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 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.

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 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.

Separation axioms in fuzzy convex spaces

2021 ◽  
Vol 40 (1) ◽  
pp. 439-447
Author(s):  
Hui Yang
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Mathematical Structures ◽  
Separation Axioms ◽  
Convex Spaces

In fuzzy set theory, fuzzy convex structures are important mathematical structures. In this paper, we focus on separation axioms in fuzzy convex spaces. Concretely, we introduce S0, S1 and S2 separation axioms in fuzzy convex spaces and establish their relationships. Furthermore, we investigate their hereditary and productive properties.

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.

Reliability Analysis for Environment Systems Using Dual Hesitant Fuzzy Set

2019 ◽  
pp. 162-173 ◽  
Author(s):  
Akshay Kumar ◽  
Mangey Ram
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Reliability Function ◽  
Hesitant Fuzzy Set ◽  
Electronic Systems ◽  
Hesitant Fuzzy Sets ◽  
Fuzzy Reliability ◽  
Dual Hesitant Fuzzy Set

In this chapter, we deal with dual hesitant fuzzy set theory and compute the fuzzy reliability with lifetime components of different electronic systems, such as series and parallel systems from a Markov chain technique. In dual hesitant fuzzy sets, we have membership and non-membership degree function whereas hesitant fuzzy sets only have membership function. In this chapter we also discuss the Weibull distribution and reliability function of the proposed systems. A numerical example is also given in the end of proposed algorithm.

Probability Theory on Fuzzy Sets

2017 ◽  
pp. 55-83
Author(s):  
Renáta Bartková ◽  
Beloslav Riečan ◽  
Anna Tirpáková
Keyword(s):  
Probability Theory ◽  
Fuzzy Sets ◽  
20Th Century ◽  
Set Theory ◽  
Significant Role ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Multivalued Logic ◽  
Probability Spaces

Similarly as the Kolmogorov probability theory in the first half of the 20th century, the Zadeh fuzzy set theory played a significant role in the second half of the 20th century. In this chapter we present probability theory on intuitionisic fuzzy sets as well as probability spaces on multivalued logic.

Generating Fuzzy Sets and Fuzzy Relations Based on Information

2021 ◽  
Vol 20 ◽  
pp. 178-185
Author(s):  
Radwan Abu- Gdairi ◽  
Ibrahim Noaman
Keyword(s):  
Fuzzy Sets ◽  
Knowledge Discovery ◽  
Set Theory ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Relation ◽  
Knowledge Discovery In Databases ◽  
Fuzzy Relations

Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced

Terminological difficulties in fuzzy set theory—The case of “Intuitionistic Fuzzy Sets”

2005 ◽  
Vol 156 (3) ◽  
pp. 485-491 ◽  
Author(s):  
Didier Dubois ◽  
Siegfried Gottwald ◽  
Petr Hajek ◽  
Janusz Kacprzyk ◽  
Henri Prade
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy

Applying Fuzzy Set Theory to Analysis Driving Maneuver

2013 ◽  
Vol 361-363 ◽  
pp. 2244-2248
Author(s):  
Yong Zhou ◽  
Ling Tian
Keyword(s):  
Fuzzy Sets ◽  
Model Validation ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Statistical Models ◽  
Driving Behavior ◽  
Car Following ◽  
Car Following Model ◽  
Validation Research

The conventional statistical models have their limitations in modeling the natural human driving behavior. This may be overcome by applying fuzzy set based approach to describe drivers decisions. This paper proposes a fuzzy set based car-following model to simulate the driving maneuver. Emphasis is placed on the research undertaken to establish fuzzy sets and systems and model validation. Research results have shown that the fuzzy set application is very encouraging.

Sign in / Sign up

Export Citation Format

Share Document