Type-2 Intuitionistic Fuzzy Sets Research Articles

Optimizing Investment Selection Through Similarity Measurement with Type-2 Intuitionistic Fuzzy Sets

Optimizing Investment Selection Through Similarity Measurement with Type-2 Intuitionistic Fuzzy Sets

Pandemic management by using sentiment analysis and trapezoidal type-2 fuzzy linguistic intuitionistic fuzzy matrix games

In order to explore effective management strategies in the context of epidemics, this study introduces a novel concept: Trapezoidal type-2 fuzzy linguistic intuitionistic fuzzy set (TrT2FLIFS) and proposes a trapezoidal type-2 fuzzy linguistic intuitionistic fuzzy matrix game (TrT2FLIFMG). Subsequently, employing sentiment analysis based on the BosonNLP sentiment lexicon, the study extracts comment data from Weibo related to epidemics made by users and calculates their textual scores. These two methods are integrated and applied to policy selection in epidemic management, along with the introduction of a new ranking function to compare the importance of alternative policies. Finally, a comparative analysis with existing methods is conducted to validate the effectiveness of the proposed approach.

Type-2 Intuitionistic Interpolation Cubic Fuzzy Bézier Curve Modeling using Shoreline Data

The notion of fuzzy sets is fast becoming a key instrument in defining the uncertainty data and has increasingly been recognised by practitioners and researchers across different disciplines in recent decades. The uncertainty data cannot be modeled directly and this causes hindrance in obtaining accurate information for analysis or predictions. Hence, this paper contributes to another approach in which an application of type-2 intuitionistic fuzzy set (T-2IFS) in geometric modeling onto complex uncertainty data where the data are defined using the type-2 fuzzy concept. T-2IFS is the generalized forms of fuzzy sets, intuitionistic fuzzy sets, interval-valued fuzzy sets, and interval-valued intuitionistic fuzzy sets. Based on the concept of T2IFS, type-2 intuitionistic fuzzy point (T-2IFP) is defined in order to generate a type-2 intuitionistic fuzzy control point (T-2IFCP). Following, the T-2IFCP will be blended with the Bernstein blending function through the interpolation method, resulting to a type-2 intuitionistic interpolation cubic fuzzy Bézier curve. Shoreline data is used as the data and further verifies that the model can be conceivably accepted. In conclusion, the proposed methods are reliable and can be expanded to many other areas.

Elliptic interval Type-2 intuitionistic fuzzy logic system for non-linear system identification

An elliptic membership function has been proposed in the literature for interval type-2 fuzzy logic system. In this paper, elliptic non- membership function is incorporated into the conventional elliptic membership function model to obtain elliptic interval type-2 intuitionistic fuzzy sets for the first time. The elliptic interval type-2 intuitionistic fuzzy logic system so formed is applied for the prediction of two benchmark non-linear systems and results compared with Gaussian interval type-2 intuitionistic fuzzy logic system. Experimental results show that the elliptic interval type-2 intuitionistic fuzzy logic system outperforms the traditional Gaussian interval type-2 intuitionistic fuzzy logic system in the problem instances investigated.

An Interactive Weighted Geometric Aggregation Operator on T2IFS

Type 2 intuitionistic fuzzy sets (T2IFS) appear to be an attractive and potentially useful tool for coping with uncertainty and inaccurate data in today’s uncertain and ambiguous world. Consequently, it is frequently employed in decision-making (DM) issues. In the DM procedure, it is essential to aggregate the information provided by the experts. The Aggregation operators (AOs) are effective information combining tools. Therefore, this study aims on developing geometric and interactive geometric AOs on T2IFSs. To demonstrate the efficacy of the proposed operator, the optimal e-learning tool selection MCDM problem is solved. The results demonstrate that the proposed interactive AO outperforms existing arithmetic AOs and is applicable to all DM problems.

An application of generalized symmetric type-2 intuitionistic fuzzy variables to a transportation problem with the effect of a new ranking function

The primary objective of this study is to establish and introduce generalized symmetric type-2 intuitionistic fuzzy set, a type-2 fuzzy set extension. The major goal of such an extension is to enable the concept of fuzzy outranking relation which is known as foot print of uncertainty (FOU) to be employed in generalized symmetric type-2 intuitionistic fuzzy number (GST2IFN) for the first time. This is interesting to deal this GST2IFNs and it is complicated to find the equivalent crisp quantities due to this special structure. Hence, we have introduced a new ranking function using the mean level set of membership and non-membership functions. Besides, the arithmetic operations of the GST2IFNs are discussed. To express the effectiveness and application of the proposed GST2IF variables, a transportation problem (TP) is formulated with all cost parameters are GST2IFNs. In addition, few different algorithmic approaches are applied to find the initial basic feasible solution (IBFS) and optimal solution of the TP. Finally, the feasibility and richness of the obtained optimal solution is discussed.

Ranking Type-2 Intuitionistic Fuzzy Sets Based on Dice Similarity Measures

Ranking fuzzy numbers is an important part of decision-making in a fuzzy domain. Similarity measures are one of the widely used methods for sorting fuzzy numbers. In this paper, a Dice similarity measure is proposed for type-2 intuitionistic fuzzy sets (T2IFSs) and the properties of similarity measure are verified. The ranking in the proposed method is accomplished by comparing the given set to the best possible set under consideration. The proposed measure is tested on a wide range of T2IFSs and the results are analyzed with existing ranking methods. The comparison shows that the proposed method outperforms some of the shortcomings of existing ranking techniques and is thus effective in ranking.

Type-2 intuitionistic fuzzy TODIM for intelligent decision-making under uncertainty and hesitancy

The classical TODIM considers the crisp numbers to handle the information. However, in a real-world applicative context, this information is bounded by noise and vagueness and hence uncertain. There are wide range of works in the literature which utilizes fuzzy sets to handle the uncertainty in the various dimensions. However, there is a constraint of hesitancy in such decision-making problems due to the involvement of various decision-makers. Also, in the TODIM method, decision-maker’s bounded rationality and psychological behavior are also taken into consideration which adds up the hesitation and considers the problem with higher dimension of uncertainty. There are various applications of fuzzy TODIM using type-2 fuzzy numbers where uncertainty is being handled in more than one dimensions and also the introduction of intuitionistic fuzzy numbers where hesitancy factor of a decision-maker is taken into account. This paper targets to handle the uncertainty in more than one dimension keeping the hesitancy part into consideration for intelligent decision-making. Therefore, a novel trapezoidal type-2 intuitionistic fuzzy set (TrT2 IFS) is proposed, which is an aggregation of several triangular IFSs having upper and lower membership along with a non-membership value. For this TrT2 IFS, we have defined the generation procedure, operations, comparison and distance between such TrT2 IFSs. In addition, the decision-maker weights and criterion weight computation are also presented with respect to the TODIM approach. Furthermore, we have applied this extended TrT2 IFS-based TODIM method into a renewable energy resource selection problem of multi-criteria decision-making.

Digital transformation project selection using Interval Valued Type-2 Intuitionistic Fuzzy TOPSIS

Digital transformation necessitates fundamental changes in business processes, business models, and even cultures of the companies. DT projects provide a substantial value to the business competition and effect their market shares. In order to reach these results, digital transformation projects should be carefully analyzed and evaluated. In this paper, we focus on digital transformation project prioritization problem under multiple criteria. Just like many other technology related decisions, digital transformation problems are inherently uncertain, which leads researchers to employ the fuzzy set theory. Interval Valued Type-2 Intuitionistic Fuzzy Sets (IVT2IFS) are a relatively new extension of fuzzy sets which take into account membership and non-membership values as an interval. In this paper, we utilize Interval Valued Type-2 Intuitionistic Fuzzy TOPSIS method for a digital transformation project prioritization problem and apply the model to a real-world example.

A New Distance Measure to Rank Type-2 Intuitionistic Fuzzy Sets and Its Application to Multi-Criteria Group Decision Making

The type 2 intuitionistic fuzzy sets (T2IFS) have a greater expressive power in representing the uncertainty involved in the information given by the experts. A very few ranking methods have been proposed to compare the T2IFS based on distance measure. This paper proposes a new distance measure called Jaccard distance for type 2 intuitionistic fuzzy set. This method ranks the T2IFS based on the dissimilarity of the given T2IFS to the ideal set. The properties of distance measure have been proved. The efficiency of proposed method is validate by comparing with existing methods. It is observed that the proposed ranking can rank the T2IFS more effectively when compared to existing methods in some tested contexts. The proposed ranking method is applied in solving a multi criteria group decision making method and the results are analyzed. From the analysis it is observed that the ordering the alternatives using proposed method agrees with the human intuition.

Graphical Representation of Type-2 Neutrosophic sets

Neutrosophic set is the universality of the fuzzy and intuitionistic fuzzy sets. If the value of grade of membership contains uncertainty then that problems or situations can be dealt by type-2 fuzzy and intuitionistic fuzzy sets. It is not possible to work in enigmatic and uncertain situations and indeterminate situations as well. This present study introduces, graphical representation of type-2 neutrosophic set (T2NS) to deal the level of uncertainty in truth, indeterminate and false part of the information from footprint of uncertainty (FOU). This graphical representation helps as a learning strategy of type-2 neutrosophic sets. Also discussed the advantage of T2NS.

Mediative Fuzzy Extension Technique and Its Consistent Measurement in the Decision Making of Medical Application

The notion of fuzzy set theory has not so far been districted over medical diagnosis. There are some added applications, for example, in image processing, pattern identification, and many medical devices. In this research article, we introduced a new mediative fuzzy ranking technique as the fuzzy extension in decision making. The proposed mediative fuzzy logic-based technique is more relevant and applicable to incomplete and doubtful situations or some contradictions present in the expert knowledge. The value of the contradictory degree for mediative fuzzy sets used in the extension principle is defined. The proposed mediative fuzzy ranking method is easily implemented in the medical field, and the proposed mediative fuzzy extension-based measured technique is useful to medical experts and doctors in many decision-making situations; the entire work is illustrated with numerical examples. We have also given some future aspects of mediative fuzzy extension in the interpretation of type-2 intuitionistic fuzzy sets.

Type-2 intuitionistic fuzzy matrix games based on a new distance measure: Application to biogas-plant implementation problem

In reality, to deal with uncertain information, researchers have introduced several extensions of fuzzy sets. But, in most cases, two-dimensional fuzzy sets (considering elements with their membership degree) are considered. However, it fails to capture all types of incomplete information. Occasionally, the inadequacy of the data depends upon the large span of source or time or both. In that case, two-dimensional fuzzy sets or type-1 fuzzy sets (T1FSs) are not sufficient to portray the situation. Type-2 fuzzy set (T2FS), a three-dimensional extent of the fuzzy set, appears here to bridge this gap. Type-2 intuitionistic fuzzy set (T2IFS) is a novel extension of T2FS. It can express the fuzzy preference of the decision-makers toward their decisions under different parameters. It also considers both the acceptance and non-acceptance of decision-makers. In the present study, we aim to develop matrix games in T2IF environment. To do this, we first define Hamacher aggregation operators in T2IF environment with their properties. We also propose the Minkowski distance of T2IFSs based on the Hausdorff metric. Then a similarity measure of T2IFS is formed. Next, we solve the matrix games by utilizing the proposed distance measure. The proposed methodology has been delineated with the biogas-plant implementation problem to check the applicability and validity.

Software Fault Prediction Based on Interval Type-2 Intuitionistic Fuzzy Logic System

With the continuous expansion and innovations in modern software development, the rate at which defects are present in software is directly proportional to how sophisticated and complex the software tends to be. Software fault prediction, therefore, continues to remain an important area of research in software engineering especially as new modeling algorithms are still emerging. In spite of the fact that the potential implementations of fuzzy set theory in software fault prediction have been explored in the past, to the best knowledge of the authors, it has not yet examined how interval type-2 intuitionistic fuzzy sets with membership and non-membership degrees could be used with parameter optimization in this domain. Therefore, this work aims to adopt an interval type-2 intuitionistic fuzzy logic system to predict fault in the requirement phase of Software Development Life Cycle. Intuitionistic fuzzy logic system deals with uncertainty using separate degrees of membership and non-membership of an element to a set as well as hesitation index, therefore becoming more appropriate and flexible tool to deal with imprecision and vagueness in data. Experimental analyses show that the obtained prediction outputs are very close to the actual outputs which confirm that the proposed approach is a more realistic alternative for software fault prediction.

Linguistic Interval-Valued Pythagorean Fuzzy Sets and Their Application to Multiple Attribute Group Decision-making Process

The paper’s aims are to present a novel concept of linguistic interval-valued Pythagorean fuzzy set (LIVPFS) or called a linguistic interval-valued intuitionistic type-2 fuzzy set, which is a robust and trustworthy tool, and to accomplish the imprecise information while solving the decision-making problems. The presented LIVPFS is a generalization of the linguistic Pythagorean fuzzy set, by characterizing the membership and non-membership degrees as the interval-valued linguistic terms to represent the uncertain information. To explore the study, we firstly define some basic operational rules, score and accuracy functions, and the ordering relations of LIVPFS with a brief study of the desirable properties. Based on the stated operational laws, we proposed several weighted averages and geometric aggregating operators to aggregate the linguistic interval-valued Pythagorean fuzzy information. The fundamental inequalities between the proposed operators and their properties are discussed in detail. Finally, a multiple attribute group decision-making (MAGDM) algorithm is promoted to solve the group decision-making problems with uncertain information using linguistic features and the proposed operators. The fundamental inequalities between the proposed operators and their properties are discussed in detail. Also, the illustration of the stated algorithm is given through several numerical examples and compared their performance with the results of the existing algorithms. Based on the stated MAGDM algorithm and the suitable operators, the decision-makers’ can be selected their best alternatives with their own attitude character towards optimism or pessimism choice. The presented LIVPFS is an extension of the several existing sets and is more generalized to utilize the uncertain and imprecise information with a wider range of information. Based on the presented aggregation operators, a decision-maker can select the desired one as per their choices to access the finest alternatives.

ORDERING METHODS OF C-CONTROL CHARTS WITH INTERVAL TYPE-2 INTUITIONISTIC FUZZY SETS

The control charts are important because it provides information about the process and the state of control of the product. With this feature, control charts are used in many areas. Intuitionistic fuzzy sets and interval valued intuitionistic fuzzy sets are useful to modelling of the real world problems. Ordering of the fuzzy numbers is investigated by a lot of scientists and it is generalised to intuitionistic fuzzy sets because of applicability. Ordering interval-valued type-2 intuitionistic fuzzy sets is significant in making decision, data analysis and artificial intelligence since interval analysis is required. In this study a new method to ordering interval-valued type-2 intuitionistic fuzzy sets is defined and numerical methods are compared to other methods.

Type-2 single-valued neutrosophic sets and their applications in multi-criteria group decision making based on TOPSIS method

Type-2 fuzzy set and type-2 intuitionistic fuzzy set are important tools for dealing with problems involving uncertainty and linguistic variables. However, it is sometimes difficult to model problems involving inconsistent data by using these approaches. In this paper, the concept of type-2 single-valued neutrosophic sets is defined in order to cope with this difficulty. Also, some distance measure methods for type-2 single-valued neutrosophic sets based on Hausdorff, Hamming and Euclidean distances are introduced and some properties of them are investigated. Furthermore, a multi-criteria group decision-making method is developed based on TOPSIS approach under the type-2 single-valued neutrosophic environment. Finally, an illustrative example is given in order to show the validity and process of the proposed method.

The algebraic and lattice structures of type-2 intuitionistic fuzzy sets

Type-2 intuitionistic fuzzy sets are proposed as functions from non empty set U to $${\mathbf {T}}^{\mathbf {T}}$$ where $${\mathbf {T}}=\{(\mu ,\nu ):\mu +\nu \le 1,\mu \ge 0,\nu \ge 0\}$$ and $${\mathbf {T}}^{\mathbf {T}}$$ is the set of all mappings from $${\mathbf {T}}$$ to $${\mathbf {T}}$$. The members of $${\mathbf {T}}^{\mathbf {T}}$$ are called intuitionistic fuzzy values (IFV). In this paper, we develop a mathematical framework for IFVs by defining a set of generalized operations on $${\mathbf {T}}^{\mathbf {T}}$$ and proved it to be an algebra. The other important properties like convexity, normality of IFVs and many important subalgebras are also explored and studied. Furthermore, two partial orders based on generalized operations are defined, which enable us to study the lattices in $${\mathbf {T}}^{\mathbf {T}}$$.

Algorithm for solving group decision-making problems based on the similarity measures under type 2 intuitionistic fuzzy sets environment

Type 2 intuitionistic fuzzy set (T2IFS) is one of the most important concepts to describe fuzzy information by providing an additional degree of freedom to the decision maker to decide the decision-making process. The fundamental superiority of the T2IFS, over the intuitionistic fuzzy set, has been its ability to capture the degrees of membership of relevant membership values, where the uncertainty is handled more accurately, and hence accommodate more uncertainties. Keeping these features in mind, this paper explores the theory of T2IFS by defining some families of the similarity measures to measure the degree of similarity between the two or more T2IFSs. For this, the characteristic of each object is measured in terms of degrees of primary membership and non-membership, secondary membership and non-membership and the variance margin function between them. Based on that, several formulations of the similarities measures are defined and their properties are investigated . Also, some fundamental relation between the proposed measures is stated. Further, based on the similarity measure, a group decision-making approach is explored to rank the alternatives. An illustrative example is provided to demonstrate the approach, and the comparative analysis with some of the existing measures is performed to explore the results.

Operational risk assessment of railway train based on type-2 intuitionistic fuzzy set and dynamic VIKOR approach

This paper is devoted to applying fuzzy risk-ranking analysis for the railway train operational risk assessment. Specifically, a new risk-ranking approach of dynamic VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) combined with Type-2 intuitionistic fuzzy set (Type-2 IFS) theory is proposed under different stages, which can be better employed to rank the risk of system components considering the calculation uncertainty, expert preference, and information indeterminacy based on the hybrid index system of quantitative and qualitative information. A specific case is performed to validate the proposed approach. Based on the results, a comparative analysis between the proposed approach and the static risk assessment is presented, which shows the effectiveness and feasibility of the proposed approach.