scholarly journals Some improved interactive aggregation operators under interval-valued intuitionistic fuzzy environment and its application to decision making process

2017 ◽  
Vol 24 (5) ◽  
pp. 2581-2604 ◽  
Author(s):  
Harish Garg ◽  
Nikunj Agarwal ◽  
Alka Tripathi
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Decision Making Process ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Interval Valued

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.

Some Generalized Intuitionistic Fuzzy Geometric Aggregation Operators with Applications in Multi-Criteria Decision Making Process

2016 ◽  
pp. 159-179 ◽  
Author(s):  
Bhagawati Prasad Joshi
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Decision Making Process ◽  
Additional Parameter ◽  
Multi Criteria Decision Making ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Special Cases ◽  
Multidimensional Information

The aggregation operators play an important role in the fusion of multidimensional information in decision making process. In this study, a series of generalized aggregation operators such as: the generalized intuitionistic fuzzy weighted geometric (GIFWG) operator, the generalized intuitionistic fuzzy ordered weighted geometric (GIFOWG) operator and the generalized intuitionistic fuzzy hybrid geometric (GIHG) operator are proposed under intuitionistic fuzzy environment by controlling the power of the argument values with an additional parameter p. Some of the important properties and some special cases of these operators are also included in this study. Further, the developed approach is utilized to deal with multi-criteria decision making (MCDM) problems. Numerical examples are constructed to illustrate the developed approach effectively.

Some Generalized Intuitionistic Fuzzy Geometric Aggregation Operators With Applications in Multi-Criteria Decision Making Process

2018 ◽  
pp. 1190-1211
Author(s):  
Bhagawati Prasad Joshi
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Decision Making Process ◽  
Additional Parameter ◽  
Multi Criteria Decision Making ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Special Cases ◽  
Multidimensional Information

The aggregation operators play an important role in the fusion of multidimensional information in decision making process. In this study, a series of generalized aggregation operators such as: the generalized intuitionistic fuzzy weighted geometric (GIFWG) operator, the generalized intuitionistic fuzzy ordered weighted geometric (GIFOWG) operator and the generalized intuitionistic fuzzy hybrid geometric (GIHG) operator are proposed under intuitionistic fuzzy environment by controlling the power of the argument values with an additional parameter p. Some of the important properties and some special cases of these operators are also included in this study. Further, the developed approach is utilized to deal with multi-criteria decision making (MCDM) problems. Numerical examples are constructed to illustrate the developed approach effectively.

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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