EXTENSION OF THE TOPSIS METHOD BASED ON PROSPECT THEORY AND TRAPEZOIDAL INTUITIONISTIC FUZZY NUMBERS FOR GROUP DECISION MAKING

Considering the decision maker＇s risk psychological factors and information ambiguity under uncertainty, a novel TOPSIS based on prospect theory （PT） and trapezoidal intuitionistic fuzzy numbers （YrIFNs） for group decision making is investigated, in which the criteria values and the criteria weights take the form of TrIFNs, and weights of decision makers are unknown. Firstly, distance measures for TrIFNs are used to induce value function under trapezoidal intuitionistic fuzzy environment. Secondly, the concepts of distance measures and trapezoidal intuitionistie fuzzy weighted averaging operator are employed to induce the weights of decision makers and thus the decision makers＇ options can be aggregated. Then the PT-based separation measures and relative closeness coefficient are defined and an algorithm for ranking alternatives under trapezoidal intuitionistic fuzzy environment is proposed. Finally, a numerical example further illustrates the practicality and effectiveness of the proposed TOPSIS method.

A NOVEL APPROACH TO CHARACTERIZING HESITATIONS IN INTUITIONISTIC FUZZY NUMBERS

Building upon the concept of Dα operator introduced by Atanassov （1989）, thin article proposes an improved objective approach and a hybrid approach to operationalize Dα so that the hesitation in an intuitionistic fuzzy number （IFN） can be further refined and characterized. Numerical experiments are carried out to demonstrate the features and novelty of the proposed approach compared to existing methods in the literature. The aim is to furnish an effective way to refine hesitations in intuitionistic fuzzy assessments for more reliable and confident decision aids.

3D printing process selection model based on triangular intuitionistic fuzzy numbers in cloud manufacturing

The distributed and customized 3D printing can be realized by 3D printing services in a cloud manufacturing environment.As a growing number of 3D printers are becoming accessible on various 3D printing service platforms,there raises the concern over the validation of virtual product designs and their manufacturing procedures for novices as well as users with 3D printing experience before physical products are produced through the cloud platform.This paper presents a 3D model to help users validate their designs and requirements not only in the traditional digital 3D model properties like shape and size,but also in physical material properties and manufacturing properties when producing physical products like surface roughness,print accuracy and part cost.These properties are closely related to the process of 3D printing and materials.In order to establish the 3D model,the paper analyzes the model of the 3D printing process selection in the cloud platform.Triangular intuitionistic fuzzy numbers are applied to generate a set of 3D printers with the same process and material.Based on the 3D printing process selection model,users can establish the 3D model and validate their designs and requirements on physical material properties and manufacturing properties before printing physical products.

Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems

Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.

Entropy-based procedures for intuitionistic fuzzy multiple attribute decision making

The class of multiple attribute decision making （MADM） problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.

Derivatives and differentials for multiplicative intuitionistic fuzzy information

By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number(MIFN)and is based on the unbalanced scale(i.e.,Saaty’s 1-9 scale).In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively,in this paper,we firstly propose two new basic operational laws for MIFNs,which are the subtraction law and the division law.Secondly,we describe the change values of MIFNs when considering them as variables,classify these change values based on the basic operational laws for MIFNs,and depict the convergences of sequences of MIFNs by the subtraction and division laws.Finally,we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities,derivatives and differentials,and also give their application in selecting the configuration of a computer.

CONFLICT MEASURE MODEL FOR LARGE GROUP DECISION BASED ON INTERVAL INTUITIONISTIC TRAPEZOIDAL FUZZY NUMBER AND ITS APPLICATION

The problem of measuring conflict in large-group decision making is examined with every decision preference expressed by multiple interval intuitionistic trapezoidal fuzzy numbers （IITFNs）. First, a distance measurement between two IITFNs is given and a function of conflict between two members of the large group is proposed. Second, members of the large group are clustered. A measurement model of group conflict, which is applied to aggregating large-group preferences, is then proposed by employing the conflict measure of clusters. Finally, a simulation example is presented to validate the models. These models can deal with the preference analysis and coordination of a large-group decision, and are thus applicable to emergency group decision making.

Handling higher order time series forecasting approach in intuitionistic fuzzy environment

This study presents a new method of forecasting based on a higher order intuitionistic fuzzy time series(FTS)by transforming FTS data into intuitionistic FTS data via defining their appropriate membership and non-membership grades.The fuzzification of time series data is intuitionistic fuzzification which is based on the maximum score degree of intuitionistic fuzzy numbers.Also,the intuitionistic fuzzy logical relationship groups are defined and introduced into a defuzzification process for a higher order intuitionistic FTS that enhances in the forecasted output.In order to assess the performance of the proposed method,the method has been implemented on the historical data of rice production.The comparison result shows that the proposed method can achieve a better forecasting accuracy rate in terms of RMSE and MAPE than the existing methods such as Song and Chissom[(1993).Forecasting enrolments with fuzzy time series-Part I.Fuzzy Sets and System,54,1-9],Chen[(1996).Forecasting enrolments based on fuzzy time series.Fuzzy Sets and System,81,311-319],Singh[(2007a).A simple method of forecasting based on fuzzy time series.Applied Mathematics and Computation,186,330-339]and Abhishekh,Gautam,and Singh[(2017).A refined weighted method for forecasting based on type 2 fuzzy time series.International Journal of ModellingandSimulation,38,180-188;(2018).A score function based method of forecasting using intuitionistic fuzzy time series.New Mathematics and Natural Computation,14(1),91-111].

Dynamic multiple criteria group decision-making method based on intuitionistic fuzzy information

In the decision-making process,the decision information provided by decision makers over alter-natives may take the form of intuitionistic fuzzy numbers and come from different periods.The weight of information on decision makers,criteria,periods is usually completely unknown.To this issue,we first utilise hesitation degree information and introduce the concept of confi-dence degree function to determine the decision maker’s weights.Then we aggregate individual evaluation information into group evaluation information through intuitionistic fuzzy number weighted arithmetic averaging operator.We construct a nonlinear optimisation model to gain the criterion weights and apply the aggregate operator to gain the integrated rating value of alternatives in different periods,calculating the deviations of the integrated rating values with respect to their average.Then the period weights are been obtained by using the entropy method.According to the closeness coefficient between alternatives and ideal solution to sort the alternatives and select the optimal one.

Trapezoidal Intuitionistic Fuzzy Aggregation Operator Based on Choquet Integral and Its Application to Multi-Criteria Decision-Making Problems

The Choquet integral can serve as a useful tool to aggregate interacting criteria in an uncertain environment. In this paper, a trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is proposed for multi-criteria decision-making problems. The decision information takes the form of trapezoidal intuitionistic fuzzy numbers and both the importance and the interaction information among decision-making criteria are considered. On the basis of the introduction of trapezoidal intuitionistic fuzzy numbers, its operational laws and expected value are defined. A trapezoidal intuitionistic fuzzy aggregation operator based on the Choquet integral is then defined and some of its properties are investigated. A new multi-criteria decision-making method based on a trapezoidal intuitionistic fuzzy Choquet integral operator is proposed. Finally, an illustrative example is used to show the feasibility and availability of the proposed method.