Linear programming method for multiattribute group decision making using IF sets

Stochastic multiple attribute decision making with Pythagorean hesitant fuzzy set based on regret theory

The objective of this paper is to present an extended approach to address the stochastic multi-attribute decision-making problem. The novelty of this study is to consider the regret behavior of decision makers under a Pythagorean hesitant fuzzy environment. First, the group satisfaction degree of decision-making matrices is used to consider the different preferences of decision-makers. Second, the nonlinear programming model under different statues is provided to compute the weights of attributes. Then, based on the regret theory, a regret value matrix and a rejoice value matrix are constructed. Furthermore, the feasibility and superiority of the developed approach is proven by an illustrative example of selecting an air fighter. Eventually, a comparative analysis with other methods shows the advantages of the proposed methods.

A consensus reaching process based on the concordance correlation measure of intuitionistic fuzzy sets in multi-criteria decision making

Although some correlation measure of intuitionistic fuzzy sets(IFSs) have been proposed, some of them cannot express the consistency of information or satisfy the axioms of similarity measure. In this paper, we present a consensus reaching process based on the concordance correlation measure of IFSs in multi-criteria decision making problems. Firstly, we define an innovative concordance correlation measure of IFSs, which not only takes the average information deviation of IFSs into account but also overcomes the disadvantages of previous correlation measures. In addition, its properties and the relationship between the defined new concordance correlation measure and Pearson correlation coefficient of IFSs are discussed. Secondly, considering that the classical TOPSIS method cannot be applied to the correlation measure with negative values, we continue to introduce the concept of relative concordance correlation measure and propose a consensus reaching process with minimum adjustment for an innovative behavioral TOPSIS method. Furthermore, a detailed numerical example and the comparison analyses are provided to verify the advantages of the proposed method. At last, we discuss the sensitivity and stability of the method.

Power Average Operators of Trapezoidal Cubic Fuzzy Numbers and Application to Multi-attribute Group Decision Making

Trapezoidal cubic fuzzy numbers (TzCFNs) are an extraordinary cubic fuzzy set on a real number set. TzCFNs are useful for dealing with well-known quantities in decision data and decision making problems themselves. This paper is about multi-attribute group decision making problems in which the attribute values are stated with TzCFNs, which are solved by developing a new decision method based on power average operators of TzCFNs. The new operation laws for TzCFNs are given. Hereby, the power average operator of real numbers is extended to four kinds of power average operators of TzCFNs, involving the power average operator of TzCFNs, the weighted power average operator of TzCFNs, the power ordered weighted average operator of TzCFNs, and the power hybrid average operator of TzCFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TzCFNs. Applying the hybrid average operator of TzCFNs, the specific general evaluation standards of alternatives are then combined into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method.

Global Research Trends of Intuitionistic Fuzzy Set: A Bibliometric Analysis

Despite the fast growth of intuitionistic fuzzy publications, only a small part of these groundbreaking researches have significantly impacted the field. The main purpose of this paper was to identify and investigate the 100 most cited publications in the intuitionistic fuzzy field. Topic search based on the keyword “intuitionistic fuzzy” in the Science Citation Index and Social Sciences Citation Index databases was conducted to identify the 100 most cited articles. Bibliometric analysis methods were employed to describe these articles from different angles, such as the citation amount and rate, distribution among journals, institutions and countries/regions, author frequency, and citation distribution over time. This paper provides an insight on the characteristics of the highly cited intuitionistic fuzzy publications. The achievements of this study may provide useful information for researchers in the fields related to intuitionistic fuzzy.

Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making

This paper proposes a neutrosophic hesitant fuzzy linguistic term set (NHFLTS) based on hesitant fuzzy linguistic term set (HFLTS) and neutrosophic set (NS), which can express the inconsistent and uncertainty information flexibly in multiple criteria decision making problems. The basic operational laws of NHFLTS based on linguistic scale function are also discussed. Then we propose the generalized neutrosophic hesitant fuzzy linguistic distance measure and discuss its properties. Furthermore, a new similarity measure of NHFLTS combines the generalized neutrosophic hesitant fuzzy linguistic distance measure and the cosine function is given. A corresponding cosine distance measure between NHFLTSs is proposed according to the relationship between the similarity measure and the distance measure, and we develop the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained cosine distance measure. The main advantages of the proposed NHFLTS is defined on linguistic scale function, the decision makers can flexibly convert the linguistic information to semantic values, and the proposed cosine distance measure between NHFLTSs with TOPSIS method can deal with the related decision information not only from the point of view of algebra, but also from the point of view of geometry. Finally, the reasonableness and effectiveness of the proposed method is demonstrated by the illustrative example, which is also compared to the other existing methods.

IFWA and IFWGM Methods for MADM under Atanassov's Intuitionistic Fuzzy Environment

In this paper, we first give the formula of possibility degree to rank the Atanassov's intuitionistic fuzzy numbers. Two methods called Atanassov's intuitionistic fuzzy weighted average (IFWA) and Atanassov's intuitionistic fuzzy weighted geometric mean (IFWGM) are developed to solve the multiple attribute decision making problems under Atanassov's intuitionistic fuzzy environment, in which the performance ratings of alternatives and relative importance of attributes are expressed with Atanassov's intuitionistic fuzzy sets. The IFWA and IFWGM methods, respectively, are treated as an auxiliary pair of fractional programming models and two linear programming (LP) solution procedures are proposed simultaneously by using Charnes and Cooper transformation. Furthermore, two algorithms which are based on the IFWA and IFWGM models, respectively, are developed to solve Atanassov's intuitionistic fuzzy decision making problems where attribute values and weights of attributes are all in Atanassov's intuitionistic fuzzy numbers. The order relationship between IFWA and IFWGM are investigated. Finally, a numerical example is illustrated to show the feasibility and effectiveness of the proposed methods.

Hesitant fuzzy linguistic multicriteria decision-making method based on generalized prioritized aggregation operator

Based on linguistic term sets and hesitant fuzzy sets, the concept of hesitant fuzzy linguistic sets was introduced. The focus of this paper is the multicriteria decision-making (MCDM) problems in which the criteria are in different priority levels and the criteria values take the form of hesitant fuzzy linguistic numbers (HFLNs). A new approach to solving these problems is proposed, which is based on the generalized prioritized aggregation operator of HFLNs. Firstly, the new operations and comparison method for HFLNs are provided and some linguistic scale functions are applied. Subsequently, two prioritized aggregation operators and a generalized prioritized aggregation operator of HFLNs are developed and applied to MCDM problems. Finally, an illustrative example is given to illustrate the effectiveness and feasibility of the proposed method, which are then compared to the existing approach.

A value and ambiguity-based ranking method of trapezoidal intuitionistic fuzzy numbers and application to decision making

The aim of this paper is to develop a method for ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) in the process of decision making in the intuitionistic fuzzy environment. Firstly, the concept of TrIFNs is introduced. Arithmetic operations and cut sets over TrIFNs are investigated. Then, the values and ambiguities of the membership degree and the nonmembership degree for TrIFNs are defined as well as the value-index and ambiguity-index. Finally, a value and ambiguity-based ranking method is developed and applied to solve multiattribute decision making problems in which the ratings of alternatives on attributes are expressed using TrIFNs. A numerical example is examined to demonstrate the implementation process and applicability of the method proposed in this paper. Furthermore, comparison analysis of the proposed method is conducted to show its advantages over other similar methods.

Multi-Criteria Decision Making Methods Based on Interval-Valued Intuitionistic Fuzzy Sets

Fuzziness is inherent in decision data and decision making process. In this paper, interval-valued intuitionistic fuzzy set is used to capture fuzziness in multi-criteria decision making problems. The purpose of this paper is to develop a new method for solving multi-criteria decision making problem in interval-valued intuitionistic fuzzy environments. First, we introduce and discuss the concept of interval-valued intuitionistic fuzzy point operators. Using the interval-valued intuitionistic fuzzy point operators, we can reduce the degree of uncertainty of the elements in a universe corresponding to an interval-valued intuitionistic fuzzy set. Then, we define an evaluation function for the decision-making problem to measure the degrees to which alternatives satisfy and do not satisfy the decision-maker's requirement. Furthermore, a series of new score functions are defined for multi-criteria decision making problem based on the interval-valued intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.

MULTI-ATTRIBUTE DECISION MAKING METHOD BASED ON POSSIBILITY VARIANCE COEFFICIENT OF TRIANGULAR INTUITIONISTIC FUZZY NUMBERS

Triangular intuitionistic fuzzy numbers (TIFNs) are a special case of intuitionistic fuzzy sets. The purpose of this paper is to develop a new decision making method based on possibility variance coefficient to solve the multi-attribute decision making (MADM) problems, in which the attribute values are in the form of TIFNs and the weight preference information is incomplete. The possibility mean, variance and standard deviation for a TIFN are introduced as well as the possibility variance coefficient. Hereby, a new method to rank TIFNs is given on the basis of the possibility variance coefficients. The bi-objective mathematical programming, which minimizes the possibility variance coefficients of membership and non-membership functions for alternative's overall attribute values, is constructed. Using the max-min method, two non-linear fractional programming models are transformed into the linear programming models through the Charnes and Cooper transformation. Thus, the Pareto optimal solution to the bi-objective mathematical programming can be derived by solving the single-objective programming model. The ranking order of alternatives is obtained according to the minimum possibility variance coefficients. A personal selection example is given to verify the developed method and to demonstrate its feasibility and effectiveness. The analysis of comparison with other method is also conducted.