Modeling humanoid robots facial expressions using Pythagorean fuzzy sets

2020 ◽  
Vol 39 (5) ◽  
pp. 6507-6515
Author(s):  
Cengiz Kahraman ◽  
Eda Boltürk ◽  
Sezi Cevik Onar ◽  
Basar Oztaysi
Keyword(s):  
Fuzzy Sets ◽  
Facial Expressions ◽  
Humanoid Robot ◽  
Humanoid Robots ◽  
Intuitionistic Fuzzy Sets ◽  
Decision Makers ◽  
Pythagorean Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Human Emotions ◽  
And Behaviors

Pythagorean fuzzy sets (PFS) are an extension of intuitionistic fuzzy sets introduced by Atanassov [1]. PFSs have the advantage of providing larger domains for assigning membership and non-membership degrees satisfying that their squared sum is at most equal to one. PFS have been often used in modeling the problems under vagueness and impreciseness in order to better define the problems together with the hesitancy of decision makers. Different human emotions and behaviors can be modeled in humanoid robots (HR) by fuzzy sets. In this paper, facial expressions of a humanoid robot are modeled depending on the degrees of the emotions. Larger degree of emotion causes a stronger indicator of the facial mimic.

scholarly journals A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 142 ◽  
Author(s):  
Qianli Zhou ◽  
Hongming Mo ◽  
Yong Deng
Keyword(s):  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Distance Measure ◽  
Belief Function ◽  
Intuitionistic Fuzzy Sets ◽  
Divergence Measure ◽  
Pythagorean Fuzzy Sets ◽  
Practical Applications ◽  
Intuitionistic Fuzzy ◽  
Jensen Shannon Divergence

As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.

scholarly journals The n-Pythagorean Fuzzy Sets

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1772
Author(s):  
Anna Bryniarska
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Quadratic Function ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Functions ◽  
Power Functions ◽  
Pythagorean Fuzzy Sets ◽  
Conceptual Apparatus ◽  
Intuitionistic Fuzzy ◽  
Classic Theory

The following paper presents deductive theories of n-Pythagorean fuzzy sets (n-PFS). N-PFS objects are a generalization of the intuitionistic fuzzy sets (IFSs) and the Yager Pythagorean fuzzy sets (PFSs). Until now, the values of membership and non-membership functions have been described on a one-to-one scale and a quadratic function scale. There is a symmetry between the values of this membership and non-membership functions. The scales of any power functions are used here in order to increase the scope of the decision-making problems. The theory of n-PFS introduces a conceptual apparatus analogous to the classic theory of Zadeh fuzzy sets, consistently striving to correctly define the n-PFS algebra.

DATA CONSTRUCTION PROCESS AND QUALIFLEX-BASED METHOD FOR MULTIPLE-CRITERIA GROUP DECISION MAKING WITH INTERVAL-VALUED INTUITIONISTIC FUZZY SETS

2013 ◽  
Vol 12 (03) ◽  
pp. 425-467 ◽  
Author(s):  
TING-YU CHEN
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Uncertainty Indices ◽  
Interval Valued

Based on Jacquet-Lagreze's permutation method, QUALIFLEX is an outranking model that investigates all possible permutations of alternatives with respect to the consequences of all criteria. The purpose of this paper is to develop a QUALIFLEX-based method for multiple criteria group decision making within a decision environment of interval-valued intuitionistic fuzzy sets. We conduct a statistical inference approach with finite population correction to construct interval-valued intuitionistic fuzzy numbers. In addition, we incorporate the relative importance of decision makers and fuse individual opinions to form collective ratings using a modified method with weighted interval estimations. In view of diversiform preference types (weak order, strict order, difference order, interval bound, and ratio bound), we represent multiple decision makers' various forms of preference structures and assess criterion weights under incomplete information. By means of score functions, accuracy functions, membership-uncertainty indices, and hesitation-uncertainty indices, a ranking procedure is employed to identify a criterion-wise preference of alternatives. A QUALIFLEX-based model is then established to measure the level of concordance of the complete preference order for handling multiple criteria group decisions. The feasibility of the proposed method is illustrated by a practical problem relating to the selection of a landfill site. As indicated in the application, the proposed method is useful for handling complicated group decision-making problems that involve comprehensive criteria and limited alternatives.

scholarly journals Multicriteria Decision-Making Approach with Hesitant Interval-Valued Intuitionistic Fuzzy Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Juan-juan Peng ◽  
Jian-qiang Wang ◽  
Jing Wang ◽  
Xiao-hong Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Definition Of ◽  
Interval Valued

The definition of hesitant interval-valued intuitionistic fuzzy sets (HIVIFSs) is developed based on interval-valued intuitionistic fuzzy sets (IVIFSs) and hesitant fuzzy sets (HFSs). Then, some operations on HIVIFSs are introduced in detail, and their properties are further discussed. In addition, some hesitant interval-valued intuitionistic fuzzy number aggregation operators based ont-conorms andt-norms are proposed, which can be used to aggregate decision-makers' information in multicriteria decision-making (MCDM) problems. Some valuable proposals of these operators are studied. In particular, based on algebraic and Einsteint-conorms andt-norms, some hesitant interval-valued intuitionistic fuzzy algebraic aggregation operators and Einstein aggregation operators can be obtained, respectively. Furthermore, an approach of MCDM problems based on the proposed aggregation operators is given using hesitant interval-valued intuitionistic fuzzy information. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the developed approach, and the study is supported by a sensitivity analysis and a comparison analysis.

Interval-Valued Intuitionistic Fuzzy Sets based Method for Multiple Criteria Decision-Making

2016 ◽  
Vol 5 (4) ◽  
pp. 192-210 ◽  
Author(s):  
Bhagawati Prasad Joshi
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Multiple Criteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Due to the huge applications of fuzzy set theory, many generalizations were available in literature. Atanassov (1983) and Atanassov and Gargov (1989) introduced the notions of intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs) respectively. It is observed that IFSs and IVIFSs are more suitable tools for dealing with imprecise information and very powerful in modeling real life problems. However, many researchers made efforts to rank IVIFSs due to its importance in fusion of information. In this paper, a new ranking method is introduced and studied for IVIFSs. The proposed method is compared and illustrated with other existing methods by numerical examples. Then, it is utilized to identify the best alternative in multiple criteria decision-making problems in which criterion values for alternatives are IVIFSs. On the basis of the developed approach, it would provide a powerful way to the decision-makers to make his or her decision under IVIFSs. The validity and applicability of the proposed method are illustrated with practical examples.

scholarly journals Intuitionistic Fuzzy MOORA for Supplier Selection

DYNA ◽  
2015 ◽  
Vol 82 (191) ◽  
pp. 34-41 ◽  
Author(s):  
Luis Pérez-Domínguez ◽  
Alejandro Alvarado-Iniesta ◽  
Iván Rodríguez-Borbón ◽  
Osslan Vergara-Villegas
Keyword(s):  
Fuzzy Sets ◽  
Supplier Selection ◽  
Complex Problem ◽  
Intuitionistic Fuzzy Sets ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Group Environment ◽  
Critical Activity ◽  
Fuzzy Moora ◽  
Selection Of

<p class="ADYNAAbstrac"><span lang="EN-US">The supplier selection is a critical activity within the administration of the supply chain. It is considered a complex problem given that it involves different aspects such as the alternatives to evaluate, the multiple criteria involved as well as the group of decision makers with different opinions. In this sense, the literature reports several methods to help in this difficult activity of selecting the best supplier. However, there are still some gaps in these methods; therefore, it is imperative to further develop research. Thus, the purpose of this paper is to report a hybrid method between MOORA and intuitionistic fuzzy sets for the selection of suppliers with a focus on multi-criteria and multi-group environment. The importance of decision makers, criteria and alternatives are evaluated in terms of intuitionistic fuzzy sets. Then, MOORA is used in order to determine the best supplier. An experimental case is developed in order to explain the proposed method in detail and to demonstrate its practicality and effectiveness.</span></p>

scholarly journals New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1600
Author(s):  
Neeraj Gandotra ◽  
Bartłomiej Kizielewicz ◽  
Abhimanyu Anand ◽  
Aleksandra Bączkiewicz ◽  
Andrii Shekhovtsov ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Pythagorean Fuzzy Set ◽  
Additional Advantage ◽  
Pythagorean Fuzzy Sets ◽  
Intuitionistic Fuzzy

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.

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