Fuzzy Logic in the Broad Sense

2017 ◽  
Author(s):  
Radim Bělohlávek ◽  
Joseph W. Dauben ◽  
George J. Klir
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Human Reasoning ◽  
Human Beings ◽  
Real Numbers ◽  
New Directions ◽  
Gradual Development

The chapter begins by introducing the important and useful distinction between the research agendas of fuzzy logic in the narrow and the broad senses. The chapter deals with the latter agenda, whose ultimate goal is to employ intuitive fuzzy set theory for emulating commonsense human reasoning in natural language and other unique capabilities of human beings. Restricting to standard fuzzy sets, whose membership degrees are real numbers in the unit interval [0,1], the chapter describes how this broad agenda has become increasingly specific via the gradual development of standard fuzzy set theory and the associated fuzzy logic. An overview of currently recognized nonstandard fuzzy sets, which open various new directions in fuzzy logic, is presented in the last section of this chapter.

scholarly journals Pythagorean Picture Fuzzy Sets, Part 1- basic notions

2019 ◽  
Vol 35 (4) ◽  
pp. 293-304
Author(s):  
Bui Cong Cuong
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Set ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
Picture Fuzzy Sets

Picture fuzzy set (2013) is a generalization of the Zadeh‟ fuzzy set (1965) and the Antanassov‟intuitionistic fuzzy set. The new concept could be useful for many computational intelligentproblems. Basic operators of the picture fuzzy logic were studied by Cuong, Ngan [10,11 ].Newconcept –Pythagorean picture fuzzy set ( PPFS) is a combination of Picture fuzzy set with theYager‟s Pythagorean fuzzy set [12-14].First, in the Part 1 of this paper, we consider basic notionson PPFS as set operators of PPFS‟s , Pythagorean picture relation, Pythagorean picture fuzzy softset. Next, the Part 2 of the paper is devoted to main operators in fuzzy logic on PPFS: picturenegation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS.As aresult we will have a new branch of the picture fuzzy set theory.

Fuzzy Set Theory Applied to Accounting Sciences

2020 ◽  
Vol 16 (01) ◽  
pp. 1-16
Author(s):  
Carmen Lozano ◽  
Enriqueta Mancilla-Rendón
Keyword(s):  
Social Sciences ◽  
Fuzzy Logic ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Hamming Distance ◽  
Great Acceptance ◽  
Classical Mathematics ◽  
Triangular Numbers ◽  
And Mathematics

Fuzzy set theory and fuzzy logic have been successfully developed in engineering and mathematics. However, these concepts have found great acceptance in social sciences in recent years since they provide an answer to those problems in the real world that cannot be modeled using classical mathematics. In this paper, we propose a new methodology for accounting science based on fuzzy triangular numbers. The methodology uses Hamming distance between fuzzy triangular numbers and arithmetic operations to evaluate corporate governance of multinational public stock corporations (PSCs) in the telecommunications sector.

scholarly journals A method for classification of red, blue, and green galaxies using fuzzy set theory

2020 ◽  
Vol 499 (1) ◽  
pp. L31-L35
Author(s):  
Biswajit Pandey
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Sloan Digital Sky Survey ◽  
Sky Survey ◽  
Blue Galaxies ◽  
Boundary Sets ◽  
Red Galaxies

ABSTRACT Red and blue galaxies are traditionally classified using some specific cuts in colour or other galaxy properties, which are supported by empirical arguments. The vagueness associated with such cuts are likely to introduce a significant contamination in these samples. Fuzzy sets are vague boundary sets that can efficiently capture the classification uncertainty in the absence of any precise boundary. We propose a method for classification of galaxies according to their colours using fuzzy set theory. We use data from the Sloan Digital Sky Survey (SDSS) to construct a fuzzy set for red galaxies with its members having different degrees of ‘redness’. We show that the fuzzy sets for the blue and green galaxies can be obtained from it using different fuzzy operations. We also explore the possibility of using fuzzy relation to study the relationship between different galaxy properties and discuss its strengths and limitations.

scholarly journals Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 432 ◽  
Author(s):  
Vilém Novák
Keyword(s):  
Fuzzy Logic ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rough Sets ◽  
Type Theory ◽  
Rough Set Theory ◽  
Basic Concepts ◽  
Alternative Set

In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included in AST. Using fuzzy type theory, we generalize basic concepts of rough set theory and the topological concepts of AST to become the concepts of the fuzzy set theory. We will give mostly syntactic proofs of the main properties and relations among all the considered concepts, thus showing that they are universally valid.

scholarly journals Fuzzy Set Theory and Topos Theory

1986 ◽  
Vol 29 (4) ◽  
pp. 501-508 ◽  
Author(s):  
Michael Barr
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Topos Theory

AbstractThe relation between the categories of Fuzzy Sets and that of Sheaves is explored and the precise connection between them is explicated. In particular, it is shown that if the notion of fuzzy sets is further fuzzified by making equality (as well as membership) fuzzy, the resultant categories are indeed toposes.

FUZZY SETS AND FUZZY RELATIONAL STRUCTURES AS CHU SPACES

2000 ◽  
Vol 08 (04) ◽  
pp. 471-479 ◽  
Author(s):  
BASIL K. PAPADOPOULOS ◽  
APOSTOLOS SYROPOULOS
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Linear Logic ◽  
Relational Structure ◽  
Mathematical Structures ◽  
Relational Structures ◽  
Chu Spaces

Chu spaces, which derive from the Chu construct of *-autonomous categories, can be used to represent most mathematical structures. Moreover, the logic of Chu spaces is linear logic. Most efforts to incorporate fuzzy set theory into the realm of linear logic are based on the assumption that fuzzy and linear negation are identical operations. We propose an incorporation based on the opposite assumption and we provide an interpretation of some linear connectives. Furthermore, we show that it is possible to represent any fuzzy relational structure as a Chu space by means of the functor G.

scholarly journals THE PROBLEM OF OBJECTIVE ASSESSMENT OF THE STUDENT’S KNOWLEDGE

2021 ◽  
Vol 7 (73) (1) ◽  
pp. 77-85
Author(s):  
N. V. Apatova ◽  
A. I. Gaponov
Keyword(s):  
Fuzzy Logic ◽  
Knowledge Acquisition ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Educational Material ◽  
Specific Situation ◽  
Mathematical Apparatus ◽  
Subjective Factor ◽  
Hierarchy Analysis

In the modern pedagogical literature a large number of works are devoted to the issue of evaluating students mastered knowledge. Ensuring the quality of diagnostics of the level of knowledge acquisition by students of educational organizations is based on an adequate, reasonable, acceptable and accessible mathematical apparatus. The adequacy and validity of the mathematical apparatus allows you to significantly reduce the influence of the subjective factor on the assessment of knowledge acquisition and minimize objections to its application. On the other hand, acceptability makes it possible to use a specific situation under consideration as a diagnosis, taking into account only its inherent nuances. Accessibility also means the ability to use the proposed mathematical algorithm by teachers who have the necessary minimum of elements of the proposed mathematical apparatus. The article considers the possibility of determining the level of development of the studied topic by students on the basis of five factors of knowledge acquisition: 1. Understanding; 2. Recognition; 3.Reproduction; 4. Application; 5. Creativity. In this case, the calculations are performed by using a simplified method of hierarchy analysis and fuzzy set theory in order to reduce the subjectivity inherent in the rating system of evaluation, the use of elements of the hierarchy analysis method and fuzzy logic is proposed. The fuzzy set theory algorithm is implemented using the fuzzy Logic Toolbox application package of the MATLAB software environment. Using the method of hierarchy analysis is to aggregate scores based on the application of a matrix of paired comparisons. The synthesis of these methods allows us to obtain a fairly effective comparative assessment of students development of educational material. On the basis of the considered methodology for evaluating students assimilation of educational material, it is suggested that it is possible to reduce the influence of a subjective factor to a minimum.

scholarly journals Fuzzy Logic in Aircraft Onboard Systems Reliability Evaluation—A New Approach

Sensors ◽  
2021 ◽  
Vol 21 (23) ◽  
pp. 7913
Author(s):  
Andrzej Żyluk ◽  
Konrad Kuźma ◽  
Norbert Grzesik ◽  
Mariusz Zieja ◽  
Justyna Tomaszewska
Keyword(s):  
Fuzzy Logic ◽  
Reliability Analysis ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Probabilistic Model ◽  
Expert Knowledge ◽  
Operation Time ◽  
Theory Approach ◽  
Operational Data

This paper is a continuation of research into the possibility of using fuzzy logic to assess the reliability of a selected airborne system. The research objectives include an analysis of statistical data, a reliability analysis in the classical approach, a reliability analysis in the fuzzy set theory approach, and a comparison of the obtained results. The system selected for the investigation was the aircraft gun system. In the first step, after analysing the statistical (operational) data, reliability was assessed using a classical probabilistic model in which, on the basis of the Weibull distribution fitted to the operational data, the basic reliability characteristics were determined, including the reliability function for the selected aircraft system. The second reliability analysis, in a fuzzy set theory approach, was conducted using a Mamdani Type Fuzzy Logic Controller developed in the Matlab software with the Fuzzy Logic Toolbox package. The controller was designed on the basis of expert knowledge obtained by a survey. Based on the input signals in the form of equipment operation time (number of flying hours), number of shots performed (shots), and the state of equipment corrosion (corrosion), the controller determines the reliability of air armament. The final step was to compare the results obtained from two methods: classical probabilistic model and fuzzy logic. The authors have proved that the reliability model using fuzzy logic can be used to assess the reliability of aircraft airborne systems.

scholarly journals Decision-Making Approach under Pythagorean Fuzzy Yager Weighted Operators

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 70 ◽  
Author(s):  
Gulfam Shahzadi ◽  
Muhammad Akram ◽  
Ahmad N. Al-Kenani
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Ordered Weighted Averaging ◽  
Multi Attribute Decision Making ◽  
Parametric Families

In fuzzy set theory, t-norms and t-conorms are fundamental binary operators. Yager proposed respective parametric families of both t-norms and t-conorms. In this paper, we apply these operators for the analysis of Pythagorean fuzzy sets. For this purpose, we introduce six families of aggregation operators named Pythagorean fuzzy Yager weighted averaging aggregation, Pythagorean fuzzy Yager ordered weighted averaging aggregation, Pythagorean fuzzy Yager hybrid weighted averaging aggregation, Pythagorean fuzzy Yager weighted geometric aggregation, Pythagorean fuzzy Yager ordered weighted geometric aggregation and Pythagorean fuzzy Yager hybrid weighted geometric aggregation. These tools inherit the operational advantages of the Yager parametric families. They enable us to study two multi-attribute decision-making problems. Ultimately we can choose the best option by comparison of the aggregate outputs through score values. We show this procedure with two practical fully developed examples.

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