Fuzzy Subsets and Fuzzy Subgroups

Lattices of fuzzy objects

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171296001056 ◽

1996 ◽

Vol 19 (4) ◽

pp. 759-766 ◽

Cited By ~ 1

Author(s):

Arturo A. L. Sangalli

Keyword(s):

Complete Lattice ◽

Binary Relations ◽

Special Cases ◽

Fuzzy Objects ◽

Fuzzy Subgroups ◽

Special Case ◽

Fuzzy Subsets

The collection of fuzzy subsets of a setXforms a complete lattice that extends the complete lattice𝒫(X)of crisp subsets ofX. In this paper, we interpret this extension as a special case of the fuzzification of an arbitrary complete latticeA. We show how to construct a complete latticeF(A,L)theL-fuzzificatio ofA, whereLis the valuation lattice that extendsAwhile preserving all suprema and infima. The fuzzy objects inF(A,L)may be interpreted as the sup-preserving maps fromAto the dual ofL. In particular, each complete lattice coincides with its2-fuzzification, where2is the twoelement lattice. Some familiar fuzzifications (fuzzy subgroups, fuzzy subalgebras, fuzzy topologies, etc.) are special cases of our construction. Finally, we show that the binary relations on a setXmay be seen as the fuzzy subsets ofXwith respect to the valuation lattice𝒫(X).

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Redefined sup-min product of fuzzy subsets and join of fuzzy subgroups

Fuzzy Sets and Systems ◽

10.1016/s0165-0114(96)00004-8 ◽

1997 ◽

Vol 87 (1) ◽

pp. 99-109 ◽

Cited By ~ 1

Author(s):

Jae-Gyeom Kim

Keyword(s):

Fuzzy Subgroups ◽

Fuzzy Subsets

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RELASI FUZZY PADA GRUP FAKTOR FUZZY

JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON ◽

10.20527/epsilon.v14i1.2394 ◽

2020 ◽

Vol 14 (1) ◽

pp. 33

Author(s):

Ahmad Madani ◽

Saman Abdurrahman ◽

Na'imah Hijriati

Keyword(s):

Group Theory ◽

Fuzzy Set ◽

Fuzzy Relation ◽

Factor Group ◽

Fuzzy Relations ◽

Fuzzy Group ◽

Congruence Relations ◽

Fuzzy Congruence ◽

Fuzzy Subgroups ◽

Fuzzy Subsets

Fuzzy subsets on the non-empty set is a mapping of this set to the interval . The concept of fuzzy subgroups introduced from advanced concept of fuzzy set in group theory. In concept of fuzzy set there is the concept of relations is fuzzy relations. In this study examined that fuzzy relations related to the equivalence and congruence on a fuzzy group and fuzzy factor group. The results of this study was to show that a fuzzy relation if and if is a fuzzy congruence relations on fuzzy group and a fuzzy relation defined of is a fuzzy congruence relations on fuzzy factor group.

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The Process of Medical Diagnosis: Routes of Mathematical Investigations

Methods of Information in Medicine ◽

10.1055/s-0038-1636611 ◽

1978 ◽

Vol 17 (01) ◽

pp. 1-10 ◽

Cited By ~ 7

Author(s):

P. Tautu ◽

G. Wagner

Keyword(s):

Decision Theory ◽

Medical Diagnosis ◽

Pattern Analysis ◽

Logical Probability ◽

Inquiry Process ◽

Fuzzy Subsets

This paper is an analysis of the most important mathematical aspects of medical diagnosis: logical probability, rationality and decision theory, gambling models, pattern analysis, hazy and fuzzy subsets theory and, finally, the stochastic inquiry process.

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Fuzzy Logic for Intelligent Control System Using Soft Computing Applications

Sensors ◽

10.3390/s21082617 ◽

2021 ◽

Vol 21 (8) ◽

pp. 2617

Author(s):

Catalin Dumitrescu ◽

Petrica Ciotirnae ◽

Constantin Vizitiu

Keyword(s):

Decision Making ◽

Fuzzy Logic ◽

Soft Computing ◽

Intelligent Control ◽

Fuzzy Controller ◽

Control Technique ◽

Distributed Intelligence ◽

High Level ◽

The Impact ◽

Fuzzy Subsets

When considering the concept of distributed intelligent control, three types of components can be defined: (i) fuzzy sensors which provide a representation of measurements as fuzzy subsets, (ii) fuzzy actuators which can operate in the real world based on the fuzzy subsets they receive, and, (iii) the fuzzy components of the inference. As a result, these elements generate new fuzzy subsets from the fuzzy elements that were previously used. The purpose of this article is to define the elements of an interoperable technology Fuzzy Applied Cell Control-soft computing language for the development of fuzzy components with distributed intelligence implemented on the DSP target. The cells in the network are configured using the operations of symbolic fusion, symbolic inference and fuzzy–real symbolic transformation, which are based on the concepts of fuzzy meaning and fuzzy description. The two applications presented in the article, Agent-based modeling and fuzzy logic for simulating pedestrian crowds in panic decision-making situations and Fuzzy controller for mobile robot, are both timely. The increasing occurrence of panic moments during mass events prompted the investigation of the impact of panic on crowd dynamics and the simulation of pedestrian flows in panic situations. Based on the research presented in the article, we propose a Fuzzy controller-based system for determining pedestrian flows and calculating the shortest evacuation distance in panic situations. Fuzzy logic, one of the representation techniques in artificial intelligence, is a well-known method in soft computing that allows the treatment of strong constraints caused by the inaccuracy of the data obtained from the robot’s sensors. Based on this motivation, the second application proposed in the article creates an intelligent control technique based on Fuzzy Logic Control (FLC), a feature of intelligent control systems that can be used as an alternative to traditional control techniques for mobile robots. This method allows you to simulate the experience of a human expert. The benefits of using a network of fuzzy components are not limited to those provided distributed systems. Fuzzy cells are simple to configure while also providing high-level functions such as mergers and decision-making processes.

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Role of Operator Semirings in Characterizing Γ-semirings in Terms of Fuzzy Subsets

Fuzzy Information and Engineering ◽

10.1007/s12543-012-0115-z ◽

2012 ◽

Vol 4 (3) ◽

pp. 261-272 ◽

Cited By ~ 2

Author(s):

Sujit Kumar Sardar ◽

Sarbani Goswami ◽

Y. B. Jun

Keyword(s):

Fuzzy Subsets

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Image development in the framework of ξ –complex fuzzy morphisms

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201261 ◽

2021 ◽

pp. 1-13

Author(s):

Aneeza Imtiaz ◽

Umer Shuaib ◽

Abdul Razaq ◽

Muhammad Gulistan

Keyword(s):

Decision Making ◽

Comparative Analysis ◽

Fuzzy Sets ◽

Unit Disk ◽

Homomorphic Image ◽

Significant Role ◽

Original Form ◽

Mathematical Tool ◽

Fuzzy Subgroups ◽

Fundamental Theorems

The study of complex fuzzy sets defined over the meet operator (ξ –CFS) is a useful mathematical tool in which range of degrees is extended from [0, 1] to complex plane with unit disk. These particular complex fuzzy sets plays a significant role in solving various decision making problems as these particular sets are powerful extensions of classical fuzzy sets. In this paper, we define ξ –CFS and propose the notion of complex fuzzy subgroups defined over ξ –CFS (ξ –CFSG) along with their various fundamental algebraic characteristics. We extend the study of this idea by defining the concepts of ξ –complex fuzzy homomorphism and ξ –complex fuzzy isomorphism between any two ξ –complex fuzzy subgroups and establish fundamental theorems of ξ –complex fuzzy morphisms. In addition, we effectively apply the idea of ξ –complex fuzzy homomorphism to refine the corrupted homomorphic image by eliminating its distortions in order to obtain its original form. Moreover, to view the true advantage of ξ –complex fuzzy homomorphism, we present a comparative analysis with the existing knowledge of complex fuzzy homomorphism which enables us to choose this particular approach to solve many decision-making problems.

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