Fuzzy and Probabilistic Object Bases

2011 ◽  
pp. 46-84 ◽  
Author(s):  
Tru Hoang Cao ◽  
Hoa Nguyen
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Relational Databases ◽  
Probabilistic Reasoning ◽  
Cartesian Product ◽  
Database Systems ◽  
Object Orientation ◽  
Probabilistic Interpretation ◽  
Algebraic Operations

Database systems have evolved from relational databases to those integrating different modeling and computing paradigms, in particular, object orientation and probabilistic reasoning. This chapter introduces an extension of the probabilistic object base model by Eiter et al. (2001), using fuzzy sets for representing and handling vague and imprecise values of object attributes. A probabilistic interpretation of relations on fuzzy set values is proposed to integrate them into that probability-based framework. Then, the definitions of fuzzy-probabilistic object base schemas, instances, and selection operation are presented. Other algebraic operations, namely, projection, renaming, Cartesian product, join, intersection, union, and difference of the probabilistic object base model are also adapted for its fuzzy extension.

Interval-Valued Fuzzy H-Ideals on ß-Algebra

2020 ◽  
pp. 244-274
Author(s):  
Prakasam Muralikrishna ◽  
Tapan Senapati ◽  
Perumal Hemavathi
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Algebraic Structures ◽  
Interval Valued

The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzzy sets. Using interval valued fuzzy set, various algebraic structures and related topics were discussed. This chapter extends fuzzy H-ideal into interval valued fuzzy H-ideals of β-algebra and deals some related results. It also provides the study on homomorphic images of an interval valued fuzzy H-ideals of β-algebra and the idea of Cartesian product of interval valued fuzzy H-ideals of β-algebra.

Complex bipolar fuzzy sets: An application in a transport’s company

2020 ◽  
pp. 1-17
Author(s):  
Muhammad Gulistan ◽  
Naveed Yaqoob ◽  
Ahmed Elmoasry ◽  
Jawdat Alebraheem
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Cartesian Product ◽  
Real Numbers ◽  
Wide Range ◽  
Fuzzy Aggregation ◽  
Bipolar Fuzzy Sets ◽  
Range Of Values

Zadeh’s fuzzy sets are very useful tool to handle imprecision and uncertainty, but they are unable to characterize the negative characteristics in a certain problem. This problem was solved by Zhang et al. as they introduced the concept of bipolar fuzzy sets. Thus, fuzzy set generalizes the classical set and bipolar fuzzy set generalize the fuzzy set. These theories are based on the set of real numbers. On the other hand, the set of complex numbers is the generalization of the set of real numbers so, complex fuzzy sets generalize the fuzzy sets, with wide range of values to handle the imprecision and uncertainty. So, in this article, we study complex bipolar fuzzy sets which is the generalization of bipolar fuzzy set and complex fuzzy set with wide range of values by adding positive membership function and negative membership function to unit circle in the complex plane, where one can handle vagueness in a much better way as compared to bipolar fuzzy sets. Thus this paper leads us towards a new direction of research, which has many applications in different directions. We develop the notions of union, intersection, complement, Cartesian product and De-Morgan’s Laws of complex bipolar fuzzy sets. Furthermore, we develop the complex bipolar fuzzy relations, fundamental operations on complex bipolar fuzzy matrices and some operators of complex bipolar fuzzy matrices. We also discuss the distance measure on complex bipolar fuzzy sets and complex bipolar fuzzy aggregation operators. Finally, we apply the developed approach to a numerical problem with the algorithm.

scholarly journals Multivariate Extension Principle and Algebraic Operations of Intuitionistic Fuzzy Sets

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Yonghong Shen ◽  
Wei Chen
Keyword(s):  
Fuzzy Sets ◽  
General Framework ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Sets ◽  
Extension Principle ◽  
Algebraic Operation ◽  
Multivariate Extension ◽  
Intuitionistic Fuzzy ◽  
Algebraic Operations

This paper mainly focuses on multivariate extension of the extension principle of IFSs. Based on the Cartesian product over IFSs, the multivariate extension principle of IFSs is established. Furthermore, three kinds of representation of this principle are provided. Finally, a general framework of the algebraic operation between IFSs is given by using the multivariate extension principle.

AGGREGATES COMPUTED OVER FUZZY SETS AND THEIR INTEGRATION INTO SQLf

2008 ◽  
Vol 16 (06) ◽  
pp. 761-792 ◽  
Author(s):  
PATRICK BOSC ◽  
LUDOVIC LIETARD
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Relational Databases ◽  
Query Language ◽  
Fuzzy Integral ◽  
Flexible Querying

The SQLf query language is an extension of SQL to flexible querying of regular relational databases using fuzzy set theory. In this context, atomic predicates (called vague or fuzzy predicates) are expressing preferences and are defined by fuzzy sets. The main purpose of flexible querying is to provide the user with a set of discriminated answers (in the form of a fuzzy set). Until now, the use of aggregates (such as maximum or average) in SQLf queries is limited to the particular case where the aggregate applies to a crisp set. The objective of this paper is to propose an approach to define SQLf queries where the aggregate applies to a fuzzy set of items. The approach proposed here can indeed be seen as a generalization of Sugeno's fuzzy integral.

scholarly journals Extended Fuzzy Sets and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 770
Author(s):  
Bahram Farhadinia ◽  
Francisco Chiclana
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Algebraic Operations ◽  
Innovative Concept

This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of the fuzzy set (FS), but it also includes the concepts of the intuitionistic fuzzy set (IFS), the Pythagorean fuzzy set (PFS) and the p-rung orthopair fuzzy set (p-ROFS). In order to explore the features of the E-FS concept, set and algebraic operations on E-FSs, average and geometric operations of E-FSs are studied and an E-FS score function is defined. The superiority of the E-FS concept is further confirmed with a score-based decision making technique in which the concepts of FS, IFS, PFS and p-ROFS do not make sense.

scholarly journals Hierarchical Fuzzy Sets to Query Possibilistic Databases

2011 ◽  
pp. 299-324
Author(s):  
Rallou Thomopoulos ◽  
Patrice Buche ◽  
Ollivier Haemmerlé
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Current Literature ◽  
Fuzzy Set ◽  
User Interfaces ◽  
Fuzzy Set Theory ◽  
Relational Databases ◽  
Experimental Results ◽  
Relational Model ◽  
Flexible Querying

Within the framework of flexible querying of possibilistic databases, based on the fuzzy set theory, this chapter focuses on the case where the vocabulary used both in the querying language and in the data is hierarchically organized, which occurs in systems that use ontologies. We give an overview of previous works concerning two issues: first, flexible querying of imprecise data in the relational model and, second, the introduction of fuzziness in hierarchies. Concerning the latter point, we develop an aspect where there is a lack of study in current literature: fuzzy sets whose definition domains are hierarchies. Hence, we propose the concept of hierarchical fuzzy set and present its properties. We present its application in the MIEL flexible querying system for the querying of two imprecise relational databases, including user interfaces and experimental results.

Closed Sets of Boolean Terms in Relational Databases

1991 ◽  
Vol 14 (3) ◽  
pp. 367-385
Author(s):  
Andrzej Jankowski ◽  
Zbigniew Michalewicz
Keyword(s):  
Computational Complexity ◽  
Incomplete Information ◽  
Relational Databases ◽  
The Other ◽  
New Approach ◽  
Closed Sets ◽  
Null Value ◽  
Algebraic Operations

A number of approaches have been taken to represent compound, structured values in relational databases. We review a few such approaches and discuss a new approach, in which every set is represented as a Boolean term. We show that this approach generalizes the other approaches, leading to more flexible representation. Boolean term representation seems to be appropriate in handling incomplete information: this approach generalizes some other approaches (e.g. null value mark, null variables, etc). We consider definitions of algebraic operations on such sets, like join, union, selection, etc. Moreover, we introduce a measure of computational complexity of these operations.

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.

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.

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