Intuitionistic Fuzzy Probabilistic Aggregation Operators Based on the Choquet Integral: Application in Multicriteria Decision-Making

2017 ◽  
Vol 16 (01) ◽  
pp. 245-279 ◽  
Author(s):  
Gia Sirbiladze ◽  
Otar Badagadze
Keyword(s):  
Decision Making ◽  
Choquet Integral ◽  
Core Competencies ◽  
Multicriteria Decision Making ◽  
Fuzzy Measure ◽  
Intuitionistic Fuzzy ◽  
Conjugate Connections ◽  
Decision Making Problem ◽  
Global Supplier ◽  
Geometric Operator

Associated Intuitionistic Fuzzy Probabilistic Averaging (As-IFPA) and Associated Intuitionistic Fuzzy Probabilistic Geometric (As-IFPG) operators based on the Choquet integral and an associated probability class of a fuzzy measure are constructed. Propositions on the correctness of the extensions are proved: (1) The As-IFPA (As-IFPG) operator for the fuzzy measure — capacity of order two coincides with the Intuitionistic Fuzzy Choquet Averaging (Intuitionistic Fuzzy Choquet Geometric) operator; (2) The As-IFPA (As-IFPG) operator coincides with the Intuitionistic Fuzzy Probabilistic Averaging (Intuitionistic Fuzzy Probabilistic Geometric) operator when a probability measure is used in the role of a fuzzy measure. Connections between the constructed operators and the compositions of dual triangular norms [Formula: see text] and [Formula: see text] are constructed. The conjugate connections between the constructed operators are shown. Two illustrative examples on the applicability of the As-IFPA and As-IFPG operators are presented. Several variants of the new operators (1) for the decision-making problem regarding the fiscal policy of a country; (2) for the decision-making problem regarding the best global supplier selection according to the core competencies of suppliers for a manufacturing company are used. Interactions and dependencies among all the combinations of the criteria in the decision-making process are considered.

Additive Intuitionistic Fuzzy Aggregation Operators Based on Fuzzy Measure

2016 ◽  
Vol 24 (01) ◽  
pp. 1-12 ◽  
Author(s):  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Probability Measure ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Fuzzy Measure ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Aggregation ◽  
The World ◽  
Multi Attribute Decision Making

Intuitionistic fuzzy sets can describe the uncertainty and complexity of the world flexibly, so it has been widely used in multi-attribute decision making. Traditional intuitionistic fuzzy aggregation operators are usually based on the probability measure, namely, they consider that the attributes of objects are independent. But in actual situations, it is difficult to ensure the independence of attributes, so these operators are unsuitable in such situations. Fuzzy measure is able to depict the relationships among the attributes more comprehensively, so it can complement the traditional probability measure in dealing with the multi-attribute decision making problems. In this paper, we first analyze the existing intuitionistic fuzzy operators based on fuzzy measure, then introduce two novel additive intuitionistic fuzzy aggregation operators based on the Shapley value and the Choquet integral, respectively, and show their advantages over other ones.

scholarly journals Interval-Valued Intuitionistic Fuzzy Multicriteria Group Decision Making Based on VIKOR and Choquet Integral

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Chunqiao Tan ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Choquet Integral ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Problem ◽  
Multicriteria Group Decision Making ◽  
Interval Valued

An effective decision making approach based on VIKOR and Choquet integral is developed to solve multicriteria group decision making problem with conflicting criteria and interdependent subjective preference of decision makers in a fuzzy environment where preferences of decision makers with respect to criteria are represented by interval-valued intuitionistic fuzzy sets. First, an interval-valued intuitionistic fuzzy Choquet integral operator is given. Some of its properties are investigated in detail. The extended VIKOR decision procedure based on the proposed operator is developed for solving the multicriteria group decision making problem where the interactive criteria weight is measured by Shapley value. An illustrative example is given for demonstrating the applicability of the proposed decision procedure for solving the multi-criteria group decision making problem in interval-valued intuitionistic fuzzy environment.

Associated probabilities aggregations in multistage investment decision-making

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gia Sirbiladze ◽  
Harish Garg ◽  
Irina Khutsishvili ◽  
Bezhan Ghvaberidze ◽  
Bidzina Midodashvili
Keyword(s):  
Decision Making ◽  
Choquet Integral ◽  
Fuzzy Measure ◽  
Investment Model ◽  
Content Type ◽  
Owa Operators ◽  
Second Stage ◽  
Intuitionistic Fuzzy ◽  
Classical Criterion ◽  
New Criterion

PurposeThe attributes that influence the selection of applicants and the relevant crediting decisions are naturally distinguished by interactions and interdependencies. A new method of possibilistic discrimination analysis (MPDA) was developed for the second stage to address this phenomenon. The method generates positive and negative discrimination measures for each alternative applicant in relation to a particular attribute. The obtained discrimination pair reflects the interaction of attributes and represents intuitionistic fuzzy numbers (IFNs). For the aggregation of applicant's discrimination intuitionistic fuzzy assessments (with respect to attributes), new intuitionistic aggregation operators, such as AsP-IFOWA and AsP-IFOWG, are defined and studied. The new operators are certain extensions of the well-known Choquet integral and Yager OWA operators. The extensions, in contrast to the Choquet aggregation, take into account all possible interactions of the attributes by introducing associated probabilities of a fuzzy measure.Design/methodology/approachFor optimal planning of investments distribution and decreasing of credit risks, it is crucial to have selected projects ranked within deeply detailed investment model. To achieve this, a new approach developed in this article involves three stages. The first stage is to reduce a possibly large number of applicants for credit, and here, the method of expertons is used. At the second stage, a model of improved decisions is built, which reduces the risks of decision making. In this model, as it is in multi-attribute decision-making (MADM) + multi-objective decision-making (MODM), expert evaluations are presented in terms of utility, gain, and more. At the third stage, the authors construct the bi-criteria discrete intuitionistic fuzzy optimization problem for making the most profitable investment portfolio with new criterion: 1) Maximization of total ranking index of selected applicants' group and classical criterion and 2) Maximization of total profit of selected applicants' group.FindingsThe example gives the Pareto fronts obtained by both new operators, the Choquet integral and Yager OWA operators also well-known TOPSIS approach, for selecting applicants and awarding credits. For a fuzzy measure, the possibility measure defined on the expert evaluations of attributes is taken.Originality/valueThe comparative analysis identifies the applicants who will receive the funding sequentially based on crediting resources and their requirements. It has become apparent that the use of the new criterion has given more credibility to applicants in making optimal credit decisions in the environment of extended new operators, where the phenomenon of interaction of all attributes was also taken into account.

scholarly journals INTUITIONISTIC FUZZY EINSTEIN CHOQUET INTEGRAL OPERATORS FOR MULTIPLE ATTRIBUTE DECISION MAKING

2014 ◽  
Vol 20 (2) ◽  
pp. 227-253 ◽  
Author(s):  
Yejun Xu ◽  
Huimin Wang ◽  
José M. Merigó
Keyword(s):  
Decision Making ◽  
Water Resource Management ◽  
Choquet Integral ◽  
Integral Operators ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Decision Making Problem ◽  
Einstein Operations

In this paper, we propose some new aggregation operators which are based on the Choquet integral and Einstein operations. The operators not only consider the importance of the elements or their ordered positions, but also consider the interactions phenomena among the decision making criteria or their ordered positions. It is shown that the proposed operators generalize several intuitionistic fuzzy Einstein aggregation operators. Moreover, some of their properties are investigated. We also study the relationship between the proposed operators and the existing intuitionistic fuzzy Choquet aggregation operators. Furthermore, an approach based on intuitionistic fuzzy Einstein Choquet integral operators is presented for multiple attribute decision-making problem. Finally, a practical decision making problem involving the water resource management is given to illustrate the multiple attribute decision making process.

Extensions of Probability Intuitionistic Fuzzy Aggregation Operators in Fuzzy MCDM/MADM

2018 ◽  
Vol 17 (02) ◽  
pp. 621-655 ◽  
Author(s):  
Gia Sirbiladze ◽  
Anna Sikharulidze
Keyword(s):  
Decision Making ◽  
Choquet Integral ◽  
Aggregation Operators ◽  
Intuitionistic Fuzzy ◽  
New Family ◽  
Conjugate Connections ◽  
Fuzzy Aggregation ◽  
Aggregation Of Information ◽  
Fuzzy Mcdm ◽  
Development Risks

New family of intuitionistic fuzzy operators for aggregation of information on interactive criteria/attributes in Multi-Criteria/attributes Decision Making (MCDM/MADM) problems are constructed. New aggregations are based on the Choquet integral and the associated probability class of a fuzzy measure. Propositions on the correctness of the extension are presented. Connections between the operators and the compositions of dual triangular norms [Formula: see text] and [Formula: see text] are described. The conjugate connections between the constructed operators are considered. It is known that when interactions between criteria/attributes are strong, aggregation operators based on Choquet integral reflect these interactions at a certain degree, but these operators consider only consonant structure of criteria/attributes. New operators reflect interactions among all the combinations of the criteria/attributes in the fuzzy MCDM/MADM process. Several variants of new operators are used in the decision making problem regarding the assessment of software development risks.

scholarly journals A Novel Method for Dynamic Multicriteria Decision Making with Hybrid Evaluation Information

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Shihu Liu ◽  
Tauqir Ahmed Moughal
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Ideal Solutions ◽  
Interval Valued ◽  
Evaluation Information

How to select the most desirable pattern(s) is often a crucial step for decision making problem. By taking uncertainty as well as dynamic of database into consideration, in this paper, we construct a dynamic multicriteria decision making procedure, where the evaluation information of criteria is expressed by real number, intuitionistic fuzzy number, and interval-valued intuitionistic fuzzy number. During the process of algorithm construction, the evaluation information at all time episodes is firstly aggregated into one, and then it is transformed into the unified interval-valued intuitionistic fuzzy number representational form. Similar to most multicriteria decision making approaches, the TOPSIS method is applied in the proposed decision making algorithm. In particular, the distance between possible patterns and the ideal solutions is defined in terms of cosine similarity by considering all aspects of the unified evaluation information. Experimental results show that the proposed decision making approach can effectively select desirable pattern(s).

Aggregation Operators of Trapezoidal Intuitionistic Fuzzy Sets to Multicriteria Decision Making

2017 ◽  
Vol 13 (4) ◽  
pp. 1-22 ◽  
Author(s):  
Jufeng Ye
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Multicriteria Decision Making ◽  
Weighted Averaging ◽  
Intuitionistic Fuzzy Number ◽  
Fuzzy Information ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem ◽  
Trapezoidal Intuitionistic Fuzzy Number

This paper presents the trapezoidal intuitionistic fuzzy weighted averaging (TIFWA) operator, trapezoidal intuitionistic fuzzy ordered weighted averaging (TIFOWA) operator, trapezoidal intuitionistic fuzzy weighted geometric (TIFWG) operator, and trapezoidal intuitionistic fuzzy ordered weighted geometric (TIFOWG) operator to aggregate the trapezoidal intuitionistic fuzzy information and investigates their properties. Furthermore, a multicriteria decision making method based on the TIFOWA and TIFOWG operators and the score function and accuracy function of a trapezoidal intuitionistic fuzzy number is established to deal with the multicriteria decision making problem with trapezoidal intuitionistic fuzzy information. Finally, an illustrative example demonstrates the application of the proposed method.

scholarly journals Multi-criteria decision making based on induced generalized interval neutrosophic Choquet integral

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0242449
Author(s):  
Yangyang Jiao ◽  
Lu Wang ◽  
Jianxia Liu ◽  
Gang Ma
Keyword(s):  
Decision Making ◽  
Choquet Integral ◽  
Investment Decision ◽  
Aggregation Operators ◽  
Optimal Decision ◽  
Multi Criteria Decision Making ◽  
Investment Decision Making ◽  
Decision Making Problem ◽  
Geometric Operator ◽  
Integral Average

In this paper, two new aggregation operators based on Choquet integral, namely the induced generalized interval neutrosophic Choquet integral average operator(IGINCIA) and the induced generalized interval neutrosophic Choquet integral geometric operator(IG-INCIG), are proposed for multi-criteria decision making problems (MCDM). Firstly, the criteria are dependent to each other and the evaluation information of the criteria are expressed by interval neutrosophic numbers. Moreover, two indices which are inspired by the geometrical structure are established to compare the interval neutrosophic numbers. Then, a MCDM method is proposed based on the proposed aggregation operators and ranking indices to cope with MCDM with interactive criteria. Lastly, an investment decision making problem is provided to illustrate the practicality and effectiveness of the proposed approach. The validity and advantages of the proposed method are analyzed by comparing with some existing approaches. By a numerical example in company investment to expand business though five alternatives with considering four criteria, the optimal decision is made.

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