scholarly journals Filters in Strong BI-Algebras and Residuated Pseudo-SBI-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1513
Author(s):  
Xiaohong Zhang ◽  
Xiangyu Ma ◽  
Xuejiao Wang
Keyword(s):  
Fuzzy Logic ◽  
Special Kind ◽  
Algebra Structure ◽  
Algebraic Structures ◽  
Commutative Case ◽  
Filter Theory ◽  
Fuzzy Implication ◽  
Implication Algebra ◽  
Common Extension ◽  
The Common

The concept of basic implication algebra (BI-algebra) has been proposed to describe general non-classical implicative logics (such as associative or non-associative fuzzy logic, commutative or non-commutative fuzzy logic, quantum logic). However, this algebra structure does not have enough characteristics to describe residual implications in depth, so we propose a new concept of strong BI-algebra, which is exactly the algebraic abstraction of fuzzy implication with pseudo-exchange principle (PEP). Furthermore, in order to describe the characteristics of the algebraic structure corresponding to the non-commutative fuzzy logics, we extend strong BI-algebra to the non-commutative case, and propose the concept of pseudo-strong BI (SBI)-algebra, which is the common extension of quantum B-algebras, pseudo-BCK/BCI-algebras and other algebraic structures. We establish the filter theory and quotient structure of pseudo-SBI- algebras. Moreover, based on prequantales, semi-uninorms, t-norms and their residual implications, we introduce the concept of residual pseudo-SBI-algebra, which is a common extension of (non-commutative) residual lattices, non-associative residual lattices, and also a special kind of residual partially-ordered groupoids. Finally, we investigate the filters and quotient algebraic structures of residuated pseudo-SBI-algebras, and obtain a unity frame of filter theory for various algebraic systems.

scholarly journals Some New De Morgan Picture Operator Triples in Picture Fuzzy Logic

2018 ◽  
Vol 33 (2) ◽  
pp. 143-164
Author(s):  
Cuong Bui Cong ◽  
Roan Thi Ngan ◽  
Le Ba Long
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Basic Algebra ◽  
Algebra Structure ◽  
Picture Fuzzy Sets

A new concept of picture fuzzy sets (PFS) were introduced in 2013, which are directextensions of the fuzzy sets and the intuitonistic fuzzy sets. Then some operations on PFS withsome properties are considered in [ 9,10 ]. Some basic operators of fuzzy logic as negation, tnorms, t-conorms for picture fuzzy sets firstly are defined and studied in [13,14]. This paper isdevoted to some classes of representable picture fuzzy t-norms and representable picture fuzzyt-conorms on PFS and a basic algebra structure of Picture Fuzzy Logic – De Morgan triples ofpicture operators.

On the Ordering Property and Law of Importation in Fuzzy Logic

2010 ◽  
Vol 1 (3) ◽  
pp. 17-30
Author(s):  
Huiwen Deng ◽  
Huan Jiang
Keyword(s):  
Fuzzy Logic ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Fuzzy Implications ◽  
Fuzzy Implication ◽  
The Law ◽  
Necessary And Sufficient ◽  
Triple I Method

In this paper, the authors investigate the ordering property (OP), , together with the general form of the law of importation(LI), i.e., , whereis a t-norm andis a fuzzy implication for the four main classes of fuzzy implications. The authors give necessary and sufficient conditions under which both (OP) and (LI) holds for S-, R-implications and some specific families of QL-, D-implications. Following this, the paper proposes the sufficient condition under which the equivalence between CRI and triple I method for FMP can be established. Moreover, this conclusion can be viewed as a unified triple I method, a generalized form of the known results proposed by Wang and Pei.

Algebraic structures in fuzzy logic

1992 ◽  
Vol 52 (2) ◽  
pp. 181-188 ◽  
Author(s):  
Esko Turunen
Keyword(s):  
Fuzzy Logic ◽  
Algebraic Structures

scholarly journals Constantine Lascaris, his manuscripts and his ethical concerns

2021 ◽  
Vol 15 (2) ◽  
pp. 538-572
Author(s):  
Juan Felipe Gonzalez-Calderon
Keyword(s):  
Common Good ◽  
Special Kind ◽  
Way Of Life ◽  
Spiritual Exercise ◽  
Ethical Concerns ◽  
The Common Good ◽  
Moral Improvement ◽  
The Common ◽  
Virtuous Life ◽  
Intellectual Activities

This article aims to examine Constantine Lascaris’s work on Aristoteles’ ethical corpus. We consider evidence from the textual witnesses of the Nicomachean Ethics, the Eudemian Ethics, the Magna Moralia, and some other minor ethical writings, which belonged to Lascaris, in order to reconstruct his working methods. We also explore Lascaris’ own statements about virtuous life; a life devoted to the service of the common good, to philosophy and to the study of texts. For him philosophy was a way of life, rather than simply a discourse. We look at the link between written culture and philosophical life and propose further research into how Byzantine and Renaissance scholars understood their own intellectual activities to be a special kind of spiritual exercise intended to promote moral improvement in both individuals and societies.

TAUTOLOGY THEORY IN PROPOSITIONAL FUZZY LOGIC BASED ON LUKASIEWICZ IMPLICATION ALGEBRA ON [0,1]

2008 ◽  
Author(s):  
Xiaodong Pan ◽  
Kaijun Xu ◽  
Xiaobing Li ◽  
Jiajun Lai ◽  
Yang Xu
Keyword(s):  
Fuzzy Logic ◽  
Implication Algebra

Fuzzy Logic in Healthcare

2015 ◽  
pp. 679-707
Author(s):  
Güney Gürsel
Keyword(s):  
Fuzzy Logic ◽  
Medical Data ◽  
Fuzzy Cognitive Maps ◽  
Medical Decision ◽  
Medical Data Mining ◽  
Medical Field ◽  
Medical Databases ◽  
Diagnosis And Prognosis ◽  
Fuzzy Expert Systems ◽  
The Common

The medical decision-making process is fuzzy in its nature. The physician handles linguistic concepts in deciding the diagnosis and prognosis. The conversion from this fuzzy nature into crisp real world outcome causes the loss of precision. Fuzzy logic is a suitable way to provide the physician with the support he needs in handling linguistic concepts and get rid of the loss of precision. Fuzzy logic technologies are applied to each area of medicine, and they have been proven to be successful. The literature shows that the medical area has a great compatibility with fuzzy logic technology. Fuzzy cognitive maps, fuzzy expert systems, fuzzy medical image processing, fuzzy applications in information retrieval from medical databases, fuzzy medical data mining, and hybrid fuzzy applications are the common and most known fuzzy logic usage areas in the medical field. This chapter is a descriptive study that examines and explains the common fuzzy logic applications in the medical field after an introduction to fuzzy logic.

Causing something to be one way rather than another

Kybernetes ◽  
2014 ◽  
Vol 43 (6) ◽  
pp. 865-881 ◽  
Author(s):  
Barbara Osimani
Keyword(s):  
Genetic Information ◽  
Design Methodology ◽  
Special Kind ◽  
Developmental Systems ◽  
Content Type ◽  
The Common ◽  
Definition Of ◽  
Combinatorial Mechanism ◽  
And Linguistics ◽  
Causal Specificity

Purpose – The purpose of this paper is to suggest a definition of genetic information by taking into account the debate surrounding it. Particularly, the objections raised by Developmental Systems Theory (Griffiths, 2001; Oyama 1985; Griffiths and Knight 1998) to Teleosemantic endorsements of the notion of genetic information (Sterelny et al. 1996; Maynard Smith, 2000; Jablonka, 2002) as well as deflationist approaches which suggest to ascribe the notion of genetic information a heuristic value at most, and to reduce it to that of causality (Godfrey-Smith, 2000; Boniolo, 2003, 2008). Design/methodology/approach – The paper presents the notion of genetic information through its historical evolution and analyses it with the conceptual tools offered by philosophical theories of causation on one side (“causation as influence,” Woodward, 2010; Waters, 2007; Lewis, 2000) and linguistics on the other (“double articulation” Martinet, 1960). Findings – The concept of genetic information is defined as a special kind of cause which causes something to be one way rather than another, by combining elementary units one way rather than another. Tested against the notion of “genetic error” this definition demonstrates to provide an exhaustive account of the common denominators associated with the notion of genetic information: causal specificity; combinatorial mechanism; arbitrariness. Originality/value – The definition clarifies how the notion of information is understood when applied to genetic phenomena and also contributes to the debate on the notion of information, broadly meant, which is still affected by lack of consensus (Floridi, 2013).

scholarly journals Q-Filters of Quantum B-Algebras and Basic Implication Algebras

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 573 ◽  
Author(s):  
Xiaohong Zhang ◽  
Rajab Borzooei ◽  
Young Jun
Keyword(s):  
Algebraic Semantics ◽  
Fuzzy Logics ◽  
Quantum Logics ◽  
Filter Theory ◽  
Implication Algebras ◽  
Implication Algebra

The concept of quantum B-algebra was introduced by Rump and Yang, that is, unified algebraic semantics for various noncommutative fuzzy logics, quantum logics, and implication logics. In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods). Moreover, a new, more general, implication algebra is proposed, which is called basic implication algebra and can be regarded as a unified frame of general fuzzy logics, including nonassociative fuzzy logics (in contrast, quantum B-algebra is not applied to nonassociative fuzzy logics). The filter theory of basic implication algebras is also established.

scholarly journals Algebraic Structures Based on a Classifying Space of a Compact Lie Group

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Dae-Woong Lee
Keyword(s):  
Lie Group ◽  
Free Lie Algebra ◽  
Homotopy Groups ◽  
Algebra Structure ◽  
Compact Lie Group ◽  
Algebraic Structures ◽  
Primitive Elements ◽  
Classifying Space ◽  
Rational Homology ◽  
Cup Products

We analyze the algebraic structures based on a classifying space of a compact Lie group. We construct the connected graded free Lie algebra structure by considering the rationally nontrivial indecomposable and decomposable generators of homotopy groups and the cohomology cup products, and we show that the homomorphic image of homology generators can be expressed in terms of the Lie brackets in rational homology. By using the Milnor-Moore theorem, we also investigate the concrete primitive elements in the Pontrjagin algebra.

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