Intuitionistic Fuzzy Values Research Articles

An information measure based extended VIKOR method in intuitionistic fuzzy valued neutrosophic value setting for multi-criteria group decision making

The paper presents an extended VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method for solving group decision-making problems. The uncertainties given in the data are handled with the help of the intuitionistic fuzzy valued neutrosophic values (IFVNVs), which allow decision-makers to carry more detailed information while providing their preferences in the imprecise environment. The proposed VIKOR method utilized the features of IFVNVs and computed the distance measures between their pairs using $L^p$-metric and $L^\infty$-metric. The weights of the different criteria are computed by using the entropy-based measures for the families of IFVNVs. The presented method has been illustrated with a numerical example. A comparative interpretation and the sensitivity analysis of the parameter associated with the technique are achieved to reveal their influences.

Multiple attributes group decision-making based on trigonometric operators, particle swarm optimization and complex intuitionistic fuzzy values

Multiple attributes group decision-making based on trigonometric operators, particle swarm optimization and complex intuitionistic fuzzy values

Multiattribute decision making based on nonlinear programming methodology and novel score function of interval-valued intuitionistic fuzzy values

In this paper, we propose a novel multiattribute decision making (MADM) method using the nonlinear programming (NLP) methodology and the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a new score function of IVIFVs to conquer the drawbacks of the existing score functions of IVIFVs. Then, we construct the converted matrix based on the proposed score function of IVIFVs by calculating the score value of each IVIFV in the decision matrix (DM) offered by the decision maker (DMK). Then, we construct the NLP model via the obtained converted matrix and the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute given by the DMK. Then, we solve the NLP model to obtain the optimal weight for each attribute. Then, based on the obtained converted matrix and the obtained optimal weight of each attribute, we calculate the weighted score of each alternative. Finally, the alternatives are ranked on the basis of the obtained weighted scores of the alternatives. The larger the weighted score of an alternative, the better the preference order of the alternative. The proposed MADM method can overcome the drawbacks of the existing MADM methods. It offers us a very useful approach for MADM in IVIF settings.

IoT System Selection as a Fuzzy Multi-Criteria Problem.

This research aims to analyse the applications of IoT in agriculture and to compare the most widely used IoT platforms. The problem of determining the most appropriate IoT system depends on many factors, often expressed by incomplete and uncertain estimates. In order to find a feasible decision, this study develops a multi-criteria framework for IoT solution selection in a fuzzy environment. In the proposed framework, a new modification of the Multi-Attribute Border approximation Area Comparison (MABAC) method with a specific distance measure via intuitionistic fuzzy values has been presented as a decision analysis method. The new technique is more precise than existing crisp and fuzzy analogues, as it includes the three components of intuitionistic numbers (degree of membership, degree of non-membership and hesitancy degree) and the relationships between them. The effectiveness of the new decision-making framework has been verified through an illustrative example of ranking IoT platforms.

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.

An Improved Ranking Method for Multi Attributes Decision Making Problem Based on Interval Valued Intuitionistic Fuzzy Values

In this present work, a new ranking order technique has been discussed for interval valued intuitionistic fuzzy values. Firstly, some drawbacks of proposed method by Kumar and Chen have been discussed with examples. Then we discussed a new ranking order technique. The proposed method is based on a new converted decision matrix, probability density functions of the interval valued intuitionistic fuzzy values. Here, a new converted decision matrix has been introduced which overcomes some delusions of the proposed method by Kumar and Chen. Then the probability density functions have been defined based on the converted decision matrix. From this probability density functions the mean value and the standard deviation for each alternative has been derived. Using these mean and standard deviation the z-score decision matrix has been derived. The transform weight for each alternative has been derived from the interval valued intuitionistic fuzzy weight vales. Finally, the ranking order has been derived from the transformed weight and z-score decision matrix. Some examples also have been considered to compare the proposed method with other existing methods. The proposed method has been applied to a selection of house among some houses with different criteria. So, the proposed method remove the drawbacks exist in the previous existing methods and it is very much useful for different types of multi criteria decision making problems.

Sanal sezgisel bulanık parametreli sezgisel bulanık esnek kümeler ve karar verme üzerine bir uygulaması

In this paper, it is aimed to express more accurately the intuitionistic fuzzy values expressed by the decision-makers for intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets. For this purpose, virtual intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets are proposed by defining the concepts of virtual lower and upper intuitionistic fuzzy approaches. Moreover, the basic set operations for this hybrid set type are examined together with their associated properties. In addition, a decision-making algorithm focusing on virtual intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets is constructed. Finally, an analysis of the obtained results was made.

An extension of rule base evidential reasoning in the interval-valued intuitionistic fuzzy setting applied to the type 2 diabetes diagnostic

This paper presents an interval-valued intuitionistic fuzzy extension of rule base evidential reasoning which generally is a synthesis of fuzzy logic, the Dempster–Shafer theory of evidence (DST) and Atanassov’s intuitionistic fuzzy sets (A-IFS) theory redefined in the framework of DST. A lot of attention is paid to situations when in the solution of decision making problem the competing fuzzy classes with intersecting membership functions in antecedent parts of fuzzy rules, e.g., such as Low and Moderate play an important role in the problem formulation. As a result, a new mathematical object “belief interval bounded belief interval” (BIBBI) is obtained. The properties of BIBBI make it possible to use it as a more reliable representation of interval-valued intuitionistic fuzzy value than that formulated in terms of A-IFS. Using the introduced DST based definition of interval-valued A-IFS, the corresponding operations with BIBBIs and the DST representation of rule base evidential reasoning in the intuitionistic fuzzy setting, a new approach to the interval-valued intuitionistic fuzzy extension of rule base evidential reasoning is developed. To prove the correctness and applicability of this approach to the solution of decision making problems, a case study of its use for the type 2 diabetes diagnostics is analyzed.

Group decision making based on advanced intuitionistic fuzzy weighted Heronian mean aggregation operator of intuitionistic fuzzy values

In this paper, we propose the advanced intuitionistic fuzzy Heronian mean (AIFHM) aggregation operator (AO) and the advanced intuitionistic fuzzy weighted Heronian mean (AIFWHM) AO of intuitonistic fuzzy values (IFVs). The proposed AIFHM AO and the proposed AIFWHM AO of IFVs have the advantage of condidering interrelationships among aggregating inputs. We also explore some properties of the proposed AIFHM AO and the proposed AIFWHM AO of IFVs. Furthermore, based on the proposed AIFWHM AO of IFVs, we propose a new group decision making (GDM) method. We also provide some examples to illustrate that the proposed GDM method can overcome the drawbacks of the existing GDM methods. The proposed GDM method offers us a very useful approach to deal with GDM problems in intuitionistic fuzzy environments.

Contingency response decision of network public opinion emergencies based on intuitionistic fuzzy entropy and preference information of decision makers

A multi-attribute group decision-making (MAGDM) method based on intuitionistic fuzzy preference information is proposed for the multi-attribute intuitionistic fuzzy group decision-making problem where the decision-makers weight and attribute weight are completely unknown and the decision-maker has preference information for the scheme. Firstly, an intuitionistic fuzzy interval judgment matrix is established to describe the original data of the key decision indicators for multiple network public opinion emergencies that erupt simultaneously. Secondly, the attribute weights are determined based on the improved intuitionistic fuzzy entropy construction method, and the expert weights are determined by using objective decision information, taking into account the intuitionistic fuzzy entropy of decision matrix. MAGDM can not only synthesize experts' professional experience in different aspects, but also avoid experts' decision-making errors caused by insufficient domain knowledge. It is necessary to continuously adjust the expert weight based on decision-making information to make the comprehensive decision-making information more accurate. Thirdly, a scheme preference model and an attribute weight optimization model are established to determine the ranking method of intuitionistic fuzzy interval values. Then, a modified distance measure of intuitionistic fuzzy sets (IFSs) is introduced to make the evaluation result more accurate and reasonable when it comes to solving the deviation between the evaluation value and ideal solution of each scheme. Finally, the effectiveness and practicability of the proposed decision-making method are verified by an example of emergency crisis severity, It assists decision makers in selecting and implementing the optimal emergency response plan in a timely and efficient manner, which improves the emergency treatment efficiency of network public opinion crisis, helps emergency departments to better deal with the network public opinion crisis, improves the ability of public opinion guidance and control, and provides a new method and idea for multi-attribute intuitionistic fuzzy group decision-making problem.

Product selection based on sentiment analysis of online reviews: an intuitionistic fuzzy TODIM method

Online reviews contain a great deal of information about consumers' purchasing preferences, which seriously affects potential consumers' purchasing decisions. Using the online review data to help customers make purchasing decisions has become a concern of customers, which has theoretical and practical application value. Therefore, a product selection model is presented based on sentiment analysis combined with an intuitionistic fuzzy TODIM method. Firstly, the product features are extracted by the Apriori algorithm based on online reviews. The sentiment orientation and intensity of the sentiment words for the product features are identified by the lexicon-based sentiment analysis approach. Next, the sentiment orientation of the product features is represented by an intuitionistic fuzzy value. Then the intuitionistic fuzzy TODIM method is used to determine the ranking results of the alternative products. Finally, the case study of mobile phone selection is given to illustrate the proposed approach. The results show that the proposed method considers the online reviews’ sentiment orientation and intensity and the consumers’ gain and loss in the purchasing product process and is more reasonable than the previous research.

Intuitionistic fuzzy-valued neutrosophic multi-sets and numerical applications to classification

A single-valued neutrosophic multi-set is characterized by a sequence of truth membership degrees, a sequence of indeterminacy membership degrees and a sequence of falsity membership degrees. Nature of a single-valued neutrosophic multi-set allows us to consider multiple information in the truth, indeterminacy and falsity memberships which is pretty useful in multi-criteria group decision making. In this paper, we consider sequences of intuitionistic fuzzy values instead of numbers to define the concept of intuitionistic fuzzy-valued neutrosophic multi-set. In this manner, such a set gives more powerful information. We also present some set theoretic operations and a partial order for intuitionistic fuzzy-valued neutrosophic sets and provide some algebraic operations between intuitionistic fuzzy-valued neutrosophic values. Then, we develop two types of weighted aggregation operators with the help of intuitionistic fuzzy t-norms and t-conorms. By considering some well-known additive generators of ordinary t-norms, we give the Algebraic weighted arithmetic and geometric aggregation operators and the Einstein weighted arithmetic and geometric aggregation operators that are the particular cases of the weighted aggregation operators defined via general t-norms and t-conorms. We also define a simplified neutrosophic valued similarity measure and we use a score function for simplified neutrosophic values to rank similarities of intuitionistic fuzzy-valued neutrosophic multi-values. Finally, we give an algorithm to solve classification problems using intuitionistic fuzzy-valued neutrosophic multi-values and proposed aggregation operators and we apply the theoretical part of the paper to a real classification problem.

Solving Intuitionistic Fuzzy Transport Equations by Intuitionistic Fuzzy Laplace Transforms

In this paper, we use an intuitionistic fuzzy Laplace transforms for solving intuitionistic fuzzy hyperbolic equations precisely the transport equation with intuitionistic fuzzy data under strongly generalized H-differentiability concept. For this purpose, the intuitionistic fuzzy transport equation is converted to the intuitionistic fuzzy boundary value problem (IFBVP) based on the intuitionistic fuzzy laplace transform. The related theorems and properties are proved in detail. Finally, we solve an example to illustrate this method.

A novel technique for parameter estimation in intuitionistic fuzzy logistic regression model

The Fuzzy Logistic Regression model can estimate the parameters when the data-set contains ambiguousness due to vagueness and cannot consider the degree of hesitation. Thus, this paper proposes a novel Intuitionistic Fuzzy Logistic Regression model to deal with the imprecise parameters containing the vagueness and hesitation degrees at a time. In this context, the revised Tanaka’s model is used to estimate the parameters. To illustrate the working efficiency of the proposed intuitionistic fuzzy logistic regression, we have presented the birth-weight data-set and applied it. The comparative study is also performed with other statistical models. The applicability and validity of the model are revealed by obtaining the goodness of fit criteria using Mean degrees of membership functions. On applying to the birth-weight data-set, it is observed that the intuitionistic fuzzy logistic regression values signify the good fit and are considered as the best fitting intuitionistic fuzzy logistic regression model for babies’ birth-weight data-set. The value of mean degree of membership is relatively more significant by using the proposed intuitionistic fuzzy logistic regression, which indicates the best fitting of the model compared to the fuzzy logistic regression model.

Information Quality for Intuitionistic Fuzzy Values with Its Application in Decision Making

Information quality has attracted increasing attention in recent years. In this paper, we propose a measure to quantify the information quality of intuitionistic fuzzy information based on a pseudo probability transformation, and derive its induced order to rank intuitionistic fuzzy values. The proposed measure and the induced order are proved to possess some well-defined properties that ensure rationality. Further, in order to rank intuitionistic fuzzy alternatives in decision making, we turn the proposed information quality into a ranking-oriented information quality, and present its induced order to generate the ranking. The decision capacity of our method is founded with the goal of rationalizing, simulating and further facilitating the interpretability and transparency in human decision making. A comparative study has been conducted, demonstrating the effectiveness of the proposed approach to ranking alternatives. The proposed approach is shown to outperform existing ranking methods via case-by-case comparisons. Finally, an application involving decision making of drug selection and an application in multi-criteria decision analysis of supplier selection are provided.

Intuitionistic fuzzy evaluation of artificial neural network model

In this paper a method that evaluates a trained artificial neural network is presented. The learning type of an artificial neural network is supervised learning which requires labeled input training vectors. Labeled medical data is provided to train the network, where the labels can either be 1 if the person is alive, or 0 if the person has deceased. The data is divided into training and validation vectors. The validation input vectors are used to evaluate the model and the results are summarized by using intuitionistic fuzzy values.

Measuring Staff Satisfaction in Transportation System using AHP Method under Uncertainty

One of the most important challenges in today world is the transportation and satisfaction of this system. Measuring satisfaction in transportation has been done quantitatively so far and, more importantly, the measurement process has not usually been scientific. This study aimed at an accurate scientific measurement. Because of ambiguity, this paper discusses how to use the intuitionistic fuzzy method, in which both membership and non-membership functions were expressed. Therefore, initially, considering the results of previous researches, as well as studying the references and standards, the characteristics and basic criteria, a researcher-made questionnaire with a reliability of 0.95 was first performed and then the weights were determined using the AHP intuitionistic fuzzy method. After performing the above steps, the intuitionistic fuzzy satisfaction value was calculated at different levels and using the method, the final number of satisfaction was defuzzified.

High performing sentiment analysis based on fast Fourier transform over temporal intuitionistic fuzzy value

Sentiment analysis or opinion mining has an extensive area in the field of research. Today we consider the huge amount of structured and unstructured data available in the web for a particular subject to get an opinion. The surplus data handling termed as big data requires some new technology to deal with. This paper considers the requirement of sentiment analysis of such huge data for fast processing. Based on fast Fourier transform on temporal intuitionistic fuzzy set generated from text, this algorithm (FFT–TIFS) expedites the sentiment classification. Fourier analysis converts a signal from its time domain to its representation in frequency domain. Such frequency domain algorithm on temporal intuitionistic fuzzy set is used in sentiment analysis for the first time. This algorithm is useful for short Twitter text, document-level as well as sentence-level binary sentiment classification. It is tested on aclImdb, Polarity, MR, Sentiment 140 and CR dataset which gives an average of 80% accuracy. The proposed method shows significant improvement in required time complexity where the method achieves 17 times faster processing in comparison with sequential fuzzy C-means (FCM) method, and again, it is at least 7 times faster than distributed FCM method present in the literature. The method presented in this paper has a novel approach towards fastest processing time and suitability of various sizes of the text sentiment analysis.

Multiattribute Decision-Making Problems in terms of the Weighted Mean Operation of Two Aggregation Operators of Orthopair Z-Numbers

The Z number defined by Zadeh can depict the fuzzy restriction/value and reliability measure by an ordered pair of fuzzy values to strengthen the reliability of the fuzzy restriction/value. However, there exist truth and falsehood Z-numbers in real life. Thus, the Z number cannot reflect both. To indicate both, this study presents an orthopair Z-number (OZN) set to depict truth and falsehood values (intuitionistic fuzzy values) and their reliability levels in uncertain and incomplete cases. Next, we define the operations, score and accuracy functions, and sorting rules of OZNs. Further, the OZN weighted arithmetic mean (OZNWAM) and OZN weighted geometric mean (OZNWGM) operators are proposed based on the operations of OZNs. According to the weighted mean operation of the OZNWAM and OZNWGM operators, a multiattribute decision-making (MADM) model is established in the case of OZNs. Lastly, a numerical example is presented to reflect the flexibility and rationality of the presented MADM model. Comparative analysis indicates that the presented MADM model can indicate its superiority in the reliability and flexibility of decision results. Meanwhile, the resulting advantage of this study is that the presented MADM model can strengthen the reliability level of orthopair fuzzy values and make the decision results more reliable and flexible.

New aggregation operators on group-based generalized intuitionistic fuzzy soft sets.

The approach of dealing with uncertainty is enhancing day-by-day with new rudiments and tools which possess their specific qualities. Usually, aggregation operators can easily manage the information in an exact manner. But each operator has different specifications in each problem. In recent few years, aggregation operators on intuitionistic fuzzy soft sets (IFSSs) or generalized intuitionistic fuzzy soft sets (GIFSSs) have been investigated but a lot of improvement is needed to obtain more accurate results. In this research, we defined new aggregation operators on GIFSSs which are used to aggregate our multi-criteria decision-making method. Reasonably, we assigned the weights with both intuitionistic fuzzy values of IFSS and intuitionistic fuzzy values of extra input in a GIFSS, and then by establishing new aggregation operators we appraised the computation in a more precise way. We defined the necessary properties of new aggregation operators and preparatory work of decision making in an algorithm. Then we expressed a real-life application by dint of the proposed methodology. Finally, we presented the comparisons of our work with already existing methods and techniques comprising aggregation operators.