scholarly journals A HEDGE ALGEBRAS BASED CLASSIFICATION REASONING METHOD WITH MULTI-GRANULARITY FUZZY PARTITIONING

2019 ◽  
Vol 35 (4) ◽  
pp. 319-336
Author(s):  
Phạm Đình Phong ◽  
Nguyen Duc Du ◽  
Nguyen Thanh Thuy ◽  
Hoang Van Thong
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Data Classification ◽  
Design Methods ◽  
Fuzzy Classification ◽  
Classification Rule ◽  
Linguistic Terms ◽  
Fuzzy Partitioning ◽  
Fuzzy Partitions ◽  
Rule Bases

During last years, lots of the fuzzy rule based classifier (FRBC) design methods have been proposed to improve the classification accuracy and the interpretability of the proposed classification models. Most of them are based on the fuzzy set theory approach in such a way that the fuzzy classification rules are generated from the grid partitions combined with the pre-designed fuzzy partitions using fuzzy sets. Some mechanisms are studied to automatically generate fuzzy partitions from data such as discretization, granular computing, etc. Even those, linguistic terms are intuitively assigned to fuzzy sets because there is no formalisms to link inherent semantics of linguistic terms to fuzzy sets. In view of that trend, genetic design methods of linguistic terms along with their (triangular and trapezoidal) fuzzy sets based semantics for FRBCs, using hedge algebras as the mathematical formalism, have been proposed. Those hedge algebras-based design methods utilize semantically quantifying mapping values of linguistic terms to generate their fuzzy sets based semantics so as to make use of fuzzy sets based-classification reasoning methods proposed in design methods based on fuzzy set theoretic approach for data classification. If there exists a classification reasoning method which bases merely on semantic parameters of hedge algebras, fuzzy sets-based semantics of the linguistic terms in fuzzy classification rule bases can be replaced by semantics - based hedge algebras. This paper presents a FRBC design method based on hedge algebras approach by introducing a hedge algebra- based classification reasoning method with multi-granularity fuzzy partitioning for data classification so that the semantic of linguistic terms in rule bases can be hedge algebras-based semantics. Experimental results over 17 real world datasets are compared to existing methods based on hedge algebras and the state-of-the-art fuzzy sets theoretic-based approaches, showing that the proposed FRBC in this paper is an effective classifier and produces good results.

scholarly journals A HEDGE ALGEBRAS BASED REASONING METHOD FOR FUZZY RULE BASED CLASSIFIER

2019 ◽  
Vol 57 (5) ◽  
pp. 631
Author(s):  
Phạm Đình Phong ◽  
Nguyễn Đức Dư ◽  
Hoàng Văn Thông
Keyword(s):  
Fuzzy Sets ◽  
Design Method ◽  
Fuzzy Rule ◽  
Design Methods ◽  
Rule Based ◽  
Classifier Design ◽  
Real World Datasets ◽  
Rule Based Classifier ◽  
Rule Bases ◽  
Sets Theory

The fuzzy rule based classifier (FRBC) design methods have intensively been being studied during last years. The ones designed by utilizing hedge algebras as a formalism to generate the optimal linguistic values along with their (triangular and trapezoidal) fuzzy sets based semantics for the FRBCs have been proposed. Those design methods generate the fuzzy sets based semantics because the classification reasoning method still bases on the fuzzy set theory.  One question which has been arisen is whether there is a pure hedge algebras classification reasoning method so that the fuzzy sets based semantic of the linguistic values in the fuzzy rule bases can be replaced with the hedge algebras based semantic. This paper answers that question by presenting a fuzzy rule based classifier design method based on hedge algebras with a pure hedge algebras classification reasoning method. The experimental results over 17 real world datasets are compared to the existing methods based on hedge algebras and fuzzy sets theory showing that the proposed method is effective and produces good results.

Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection

2021 ◽  
pp. 1-22
Author(s):  
Riaz Ali ◽  
Saleem Abdullah ◽  
Shakoor Muhammad ◽  
Muhammad Naeem ◽  
Ronnason Chinram
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Functions ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Program Selection ◽  
Maclaurin Symmetric Mean ◽  
Complex Intuitionistic Fuzzy Set

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results.

ANALYSIS OF FUZZY QUEUES BY USING PENTAGONAL FUZZY NUMBER

2021 ◽  
Vol 23 (04) ◽  
pp. 211-224
Author(s):  
Gurcharan Singh ◽  
◽  
Baljodh Singh ◽  
Neelam Kumari ◽  
◽  
...  
Keyword(s):  
Probability Theory ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Queuing Theory ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Linguistic Terms

This paper deals with the fact thatpentagonal fuzzy numbers are pre-owned and systematic outcomes are discussed in real-life situations. The fuzzy set supposition is combined with well-established classical queuing theory but the classical queuing theory is far away from real-life situations. In this approach, we can use both fuzzy and probability theory to make this work more realistic with the help of the α-cut technique. Symmetric pentagonal fuzzy numbers are used to elaborate on the situation of the queue in linguistic terms.

Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

2021 ◽  
pp. 1-17
Author(s):  
Changlin Xu ◽  
Juhong Shen
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
New Method ◽  
Fuzzy Decision Making ◽  
Multi Criteria Decision Making

 Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

Star Neutrosophic Fuzzy Topological Space

2020 ◽  
pp. 77-82
Author(s):  
A.A A.A.Salama ◽  
◽  
◽  
◽  
Hewayda ElGhawalby ◽  
...  
Keyword(s):  
Topological Space ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Topological Space ◽  
New Type

In this paper, we aim to develop a new type of neutrosophic fuzzy set called the star neutrosophic fuzzy set as a generalization to star neutrosophic crisp set defined in by Salama et al.[8], and study some of its properties. Adedd to, we introduce the notion of star neutrosophic fuzzy topological space as a generalization to some topological consepts as star neutrosophic fuzzy closure, and star neutrosophic fuzzy interior. Finally, we extend the concepts of fuzzy topological space, and intuitionistic fuzzy topological space to the case of star neutrosophic fuzzy sets.

scholarly journals Neuro-Fuzzy Assessment of Building Damage and Safety After an Earthquake

2007 ◽  
pp. 123-157 ◽  
Author(s):  
Martha Carreño ◽  
Omar Cardona ◽  
Alex Barbat
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy System ◽  
Fuzzy Rule ◽  
Neuro Fuzzy ◽  
Computational Intelligence Technique ◽  
Artificial Neural ◽  
Fuzzy Assessment ◽  
Rule Bases ◽  
Building Occupancy

This chapter describes the algorithmic basis of a computational intelligence technique, based on a neuro-fuzzy system, developed with the objective of assisting nonexpert professionals of building construction to evaluate the damage and safety of buildings after strong earthquakes, facilitating decision-making during the emergency response phase on their habitability and reparability. A hybrid neuro-fuzzy system is proposed, based on a special three-layer feedforward artificial neural network and fuzzy rule bases. The inputs to the system are fuzzy sets, taking into account that the damage levels of the structural components are linguistic variables, defined by means of qualifications such as slight, moderate or severe, which are very appropriate to handle subjective and incomplete information. The chapter is a contribution to the understanding of how soft computing applications, such as artificial neural networks and fuzzy sets, can be used to complex and urgent processes of engineering decision-making, like the building occupancy after a seismic disaster.

scholarly journals Convexity of hesitant fuzzy sets based on aggregation functions

2020 ◽  
pp. 45-45
Author(s):  
Pedro Huidobro ◽  
Pedro Alonso ◽  
Vladimír Janis ◽  
Susana Montes
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Optimization ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
Geometric Properties ◽  
Aggregation Functions ◽  
Definition Of

Convexity is one of the most important geometric properties of sets and a useful concept in many fields of mathematics, like optimization. As there are also important applications making use of fuzzy optimization, it is obvious that the studies of convexity are also frequent. In this paper we have extended the notion of convexity for hesitant fuzzy sets in order to fulfill some necessary properties. Namely, we have found an appropriate definition of convexity for hesitant fuzzy sets on any ordered universe based on aggregation functions such that it is compatible with the intersection, that is, the intersection of two convex hesitant fuzzy sets is a convex hesitant fuzzy set and it fulfills the cut worthy property.

scholarly journals Some Operational Computation for Intuitionistic or Pythagorean Fuzzy Set Using C-Programming

2020 ◽  
pp. 123-132
Author(s):  
Jwngsar Moshahary
Keyword(s):  
Fuzzy Sets ◽  
Programming Language ◽  
Fuzzy Set ◽  
Pythagorean Fuzzy Set ◽  
Pythagorean Fuzzy Sets ◽  
C Programming Language ◽  
C Programming

Intuitionistic or pythagorean fuzzy sets are the best tools to deal with uncertainty or ambiguity to solve diverse disciplines of application problems. It is often difficult to compute union, intersection, and complements when it comes to a large number of members contained in the set, also it is difficult to check whether it is a subset or not. Here, we used the C-programming language to overcome the problems, and then it is found that more effective and realistic results have been obtained.

scholarly journals Evidence Theory in Picture Fuzzy Set Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Harish Garg ◽  
R. Sujatha ◽  
D. Nagarajan ◽  
J. Kavikumar ◽  
Jeonghwan Gwak
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Evidence Theory ◽  
Belief Function ◽  
Uncertain Information ◽  
Interval Probability ◽  
Dempster Shafer Theory ◽  
Effective Manner ◽  
Picture Fuzzy Set ◽  
Shafer Theory

Picture fuzzy set is the most widely used tool to handle the uncertainty with the account of three membership degrees, namely, positive, negative, and neutral such that their sum is bound up to 1. It is the generalization of the existing intuitionistic fuzzy and fuzzy sets. This paper studies the interval probability problems of the picture fuzzy sets and their belief structure. The belief function is a vital tool to represent the uncertain information in a more effective manner. On the other hand, the Dempster–Shafer theory (DST) is used to combine the independent sources of evidence with the low conflict. Keeping the advantages of these, in the present paper, we present the concept of the evidence theory for the picture fuzzy set environment using DST. Under this, we define the concept of interval probability distribution and discuss its properties. Finally, an illustrative example related to the decision-making process is employed to illustrate the application of the presented work.

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