Generalized Bonferroni Mean Operator for Fuzzy Number Intuitionistic Fuzzy Sets and its Application to Multiattribute Decision Making

2015 ◽  
Vol 30 (5) ◽  
pp. 499-519 ◽  
Author(s):  
Rajkumar Verma
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Number ◽  
Intuitionistic Fuzzy Sets ◽  
Bonferroni Mean ◽  
Intuitionistic Fuzzy

scholarly journals Towards Better Concordance among Contextualized Evaluations in FAST-GDM Problems

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 93
Author(s):  
Marcelo Loor ◽  
Ana Tapia-Rosero ◽  
Guy De Tré
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Heterogeneous Group ◽  
Intuitionistic Fuzzy ◽  
High Level ◽  
Consensus Reaching ◽  
Novel Algorithm

A flexible attribute-set group decision-making (FAST-GDM) problem consists in finding the most suitable option(s) out of the options under consideration, with a general agreement among a heterogeneous group of experts who can focus on different attributes to evaluate those options. An open challenge in FAST-GDM problems is to design consensus reaching processes (CRPs) by which the participants can perform evaluations with a high level of consensus. To address this challenge, a novel algorithm for reaching consensus is proposed in this paper. By means of the algorithm, called FAST-CR-XMIS, a participant can reconsider his/her evaluations after studying the most influential samples that have been shared by others through contextualized evaluations. Since exchanging those samples may make participants’ understandings more like each other, an increase of the level of consensus is expected. A simulation of a CRP where contextualized evaluations of newswire stories are characterized as augmented intuitionistic fuzzy sets (AIFS) shows how FAST-CR-XMIS can increase the level of consensus among the participants during the CRP.

scholarly journals On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1485
Author(s):  
Pavel Sevastjanov ◽  
Ludmila Dymova ◽  
Krzysztof Kaczmarek
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Short Paper ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Methodological Problems ◽  
Shafer Theory ◽  
Sets Theory

In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.

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.

Introduction to Intuitionistic Fuzzy Multisets and Its Applications

2016 ◽  
pp. 43-52
Author(s):  
T. K. Shinoj ◽  
Sunil Jacob John
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Linguistic Variable ◽  
Human Reasoning ◽  
Collaborative Robots ◽  
Intuitionistic Fuzzy

In this chapter a new concept named Intuitionistic Fuzzy Multiset is introduced, which is an attempt to combine the two concepts: Intuitionistic Fuzzy sets and Fuzzy Multisets. The basic operations and their various properties are discussed. The authors discussed two significant applications of Intuitionistic Fuzzy Multisets. Most of human reasoning involves the use of variables whose values are fuzzy sets. This is the basis for the concept of a linguistic variable. But in some situations like decision making problems, the description by a linguistic variable in terms of membership function only is not adequate. There is chance of existing a non-null complement. There are situations that each element has different membership values. In such situations Intuitionistic Fuzzy Multisets is more adequate. Here the authors present Intuitionistic Fuzzy Multisets as a tool for reasoning such a situation through a medical diagnosis problem. As the second application, accuracy of Collaborative Robots using the concept of Intuitionistic Fuzzy Multiset is discussed.

Sign in / Sign up

Export Citation Format

Share Document