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Page 7351 of Mathematical Reviews Vol. , Issue 96m
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1996
Mathematical Reviews
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To define L-fuzzifying topological groups, the fuzzifying topology based on completely residuated lattice-valued logic, which is studied in the papers [M. S. ...
c A)) >
96m:22007 22A99 04A72 Shen, Ji Zhong [Shen, Ji Zhong'] (PRC-JNXN; Nanchang) Fuzzifying topological groups based on completely distributed residuated lattice-valued logic. II. Quotient groups. ...
Page 4402 of Mathematical Reviews Vol. , Issue 94h
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1994
Mathematical Reviews
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In this paper, we introduce the concept of fuzzifying groups based on a complete residuated lattice-valued logic and investigate some of their algebraic properties.” ...
Lastly, fuzzy solvability for homomorphic images and preimages has been investigated.”
94h:20078 20N25 04A72
Shen, Ji Zhong (PRC-JNXN; Nanchang)
Fuzzifying groups based on complete residuated lattice-valued ...
FUZZIFYING FILTERS IN LATTICE IMPLICATION ALGEBRAS
2009
Honam Mathematical Journal
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We introduce the concepts of a fuzzifying filter and a fuzzifying implicative filter in lattice implication algebras. ...
Shen [14] further established the theory of fuzzifying groups based on complete residuated latticevalued logic. ...
In second step Lukasiewicz generalized the three valued logic to what is called n-valued logic. ...
doi:10.5831/hmj.2009.31.3.323
fatcat:qurlfebi5fhd5aprw4cs3shnea
Page 6914 of Mathematical Reviews Vol. , Issue 2001J
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2001
Mathematical Reviews
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Let L be an infinitely distributive and lattice-ordered monoid which at the same time is commutative, complete and integral divisible.
03 MATHEMATICAL LOGIC AND FOUNDATIONS
6914
The authors define L-valued ...
Summary: “Using a t-norm T on a complete lattice L and an L-fuzzy relation R on a set X, we state definitions of an LF- semi-ideal and of its dual LF-semi-filter of the set ¥. ...
The Homomorphism Theorems of M-Hazy Rings and Their Induced Fuzzifying Convexities
2020
Mathematics
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Finally, M-fuzzifying convex spaces are induced by M-hazy rings. ...
Homomorphism is essential for group theory and ring theory, just as continuous functions are important for topology and rigid movements in geometry. ...
Shen [27] defined a fuzzifying group based on complete residuated lattice-valued logic. Liu and Shi [28] introduced an M-hazy group by using an M-fuzzy function and an M-hazy operation. ...
doi:10.3390/math8030411
fatcat:ds2iizbwxjfk5p5tlanab3amte
M-Hazy Vector Spaces over M-Hazy Field
2021
Mathematics
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Finally, it is shown that M-fuzzifying convex spaces are induced by an M-hazy subspace of M-hazy vector space. ...
Then, (M, ∨, ∧, , →, ⊥, ) is said to be a residuated lattice. A residuated lattice is defined to be a completely residuated lattice if the primary lattice is complete. ...
In the following discussion, we assume that the operation in the completely residuated lattice M is ∧; that is, the lattice valued environment M is degenerated to complete Heyting algebra. ...
doi:10.3390/math9101118
fatcat:qdm2rdemxvht5ijyctlcfeqgva
Semigroups Based on L-Valued Logic and Its Ideals
2000
Southeast Asian Bulletin of Mathematics
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In this paper, we introduce the concepts of semigroups based on complete residuated lattice-valued logic (L-valued logic, for short), and discuss the structures and the properties of subsemigronps and ...
The author [2] further discussed fuzzifying groups based on L-valued logic. In this paper, we are going to establish the theory of fuzzifying semigroups based on L-valued logic. ...
Introduction Ying [1] used a semantic method of complete residuated lattice-valued logic to propose the concept of fuzzifying topology. ...
doi:10.1007/s100120050012
fatcat:byjz325fevaybmgbaaqvyv6fxu
Semigroups Based on L-Valued Logic and Its Ideals
2000
Southeast Asian Bulletin of Mathematics
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In this paper, we introduce the concepts of semigroups based on complete residuated lattice-valued logic (L-valued logic, for short), and discuss the structures and the properties of subsemigronps and ...
The author [2] further discussed fuzzifying groups based on L-valued logic. In this paper, we are going to establish the theory of fuzzifying semigroups based on L-valued logic. ...
Introduction Ying [1] used a semantic method of complete residuated lattice-valued logic to propose the concept of fuzzifying topology. ...
doi:10.1007/s10012-000-0435-5
fatcat:ina4oesvhzfnvlhtpl3owlta5y
Page 616 of Mathematical Reviews Vol. , Issue 96b
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1996
Mathematical Reviews
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Figallo, (n+ 1)-valued modal implica- tive semilattices (190-196); Ji Zhong Shen [Ji Zhong Shen'], Fuzzifying topological groups based on completely distributive residuated lattice-valued logic. ...
s
03 MATHEMATICAL LOGIC AND FOUNDATIONS 616
for approximate reasoning—based on semantic revising method (467-473); H. ...
Page 8600 of Mathematical Reviews Vol. , Issue 2001M
[page]
2001
Mathematical Reviews
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Sci. 75 (1993), no. 1-2, 165-186; MR 94h:20078] further established the theory of fuzzi- fying groups based on complete residuated lattice-valued logic. ...
topology with the semantic method of continuous valued logic. ...
Page 39 of Mathematical Reviews Vol. , Issue 2001A
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2001
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The authors deal with the formal language J of the “graded” formal logical sys- tem associated to a (complete) residuated lattice Y = (L,V,/A,®, —,0,1) with logical constants (atomic formulas) 1, T, and ...
based on the Lukasiewicz algebra Yjo,;;. ...
An Overview of the Fuzzy Axiomatic Systems and Characterizations Proposed at Ghent University
2016
Axioms
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The main purpose of this paper consists of an invitation to continue research on these first attempts to axiomatize important concepts and systems in fuzzy set theory. ...
In the literature, many axiom systems have been introduced, but as far as we know the axiomatic system of Huntington concerning a Boolean algebra has been the only one where the axioms have been proven ...
Triangle Algebras: A Characterization of Interval-valued Residuated Lattices Residuated lattices (more precisely, bounded integral commutative residuated lattices) are bounded lattices with two extra operators ...
doi:10.3390/axioms5020017
fatcat:egsuouelmfba3mrszfte5llgxm
Exploring Users' Preferences in a Fuzzy Setting
2014
Electronical Notes in Theoretical Computer Science
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First, the relevant information is contained in a complete lattice, the concept lattice, that allows the users to browse among their preferences. ...
Based on this order they only receive the relevant formal concepts, i.e., "object-attribute clusters", where relevant corresponds to the users' point of view. ...
Definition 2.1 A complete residuated lattice with (truth-stressing) hedge L := (L, , , ⊗, →, * , 0, 1) is given by the following: (i) (L, , , 0, 1) is a complete lattice, (ii) (L, ⊗, 1) is a commutative ...
doi:10.1016/j.entcs.2014.02.003
fatcat:ak7cva342rbtrdo675glhubh4m
Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part I: Model-Based and Axiomatic Approaches
2006
Studia Logica: An International Journal for Symbolic Logic
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at the conference Trends in Logic III, dedicated to the memory of A. ...
Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets. ...
A further lattice valued generalization Another generalization of the complete Heyting algebra based approach is given by S. ...
doi:10.1007/s11225-006-7197-8
fatcat:vxo5u3lvy5g53ewkj5bdddfa6y
Fuzzy Logic Programming in Action with FLOPER
2014
Journal of Software Engineering and Applications
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Multi-Adjoint Logic Programming This section summarizes the main features of multi-adjoint logic programming (for a complete formulation of this framework, see [9]-[12]). ...
Informally speaking, in the multi-adjoint logic framework, a program can be seen as a set of rules each one annotated by a truth degree, and a goal is a query to the system, i.e., a set of atoms linked ...
To reduce this gap, the experience acquired in our research group regarding the design of techniques and methods based on fuzzy logic in close relationship with the so-called multi-adjoint logic programming ...
doi:10.4236/jsea.2014.74028
fatcat:x7aptog7c5fctgw7cy4wrkvp7u
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