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.

New Fuzzy Aggregation Operators Based on the Finite Choquet Integral — Application in the MADM Problem

2016 ◽  
Vol 15 (03) ◽  
pp. 517-551 ◽  
Author(s):  
Gia Sirbiladze
Keyword(s):  
Decision Making ◽  
Choquet Integral ◽  
Aggregation Operators ◽  
Fuzzy Measure ◽  
Weighted Averaging ◽  
Positive Real ◽  
Information Measures ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
States Of Nature

In this paper, new generalizations of the probabilistic averaging operator — Associated Fuzzy Probabilistic Averaging (As-PA and As-FPA) and Immediate Probabilistic Fuzzy Ordered Weighted Averaging (As-IP-OWA and As-IP-FOWA) operators are presented in the environment of fuzzy uncertainty. An uncertainty is presented by associated probabilities of a fuzzy measure. Expert’s evaluations as arguments of the aggregation operators are described by a variable, values of which are compatibility levels on the states of nature defined in positive real or triangular fuzzy numbers (TFNs). Two propositions on the As-FPA operator are proved: (1) The As-FPA operator for the fuzzy measure — capacity of order two coincides with the finite Choquet Averaging (CA) Operator; (2) the As-FPA operator coincides with the FPA operator when a probability measure is used in the role of a fuzzy measure. Analogous propositions for the As-IP-FOWA operator are proved. Some propositions on the connection of the As-FPA and As-IP-FOWA operators are also proved. Information measures — Orness and Divergence for the constructed operators are defined. Some propositions on the connections of these parameters with the corresponding parameters of the finite CA Operator are proved. Two illustrative examples on the applicability of the As-FPA and As-IP-FOWA operators are presented: (1) Several variants of the As-FPA and As-IP-FOWA operators are used for comparison of decision-making results for the problems regarding the fiscal policy of a country; (2) The As-FPA operator is used in the Multi-attribute decision-making (MADM) problem of choosing the best version of the students’ project.

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.

On Ranking of Intuitionistic Fuzzy Values Based on Dominance Relations

2014 ◽  
Vol 22 (02) ◽  
pp. 315-335 ◽  
Author(s):  
Xiaohan Yu ◽  
Zeshui Xu ◽  
Shousheng Liu ◽  
Qi Chen
Keyword(s):  
Decision Making ◽  
Order Relation ◽  
Aggregation Operators ◽  
Fuzzy Subset ◽  
Dominance Relations ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
Do So

For intuitionistic fuzzy values (IFVs), there are more or less some drawbacks in the existing comparison methods, so it is necessary for us to develop a more proper technique for comparing or ranking IFVs in this paper. To do so, we first formalize an IFV as a fuzzy subset in order to analyze the fuzzy meaning of an IFV, and then according to the basic properties of the fuzzy subset, we determine the dominance relation (order relation) between two IFVs by defining a dominance degree. In order to explain the feasibility of the dominance relations, we validate the monotonicity of intuitionistic fuzzy operational laws, and additionally, we improve and prove the monotonicity of several intuitionistic fuzzy aggregation operators on the basis of the dominance relations. Because it is of importance for some practical problems (e.g., intuitionistic fuzzy multi-attribute decision making) to rank IFVs, we finally develop a method for ranking IFVs by constructing a dominance matrix based on the dominance degrees. A simple example is taken to illustrate the validity of our ranking method.

scholarly journals Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Huimin Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Score Function ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Linguistic Intuitionistic Fuzzy Sets

To better deal with imprecise and uncertain information in decision making, the definition of linguistic intuitionistic fuzzy sets (LIFSs) is introduced, which is characterized by a linguistic membership degree and a linguistic nonmembership degree, respectively. To compare any two linguistic intuitionistic fuzzy values (LIFVs), the score function and accuracy function are defined. Then, based ont-norm andt-conorm, several aggregation operators are proposed to aggregate linguistic intuitionistic fuzzy information, which avoid the limitations in exiting linguistic operation. In addition, the desired properties of these linguistic intuitionistic fuzzy aggregation operators are discussed. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in multiple attribute group decision making (MAGDM).

Some Improved Linguistic Intuitionistic Fuzzy Aggregation Operators and Their Applications to Multiple-Attribute Decision Making

2017 ◽  
Vol 16 (03) ◽  
pp. 817-850 ◽  
Author(s):  
Peide Liu ◽  
Peng Wang
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making

Linguistic intuitionistic fuzzy numbers (LIFNs) is a new concept in describing the intuitionistic fuzzy information, which membership and non-membership are expressed by linguistic terms, so it can more easily express the fuzzy information, and some research results on LIFNs have been achieved. However, in the existing researches, some linguistic intuitionistic fuzzy aggregation operators are based on the traditional operational rules, and they have some drawbacks for multi-attribute decision making (MADM) in the practical application. In order to overcome these problems, in this paper, we proposed some improved operational rules based on LIFNs and verified their some properties. Then we developed some aggregation operators to fuse the decision information represented by LIFNs, including the improved linguistic intuitionistic fuzzy weighted averaging (ILIFWA) operator and the improved linguistic intuitionistic fuzzy weighted power average (ILIFWPA) operator. Further, we proved their some desirable properties. Based on the ILIFWA operator and the ILIFWPA operator, we presented some new methods to deal with the multi-attribute group decision making (MAGDM) problems under the linguistic intuitionistic fuzzy environment. Finally, we used some practical examples to illustrate the validity and feasibility of the proposed methods by comparing with other methods.

New Einstein Hybrid Aggregation Operators for Intuitionistic Fuzzy Sets and Applications in Multi-Criteria Decision-Making

2019 ◽  
pp. 252-283
Author(s):  
Bhagawati Prasad Joshi ◽  
Abhay Kumar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Decision Maker ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Processes

The fusion of multidimensional intuitionistic fuzzy information plays an important part in decision making processes under an intuitionistic fuzzy environment. In this chapter, it is observed that existing intuitionistic fuzzy Einstein hybrid aggregation operators do not follow the idempotency and boundedness. This leads to sometimes illogical and even absurd results to the decision maker. Hence, some new intuitionistic fuzzy Einstein hybrid aggregation operators such as the new intuitionistic fuzzy Einstein hybrid weighted averaging (IFEHWA) and the new intuitionistic fuzzy Einstein hybrid weighted geometric (IFEHWG) were developed. The new IFEHWA and IFEHWG operators can weigh the arguments as well as their ordered positions the same as the intuitionistic fuzzy Einstein hybrid aggregation operators do. Further, it is validated that the defined operators are idempotent, bounded, monotonic and commutative. Then, based on the developed approach, a multi-criteria decision-making (MCDM) procedure is given. Finally, a numerical example is conducted to demonstrate the proposed method effectively.

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