Intuitionistic Fuzzy Variables Research Articles

Principal component analysis based on intuitionistic fuzzy random variables

This paper suggests a principal component analysis for intuitionistic fuzzy data. For this purpose, first a notion of intuitionistic fuzzy random variable was introduced and discussed. The concept of correlation and its natural estimator between two intuitionistic fuzzy random variables was also developed and the main properties of the proposed correlation criteria were investigated. Then, the conventional principal component analysis was extended for intuitionistic fuzzy random variables. In this regard, score and loading plots were extended to analyze the first and the second principle components. A possible application of the proposed method was also illustrated via an practical psychology-relevant example.

A Novel Dynamic Intuitionistic Fuzzy MADM Approach

This paper explores the multiple attribute decision making problems with dynamic intuitionistic fuzzy information. The notion of intuitionistic fuzzy variable is defined, and one new aggregation operator: dynamic dependent intuitionistic fuzzy Einstein weighted average (DDIFEWA) operator is presented. And based on the D-DIFEWA operator, we develop a procedure to solve the dynamic intuitionistic fuzzy multi-attribute decision making (DIF-MADM) problems where all the decision information about attribute values takes the form of intuitionistic fuzzy numbers and is collected at different periods. Finally, a numerical example is presented to show the applicability of the proposed method for the advanced mathematics teaching effectiveness problem and a sensitivity analysis is conducted to demonstrate efficiency of dynamic evaluation.

A procedure for group decision making with interval-valued intuitionistic linguistic fuzzy preference relations

To express the uncertain preferred and non-preferred qualitative judgments of decision makers, interval-valued intuitionistic linguistic fuzzy sets (IVILFSs) are proposed in a similar way as Atanassov and Gargov’s interval-valued intuitionistic fuzzy sets. Considering the application of IVILFSs, the concept of interval-valued intuitionistic linguistic fuzzy variables (IVILFVs) is defined and a ranking order is offered. Then, we introduce interval-valued intuitionistic linguistic fuzzy preference relations (IVILFPRs) whose elements are IVILFVs. Furthermore, an additive consistency concept is presented and a model for judging the consistency of IVILFPRs is built. Meanwhile, optimization models for deriving additively consistent IVILFPRs and for determining missing linguistic variables in incomplete IVILFPRs are constructed, respectively. For group decision making, optimization models for determining the weights of the decision makers and for improving the consensus level are established, respectively. A procedure for group decision making with IVILFPRs is developed that can cope with inconsistent and incomplete IVILFPRs. Finally, a practical group decision-making problem about evaluating express companies is selected to show the application of the new results.

Linguistic Intuitionistic Fuzzy Group Decision Making Based on Aggregation Operators

This paper researches decision making with linguistic intuitionistic fuzzy variables. Several linguistic intuitionistic fuzzy operations are first defined. Then, several linguistic intuitionistic fuzzy aggregation operators are provided, including the linguistic intuitionistic fuzzy hybrid weighted arithmetical averaging operator, and the linguistic intuitionistic fuzzy hybrid weighted geometric mean operator. Considering the interactive characteristics between the weights of elements in a set, several linguistic intuitionistic fuzzy Shapley aggregation operators are presented, including the linguistic intuitionistic fuzzy hybrid Shapley arithmetical averaging operator, and the linguistic intuitionistic fuzzy hybrid Shapley geometric mean operator. To ensure the application reasonably, several desirable properties are discussed. When the weighting information is incompletely known, models for the optimal fuzzy and additive measures are constructed. After that, an approach to multi-criteria group decision making with linguistic intuitionistic fuzzy information is performed. Finally, a practical example about evaluating different types of engines is provided to illustrate the developed procedure.

Development of intuitionistic fuzzy data envelopment analysis models and intuitionistic fuzzy input–output targets

In this paper, we develop intuitionistic fuzzy data envelopment analysis (IFDEA) and dual IFDEA (DIFDEA) models based on $$\alpha $$ - and $$\beta $$ -cuts. We determine intuitionistic fuzzy (IF) efficiencies based on $$\alpha $$ - and $$\beta $$ -cuts. We develop an IF correlation coefficient (IFCC) between IF variables to validate the DIFDEA models. We propose an index ranking approach to rank the decision making units (DMUs). Also, we propose an approach to find the IF input–output targets which help to make inefficient DMUs as efficient DMUs in IF environment. Finally, an example and a health sector application are presented to illustrate and compare the proposed methods.

Intuitionistic fuzzy linguistic clustering algorithm based on a new correlation coefficient for intuitionistic fuzzy linguistic information

For observations to be classified, when scoring rules are imprecise or the cost of their computation is too high, the clustering method under linguistic information is necessary. Considering the accuracy of intuitionistic fuzzy linguistic variable in expressing experts’ opinions, a clustering algorithm is presented in this paper. Firstly, the concept of triangular intuitionistic fuzzy linguistic variables (TIFLVs) is introduced, and a new formula is developed for calculating correlation coefficient of TIFLVs. Then, the correlation coefficient plays a central role in our modified λ-cutting algorithm for clustering, which is utilized to construct an equivalence correlation matrix. In addition, a silhouette cluster validity index of TIFLVs is proposed to revise the results of clustering. Finally, the experimental results demonstrate the application and practicability of the clustering algorithm.

Forward and reverse flows pricing decisions for two competing supply chains with common collection centers in an intuitionistic fuzzy environment

This paper studies the selling and the acquisition price decisions for the products of two partially overlapping competing supply chains in an intuitionistic fuzzy environment. In the forward flows, the supply chains are assumed to produce substitutable products and sell them in a duopoly marketplace. The reverse flows are also concentrated on collecting and recycling the used products. While regularly it is assumed that the structures of the competing supply chains are completely separated, this paper assumes that the supply chains benefit from the services of the same collection centers. Considering the collection centers and the two supply chains to act as three integrated entities having enough bargaining powers to affect the decisions of each other, this paper concentrates on investigating the effects of different power structure scenarios on the optimal pricing decisions made by all of the parties involved in the problem. Another important feature of this study is that it employs the concept of intuitionistic fuzzy sets to integrate uncertainties and impressions inevitable in real-world situations into the decision-making process. To achieve this purpose, first, a new credibility-based definition for the concept of intuitionistic fuzzy variables is provided. This concept is then employed in the process of developing the intuitionistic fuzzy pricing models. A new expected value operator is also defined which is employed to transform the credibility-based intuitionistic fuzzy programming problems into their crisp equivalents. A numerical example is employed to discuss the properties of the introduced concepts, providing some interesting managerial implications regarding the defined problem.

An approach to interval-valued intuitionistic fuzzy decision making based on induced generalized symmetrical Choquet Shapley operator

Interval-valued intuitionistic fuzzy variables (IVIFVs) are powerful tools to denote the uncertain preferred and non-preferred degrees of decision makers. Considering the application of IVIFVs in decision making, this paper first gives some new operations that can address the shortages of previous ones. Then, an induced generalized symmetrical interval-valued intuitionistic fuzzy Choquet-Shapley (IG-SIVIFCS) operator is defined, which not only globally considers the importance of the elements but also overall reflects their interactions. After that, several desirable properties are briefly studied to provide assurance in application. In some situations, the weighting information of attributes is incompletely known. Considering this case, the Shapley function-based model for determining the optimal fuzzy measure on the attribute set is constructed. Furthermore, an approach to interval-valued intuitionistic fuzzy decision making with incomplete weighting information and interactive characteristics is developed to provide a completed theoretical framework. Finally, a practical example is provided to show the concrete practicality and validity of the proposed procedure.

Linguistic intuitionistic fuzzy Hamacher aggregation operators and their application to group decision making

Linguistic intuitionistic fuzzy variables (LIFVs) can efficiently denote the qualitative preferred and non-preferred cognitions of decision makers. This paper researches group decision making with linguistic intuitionistic fuzzy information. To do this, several Hamacher operational laws on LIFVs are defined. To derive the comprehensive evaluating values of alternatives, several linguistic intuitionistic fuzzy Hamacher aggregation operators are proposed, including the linguistic intuitionistic fuzzy Hamacher weighted average operator, the linguistic intuitionistic fuzzy Hamacher weighted geometric mean operator, the linguistic intuitionistic fuzzy Hamacher ordered weighted average operator, the linguistic intuitionistic fuzzy Hamacher ordered weighted geometric mean operator, the linguistic intuitionistic fuzzy Hamacher hybrid weighted average operator, and the linguistic intuitionistic fuzzy Hamacher hybrid weighted geometric mean operator. Then, several of their desirable properties are researched to guarantee the rationality. Methods for determining the weights of criteria, decision makers as well as the ordered positions are offered, respectively. After that, a procedure for group decision making with linguistic intuitionistic fuzzy information is provided. Finally, a group decision-making problem is offered to illustrate the application of the new results.

Credibility Measure for Intuitionistic Fuzzy Variables

Credibility measures in vague environments are to quantify the approximate chance of occurrence of fuzzy events. This paper presents a novel definition about credibility for intuitionistic fuzzy variables. We axiomatize this credibility measure and to clarify, give some examples. Based on the notion of these concepts, we provide expected values, entropy, and general formulae for the central moments and discuss them through examples.

An intuitionstic fuzzy factorial analysis model for multi-attribute decision-making under random environment

In real multi-attribute decision-making problems, attributes are usually correlated and performances of alternatives are affected by random environmental factors. This paper proposes an intuitionistic fuzzy factorial analysis model for multi-attribute decision-making, where correlative phenomenon among attributes and random decision-making environment is considered. First, the measure of correlation coefficient for random intuitionistic fuzzy variables is introduced. Based on this measure, an intuitionistic fuzzy factorial analysis model is proposed under random environment. Then, the procedure and algorithm of random multi-attribute decision-making based on intuitionistic fuzzy factorial analysis model is given. Finally, two examples are discussed, and detailed comparisons are given to demonstrate the feasibility and validity of the proposed technique.

A Scalar Expected Value of Intuitionistic Fuzzy Random Individuals and Its Application to Risk Evaluation in Insurance Companies

Randomness and uncertainty always coexist in complex systems such as decision-making and risk evaluation systems in the real world. Intuitionistic fuzzy random variables, as a natural extension of fuzzy and random variables, may be a useful tool to characterize some high-uncertainty phenomena. This paper presents a scalar expected value operator of intuitionistic fuzzy random variables and then discusses some properties concerning the measurability of intuitionistic fuzzy random variables. In addition, a risk model based on intuitionistic fuzzy random individual claim amount in insurance companies is established, in which the claim number process is regarded as a Poisson process. The mean chance of the ultimate ruin is investigated in detail. In particular, the expressions of the mean chance of the ultimate ruin are presented in the cases of zero initial surplus and arbitrary initial surplus, respectively, if individual claim amount is an exponentially distributed intuitionistic fuzzy random variable. Finally, two illustrated examples are provided.

Record value based on intuitionistic fuzzy random variables

ABSTRACTThis paper extends some basic concepts associated to record value based on intuitionistic fuzzy random variables. In this approach, αβ-values of intuituinistic fuzzy numbers are employed to construct intuitionistic fuzzy cumulative distribution function and its common estimator, an extended entropy and its estimator, intuitionistic fuzzy (upper) record value and its common estimator. Main property of the proposed concepts include large sample properties which are investigated in the space of intuitionistic fuzzy numbers. Some numerical examples are also illustrated to clarify the concepts and methods.

A New Intuitionistic Fuzzy Linguistic Hybrid Aggregation Operator and Its Application for Linguistic Group Decision Making

The linguistic aggregation operator is an important decision-making model that is proving effective for dealing with the input data that takes the form of uncertain information. In this paper, considering the principal component of the intuitionistic fuzzy linguistic variables, we develop a new intuitionistic fuzzy linguistic hybrid aggregation (NIFLHA) operator to solve group decision-making problems under the situation with intuitionistic fuzzy linguistic information. Then, we study some of its main properties by utilizing some operational laws of intuitionistic fuzzy linguistic variables and the different families of the NIFLHA operator. Moreover, the multiperson NIFLHA (MP-NIFLHA) operator is introduced to evaluate the opinions of experts. Finally, an illustrative example about a multiperson decision-making problem is developed to reveal the applicability and the availability of the raised operator.

Intuitionistic fuzzy variables: Concepts and applications in decision making

The present paper aims at advancing the well-recognized uncertainty theory built upon the credibility measure. In face of the increasing level of uncertainty embedded within the real world problem solving, it is discovered that the fuzzy variables defined in the credibility space are far from adequate to reflect the hesitance incurred during decision making. Although more complex fuzzy quantities are introduced, such as the fuzzy possibility space based type-2 fuzzy variables, the area of intuitionistic fuzzy variables is still a largely unexplored territory. Therefore, a novel concept of intuitionistic fuzzy variable is introduced hereby as an attempt to extend the uncertainty theory, which possesses a decent self-dual property compared with the fuzzy set theory. Unlike the intuitionistic fuzzy set theory, which has been widely implemented in various application fields, the intuitionistic fuzzy variables have hardly been employed in practices, especially the decision making sector. To bridge the gap, three outranking methods are developed to help evaluate intuitionistic fuzzy variables. The sufficient conditions of the three methods in distinguishing different fuzzy variables are also proved in the present work. The benefits of ranking with the three methods include the minimum amount of defuzzification, which prevents the information loss to a significant extent. Furthermore, in order to validate the proposed methods, a numerical study is performed. And the consistency of the ranking outputs from the three proposed methods is analyzed afterward. Besides, several managerial insights are presented regarding the sensitivity analysis of each ranking method.

Intuitionistic Fuzzy Linguistic Induced Ordered Weighted Averaging Operator for Group Decision Making

With respect to multiple attribute group decision making (MAGDM) problems, in which the attribute weights take the form of real numbers, and the attribute values take the form of intuitionistic fuzzy linguistic variables, a decision analysis approach is proposed. In this paper, we develop an intuitionistic fuzzy linguistic induce OWA (IFLIOWA) operator and analyze the properties of it by utilizing some operational laws of intuitionistic fuzzy linguistic variables. A new method based on the IFLIOWA operator for multiple attribute group decision making (MAGDM) is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.

An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making

The complex multi-attribute large-group decision-making problems that are based on interval-valued intuitionistic fuzzy information have become a common topic of research in the field of decision-making. Due to the complexity of this kind of problem, alternatives are usually described by multiple attributes that exhibit a high degree of interdependence or interactivity. In addition, decision makers tend to be derived from different interest groups, which cause the assumption of independence between the decision maker preferences in the same interest group to be violated. Because traditional aggregation operators are proposed based on the independence axiom, directly applying these operators to the information aggregation process in the complex multi-attribute large-group decision-making problem is not appropriate. Although these operators can obtain the overall evaluation value of each alternative, the results may be biased. Therefore, we draw the thought from the conventional principal component analysis model and propose the interval-valued intuitionistic fuzzy principal component analysis model. Based on this new model, we provide a decision-making method for the complex multi-attribute large-group decision-making problem. First, we treat the attributes and the decision makers as interval-valued intuitionistic fuzzy variables, and we transform these two types of variables into several independent variables using the proposed principal component analysis model. We then obtain each alternative's overall evaluation value by utilizing conventional information aggregation operators. Moreover, we obtain the optimal alternative(s) based on the ranks of the alternative overall evaluation values. An illustrative example is provided to demonstrate the proposed technique and evaluate its feasibility and validity.

An Integrated Maximizing Consistency and Multi-Choice Goal Programming Approach for Hybrid Multiple Criteria Group Decision Making Based on Interval-Valued Intuitionistic Fuzzy Number

Interval-valued intuitionistic fuzzy numbers (IVIFNs) characterized by a membership function and a non-membership function with values that are intervals, have strong ability to handle imprecise and ambiguous information in real-world applications. This paper proposes an integrated maximizing consistency and multi-choice goal programming (MCGP) approach to handle hybrid multi-criteria group decision making problems based on IVIFNs. Firstly, the hybrid decision infor- mation (including crisp numbers, intervals, intuitionistic fuzzy numbers and linguistic variables) are normalized into the IVIFNs. Then, an ordinal consistency index and a cardinal consistency in- dex are proposed to measure the consistency between the individual opinion and the group opinion, respectively. And an optimal model based on maximizing consistency is constructed to derive the weights of experts. Afterwards, the comprehensive ratings and the ranking values of alternatives are obtained by the hybrid weighted aggregation operator and the proposed ratio function of IVIFNs, respectively. Furthermore, a MCGP model based on the ranking values is constructed to identify the optimal alternatives and their optimum quantities. At length, an illustrative case is provided to verify the proposed approach.

An approach to Atanassov's interval-valued intuitionistic fuzzy multi-attribute decision making based on prospect theory

AbstractProspect theory is a very effective method to express behavioral decision making under uncertainty. This paper attempts to develop a method to multi-attribute decision making with Atanassov's interval-valued intuitionistic fuzzy information using prospect theory. This method first transforms Atanassov's interval-valued intuitionistic fuzzy variables into the prospect values using the value function in prospect theory. Based on the aspiration levels, Atanassov's intuitionistic fuzzy prospect gain and loss matrices are obtained. Then, using the Atanassov's interval-valued intuitionistic hybrid weight averaging (IVIHWA) operator or the Atanassov's interval-valued intuitionistic hybrid Shapley weight averaging (IVIHSWA) operator, the comprehensive Atanassov's interval-valued intuitionistic fuzzy prospect value of each alternative is calculated. According to the comprehensive Atanassov's interval-valued intuitionistic fuzzy prospect values, a ranking method of alternatives is presented. Finally, two il...

Intuitionistic fuzzy random variable and testing hypothesis about its variance

A new approach for testing statistical hypotheses about variance of population based on intuitionistic fuzzy sample is introduced. In this approach, we first define variance of intuitionistic fuzzy random variables based on a new definition of \(L_{2}\)-metric. Then, using the bootstrap method, a new method for one-sample and two-sample tests based on intuitionistic fuzzy numbers is proposed.