A Development of Set Theory in Fuzzy Logic

2003 ◽  
pp. 273-285 ◽  
Author(s):  
Petr Hájek ◽  
Zuzana Haniková
Keyword(s):  
Fuzzy Logic ◽  
Set Theory

scholarly journals Metapopulation Patterns of Iberian Butterflies Revealed by Fuzzy Logic

Insects ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 392
Author(s):  
Antonio Pulido-Pastor ◽  
Ana Luz Márquez ◽  
José Carlos Guerrero ◽  
Enrique García-Barros ◽  
Raimundo Real
Keyword(s):  
Fuzzy Logic ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Metapopulation Dynamics ◽  
Butterfly Species ◽  
Dynamics Analysis ◽  
Metapopulation Structure ◽  
Occurrence Data ◽  
Metapopulation Theory ◽  
The Cost

Metapopulation theory considers that the populations of many species are fragmented into patches connected by the migration of individuals through an interterritorial matrix. We applied fuzzy set theory and environmental favorability (F) functions to reveal the metapopulational structure of the 222 butterfly species in the Iberian Peninsula. We used the sets of contiguous grid cells with high favorability (F ≥ 0.8), to identify the favorable patches for each species. We superimposed the known occurrence data to reveal the occupied and empty favorable patches, as unoccupied patches are functional in a metapopulation dynamics analysis. We analyzed the connectivity between patches of each metapopulation by focusing on the territory of intermediate and low favorability for the species (F < 0.8). The friction that each cell opposes to the passage of individuals was computed as 1-F. We used the r.cost function of QGIS to calculate the cost of reaching each cell from a favorable patch. The inverse of the cost was computed as connectivity. Only 126 species can be considered to have a metapopulation structure. These metapopulation structures are part of the dark biodiversity of butterflies because their identification is not evident from the observation of the occurrence data but was revealed using favorability functions.

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.

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 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 Determination of the type of repair work based on the results of survey and monitoring of the technical condition of buildings

2020 ◽  
Vol 157 ◽  
pp. 06023 ◽  
Author(s):  
Aleksandr Birjukov ◽  
Anatoly Lebedkin ◽  
Yurii Birjukov ◽  
Viktor Pchelkin
Keyword(s):  
Mathematical Model ◽  
Fuzzy Logic ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Technical Condition ◽  
Capital Investments ◽  
Repair Work ◽  
Fuzzy Logic Method ◽  
Maintenance Work

This article is devoted to structural scrutiny of a building. The technical condition of buildings affects such characteristics of a building as safety, reliability, durability and maintainability. However, in the absence of reliable information on the technical condition of buildings, structural survey or monitoring of а building in order to determine the category of technical condition is necessary. The purpose of this work is to develop an economic and mathematical model for determining the type of maintenance work based on the results of structural scrutiny and monitoring of a building. The article is of importance because the final stage of the survey gives a qualified opinion on the level of structural scrutiny of a building, and on the basis of this opinion repair work eliminating physical and moral deterioration and providing in accordance with specifications renovation of the building are planned. The scientific novelty of the economic and mathematical model developed by the authors on the results of building structural scrutiny lies in the application of the fuzzy set theory and fuzzy logic method for determining of the level of physical and moral deterioration of a building consistent with a certain type of repair work and followed by the necessary capital investments.

A Fuzzy Logic-Based Approach for Multi-Places and Multi-Sensors Data Fusion

2012 ◽  
Vol 241-244 ◽  
pp. 2524-2527
Author(s):  
Yi Lv
Keyword(s):  
Fuzzy Logic ◽  
Data Fusion ◽  
Set Theory ◽  
Monitor System ◽  
Fuzzy Synthetic Evaluation ◽  
Industrial Environment ◽  
Temperature And Humidity ◽  
Fusion Approach ◽  
Incorrect Data ◽  
Synthetic Evaluation

According to the features and needs of collecting the data of temperature and humidity of current industrial environment, and the multi-places and multi-sensors data fusion as well, this paper proposes a fuzzy logic-based approach for the multi-places and multi-sensors data fusion. Firstly, this paper introduces the hardware construction of monitor system of temperature and humidity. Then, based on fuzzy set theory, the paper describes the model of fuzzy synthetic evaluation, and then proposes a novel algorithm for choosing the weights assignment proposals. Finally, a multi-places and multi-sensors data fusion approach, which is based on fuzzy synthetic evaluation, is presented. An example is also used for demonstrating the proposed approach. The results of system implementation identify that the approach can remove the influence of incorrect data on evaluating the temperature and humidity of current environment, and the data fusion result is objective and correct as well.

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