Mixed Solution Strategy for MCGDM Problems Using Entropy/Cross Entropy in Interval-Valued Intuitionistic Fuzzy Environment

2015 ◽  
Vol 17 (01) ◽  
pp. 1540007 ◽  
Author(s):  
Anjana Gupta ◽  
Aparna Mehra ◽  
S. S. Appadoo
Keyword(s):  
Weight Vector ◽  
Decision Makers ◽  
Cross Entropy ◽  
Entropy Measure ◽  
Mixed Solution ◽  
Solution Strategy ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Interval Valued

Although several weight determining methods have been studied for multiple criteria group decision making (MCGDM) problems under intuitionistic fuzzy environment, in the present study, besides the criteria values provided by the decision makers (DMs), we propose to also use the historical data of alternatives-criteria to compute the criteria weights. This is a reasonable thought as the past information may influence the decision makers' choice of entries in their respective alternatives-criteria decision matrices. To this aim, we introduce a novel mixed solution strategy to derive the criteria final weight vector. Initially, the alternatives-criteria decision matrices provided by the DMs are taken to involve interval-valued intuitionistic fuzzy numbers (IVIFNs). The entropy measure for IVIFNs, studied by Ye [2010a], is used to aggregate these decision matrices. We also introduce a new definition of cross entropy for IVIFNs and used it to rank the alternatives. Finally, an example is presented to illustrate the proposed approach.

scholarly journals THE INTERVAL-VALUED INTUITIONISTIC FUZZY GEOMETRIC CHOQUET AGGREGATION OPERATOR BASED ON THE GENERALIZED BANZHAF INDEX AND 2-ADDITIVE MEASURE

2015 ◽  
Vol 21 (2) ◽  
pp. 186-215 ◽  
Author(s):  
Fanyong MENG ◽  
Qiang ZHANG ◽  
Jiaquan ZHAN
Keyword(s):  
Geometric Mean ◽  
Fuzzy Measure ◽  
Entropy Measure ◽  
Additive Measure ◽  
Banzhaf Index ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Additive Measures ◽  
Interval Valued

Based on the operational laws on interval-valued intuitionistic fuzzy sets, the generalized Banzhaf interval-valued intuitionistic fuzzy geometric Choquet (GBIVIFGC) operator is proposed, which is also an interval-valued intuitionistic fuzzy value. It is worth pointing out that the GBIVIFGC operator can be seen as an extension of some geometric mean operators. Since the fuzzy measure is defined on the power set, it makes the problem exponentially complex. In order to overall reflect the interaction among elements and reduce the complexity of solving a fuzzy measure, we further introduce the GBIVIFGC operator w.r.t. 2-additive measures. Furthermore, if the information about weights of experts and attributes is incompletely known, the models of obtaining the optimal 2-additive measures on criteria set and expert set are given by using the introduced cross entropy measure and the Banzhaf index. Finally, an approach to pattern recognition and multi-criteria group decision making under interval-valued intuitionistic fuzzy environment is developed, respectively.

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.

scholarly journals Decision-Maker’s Risk Preference Based Intuitionistic Fuzzy Multiattribute Decision-Making and Its Application in Robot Enterprises Investment

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Liandong Zhou ◽  
Qifeng Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Weight Vector ◽  
Multiple Attribute Decision Making ◽  
Decision Makers ◽  
Research Papers ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Fuzzy Weight

At present, the utilization of hesitation information of intuitionistic fuzzy numbers is insufficient in many methods which were proposed to solve the intuitionistic fuzzy multiple attribute decision-making problems. And also there exist some flaws in the intuitionistic fuzzy weight vector constructions in many research papers. In order to solve these insufficiencies, this paper defined three construction equations of weight vectors based on the risk preferences of decision-makers. Then we developed an intuitionistic fuzzy dependent hybrid weighted operator (IFDHW) and proposed an intuitionistic fuzzy multiattribute decision-making method. Finally, the effectiveness of this method is verified by a robot manufacturing investment example.

Linguistic interval-valued intuitionistic fuzzy copula power aggregation operators for multiattribute group decision making

2021 ◽  
Vol 40 (1) ◽  
pp. 605-624 ◽  
Author(s):  
Lei Xu ◽  
Yi Liu ◽  
Haobin Liu
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Uncertain Information ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

For the sake of better handle the imprecise and uncertain information in decision making problems(DMPs), linguistic interval-valued intuitionistic fuzzy numbers(LIVIFNs) based aggregation operators (AOS) are proposed by combining extended Copulas (ECs), extended Co-copulas (ECCs), power average operator and linguistic interval-valued intuitionistic fuzzy information (LIVIFI). First of all, ECs and ECCs, some specifics of ECs and ECCs, score and accuracy functions of LIVIFNs are gained. Then, based on ECs and ECCs, several aggregation operators are proposed to aggregate LIVIFI, which can offer decision makers (DMs) desirable generality and flexibility. In addition, the desired properties of proposed AOS are discussed. Last but not least, a MAGDM approach is constructed based on proposed AOs; Consequently, the effectiveness of the proposed approach is verified by a numerical example, and then the advantages are showed by comparing with other approaches.

scholarly journals Heronian Means as Aggregation Operators for Multi-Attribute Decision Making Applications

2018 ◽  
Author(s):  
Xiaopu Shang ◽  
Jun Wang ◽  
Anupam Nanda ◽  
Weizi Li
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Novel Approach ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Heronian Mean

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

scholarly journals Large-Scale Green Supplier Selection Approach under a Q-Rung Interval-Valued Orthopair Fuzzy Environment

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 573 ◽  
Author(s):  
Liu ◽  
Cao ◽  
Shi ◽  
Tang
Keyword(s):  
Supplier Selection ◽  
Large Scale ◽  
Similarity Measures ◽  
Decision Makers ◽  
Entropy Measure ◽  
Green Supplier Selection ◽  
Fuzzy Environment ◽  
Fuzzy Aggregation ◽  
Interval Valued ◽  
Evaluation Information

As enterprises pay more and more attention to environmental issues, the green supply chain management (GSCM) mode has been extensively utilized to guarantee profit and sustainable development. Green supplier selection (GSS), which is a key segment of GSCM, has been investigated to put forward plenty of GSS approaches. At present, enterprises prefer to construct the large-scale teams of decision makers to obtain the more reasonable ranking results during GSS process. However, the existing methods pay little attention to the large-scale GSS procedure. To investigate the GSS issue with a large-scale group of decision makers, a new GSS approach under a q-rung interval-valued orthopair fuzzy environment is developed. The q-rung interval-valued orthopair fuzzy numbers are introduced to describe the evaluation information of green suppliers. Combined with a clustering approach and several clustering principles, the large-scale decision makers are divided into several subgroups. Next, the similarity measures between the evaluation matrices are computed to determine the weights of subgroups, and the collective evaluation information can be obtained using the q-rung interval-valued orthopair fuzzy aggregation operator. According to the weighted entropy measure, the weights of criteria are calculated; then, the q-rung interval-valued orthopair fuzzy multi-objective optimization on the basis of ratio analysis plus the full multiplicative form (q-RIVOF-MULTIMOORA) method is constructed to determine the best green supplier. At last, a practical GSS example is applied to show the feasibility of the proposed approach, and the sensitivity and comparative analyses indicate that for the large-scale GSS issues, the proposed approach can obtain the more robust and reasonable ranking results.

Multi-Attribute Decision Making Method Based on the Satisfaction under Interval-Valued Intuitionistic Fuzzy Environment

2014 ◽  
Vol 631-632 ◽  
pp. 1253-1256
Author(s):  
Mei Gui ◽  
Yue Lin Huang
Keyword(s):  
Decision Making ◽  
Ideal Point ◽  
Score Function ◽  
Weight Vector ◽  
Satisfaction Function ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Multi Attribute Decision Making ◽  
Interval Valued

In this paper, it discussed multi-attribute decision making (MADM) problems in which the information about attribute weights is incomplete and decision-making information is characterized by interval-valued intuitionistic fuzzy number (IVIFNs), decision-making method is proposed based on the satisfaction. First, we define positive and negative ideal point of the comprehensive attribute values and satisfaction function, and make use of satisfaction function to establish a multi-objective optimization model, apply this model to determine the attribute weight vector, calculate the comprehensive attribute values, rank the alternatives according to the score function and precise function of the comprehensive attribute values. Finally, the examples are given to show that the method is reasonable and effective.

Method of Multi-Attribute Decision Making for Interval-Valued Intuitionistic Fuzzy Sets Based on Mentality Function

2010 ◽  
Vol 44-47 ◽  
pp. 1075-1079
Author(s):  
Liang Zhong Shen ◽  
Guang Bo Li ◽  
Wen Bin Liu
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Sets ◽  
Decision Makers ◽  
Ranking Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Decision Making Model ◽  
Interval Valued

This paper has summarized the current ranking method for interval-valued intuitionistic fuzzy numbers, and then through the introduction of decision-makers’ mentality indicator, presented a new ranking method for interval-valued intuitionistic fuzzy numbers based on mentality function. Not only the nature of mentality function is deeply discussed but also the decision-making model based on the interval-valued intuitionistic fuzzy numbers is constructed. At last, an example is illustrated to prove the model's accuracy and effectiveness.

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