economic breakdown, and vulnerability are the terms that can be rightly associated with COVID-19, for the kind of impact it is having on the whole world for the last two years. COVID-19 came as a nightmare and it is still not over yet, changing its form factor with each mutation. Moreover, each unpredictable mutation causes more severeness. In the present article, we outline a decision support algorithm using Generalized Trapezoidal Intuitionistic Fuzzy Numbers (GTrIFNs) to deal with various facets of COVID-19 problems. Intuitionistic fuzzy sets (IFSs) and their continuous counterparts, viz., the intuitionistic fuzzy numbers (IFNs), have the flexibility and effectiveness to handle the uncertainty and fuzziness associated with real-world problems. Although a meticulous amount of research works can be found in the literature, a wide majority of them are based mainly on normalized IFNs rather than the more generalized approach, and most of them had several limitations. Therefore, we have made a sincere attempt to devise a novel Similarity Measure (SM) which considers the evaluation of two prominent features of GTrIFNs, which are their expected values and variances. Then, to establish the superiority of our approach we present a comparative analysis of our method with several other established similarity methods considering ten different profiles of GTrIFNs. The proposed SM is then validated for feasibility and applicability, by elaborating a Fuzzy Multicriteria Group Decision Making (FMCGDM) algorithm and it is supportedby a suitable illustrative example. Finally, the proposed SM approach is applied to tackle some significant concerns due to COVID-19. For instance, problems like the selection of best medicine for COVID-19 infected patients; proper healthcare waste disposal technique; and topmost government intervention measures to prevent the COVID-19 spread, are some of the burning issues which are handled with our newly proposed SM approach.Graphical abstract

Decision-Making Problem Based on Confidence Intuitionistic Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application

Confidence level plays an important role in decision making in daily life. Therefore, the focus of our paper is to develop the idea of confidence level. With the help of confidence level in this paper, we explore some new operators, namely confidence intuitionistic trapezoidal fuzzy Einstein weighted averaging (abbreviated as CITFEWA) operator, confidence intuitionistic trapezoidal fuzzy Einstein ordered weighted averaging (abbreviated as CITFEOWA) operator, confidence intuitionistic trapezoidal fuzzy Einstein hybrid averaging (abbreviated as CITFEHA) operator, confidence intuitionistic trapezoidal fuzzy Einstein weighted geometric (abbreviated as CITFEWG) operator, confidence intuitionistic trapezoidal fuzzy Einstein ordered weighted geometric (abbreviated as CITFEOWG) operator and confidence intuitionistic trapezoidal fuzzy Einstein hybrid geometric (abbreviated as CITFEHG) operator. The benefit of the confidence approaches is that these techniques not only deliver evidence of the problems to the experts, but these operators and methods also develop the grades of the decision makers of that these experts are familiar with the option for the selection. To develop the proposed operators, we investigate and study some of their basic properties. To show the importance and efficiency of the new methods, these methods are applied to decision making. Lastly, an example is given for the confirmation of the viability and availability of the proposed approaches and methods.

An unknown Transit technique for Solving Generalized Trapezoidal Intuitionistic Fuzzy Transportation Problems using Centroid of Centroids

In the present day by day life circumstances TP we habitually face the circumstance of unreliability in addition to unwillingness due to various unmanageable segments. To deal with unreliability and unwillingness multiple researchers have recommended the intuitionistic fuzzy (IF) delineation for material. This paper proposes the approach used by generalized trapezoidal intuitionistic fuzzy number to solve these transport problem, i.e. capacity and demand are considered as real numbers and charge of transport from origin to destination is considered as generalized trapezoidal intuitionistic fuzzy numbers as charge of product per unit. The generalized trapezoidal intuitionistic fuzzy numbers ranking function is used on the basis of IFN'S centroid of centroids. Through the traditional optimization process, we generate primary basic feasible solution and foremost solution. The numerical illustration shows efficacy of technique being suggested. A fresh technique is implemented to seek foremost solution using ranking function of a fuzzy TP of generalized trapezoidal intuitionistic fuzzy number. Without finding a IBFS, this approach explicitly provides optimal solution for GTrIFTP. Finally, for ranking function we apply a proposed GTrIFTP method illustrated Numerical example.

Reliability allocation method based on Intuitionistic Trapezoidal Fuzzy Number and Grey Correlation

The reliability allocation method of machine tools has the feature of high complexity and uncertainty. To reduce the fuzziness in the process of reliability allocation, this paper proposes a novel reliability allocation method of CNC machine tools based on Intuitionistic Trapezoidal Fuzzy Number and Grey Correlation. First, the subsystems of CNC machine tools are divided based on function, and the reliability of subsystems are also allocated. Then, expert decision matrixes are obtained based on intuitionistic trapezoidal fuzzy numbers. The result is obtained by the calculation of the grey relation degree between decision matrixes and ideal matrixes. Finally, an example is taken to verify the effectiveness of the proposed method. Compared to the traditional method, the proposed method can reduce the calculation and more convenient to use.

TRAPEZOIDAL INTUITIONISTIC FUZZY NUMBER WITH SOME ARITHMETIC OPERATIONS AND ITS APPLICATION ON RELIABILITY EVALUATION

In fuzzy mathematics fuzzy system reliability can be analysed by fuzzy sets. We can use various types of fuzzy sets for that analyzing the fuzzy system reliability but here we specially used intuitionistic fuzzy set theory. At first, TrIFNs and their arithmetic operations are introduced. Expressions for computing the fuzzy reliability of a series system, parallel system, series-parallel and parallel-series system following TrIFNs have been described. Here an imprecise failure to start of a truck is taken. To compute the imprecise failure of the above said system, failure of each component of the systems is represented by Trapezoidal Intuitionistic Fuzzy Number. This process can be utilise to measure the failure is various aspects like portfolio in stock market etc. The numerical expression also calculated and presented in this paper for the failure to start of a truck using TrIFN.

Decision Making with Unknown Criteria Weight Information in the Frame Work of Interval Valued Trapezoidal Intuitionistic Fuzzy Sets

This paper proposes an interval valued trapezoidal intuitionistic fuzzy (IVTIF) decision making model for multi criteria group decision making (MCGDM) problem by taking into consideration that the criteria weights of each decision maker may differ with respect to each other when criteria weights are unknown prior. In this process, a new method to find the criteria weight based on alternatives performance and Einstein weighted averaging operator on IVTIFSs is defined. Further, the properties of interval valued trapezoidal intuitionistic fuzzy Einstein weighted averaging (IVITFEWA) operator are proved. The proposed method is illustrated by taking a numerical example. From the results it is observed that the proposed method can effectively rank the alternatives compared to existing methods.

A Method For Solving Balanced And Unbalanced Trapezoidal Intuitionistic Fuzzy Assignment Quandary

In this paper, we discuss Trapezoidal intuitionistic fuzzy assignment quandary(TrIFAP). In classical assignment quandary, Cost always remains same. But, here we develop an method to solve Trapezoidal intuitionistic fuzzy assignment quandary where cost is not deterministic numbers but infelicitous ones. Here, the costs(profits) matrix have all the elements they are TrIFN and others have been immensely colossal demonstration against the classical method. Then its trapezoidal membership and non-membership functions are defined. In general compare the findings from different methods attested the same picture. Numerical examples show that an intuitionistic fuzzy ranking method is very efficacious and utilizable method for handling a TrIFAP.

Metric Properties between Trapezoidal Intuitionistic Fuzzy Numbers

Generally ranking of fuzzy number is more essential for convertion of fuzzy number to crisp one. In this manuscript, a new approach to rank the trapezoidal intuitionistic fuzzy numbers using cuts is established. The metric distance of the interval numbers is extended to trapezoidal intuitionistic fuzzy numbers. By using both the ranking of trapezoidal intuitionistic fuzzy numbers and cuts there is abundant scope of investigating the numerical problems in optimization.

An Improved Aggregation Operators-based Method for Multiple Attribute Group Decision Making Using Interval-valued Trapezoidal Intuitionistic Fuzzy Sets

An Improved Aggregation Operators-based Method for Multiple Attribute Group Decision Making Using Interval-valued Trapezoidal Intuitionistic Fuzzy Sets

Intuitionistic Trapezoidal Fuzzy MAGDM Problems with Sumudu Transform in Numerical Methods

Multiple attribute group decision making (MAGDM) is an important scientific, social, and economic endeavor. The ability to make consistent and correct choices is the essence of any decision process imbued with uncertainty. In situations where the information or data is in the form of an intuitionistic trapezoidal fuzzy numbers, or to construct the MAGDM problem, an intuitionistic trapezoidal fuzzy weighted averaging (ITzFWA) operator and an intuitionistic trapezoidal fuzzy hybrid aggregation (ITzFHA) operator are used. In this article, the decision maker provides the weights for aggregation in the form of an initial value problem of ordinary differential equations based on the study made on the data given by the decision maker. Decision maker weights are derived through sumudu transformation and various other numerical methods by obtaining the solution of differential equations. A numerical illustration is given to show the effectiveness and feasibility of the proposed approach.

A three-cycle decision-making selection mechanism with intuitionistic trapezoidal fuzzy preference relations

A three-cycle decision-making selection mechanism with intuitionistic trapezoidal fuzzy preference relations