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Page 7351 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
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 [page]

1994 Mathematical Reviews  
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

Seon-Yu Kim, Eun-Hwan Roh
2009 Honam Mathematical Journal  
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 [page]

2001 Mathematical Reviews  
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

Faisal Mehmood, Fu-Gui Shi, Khizar Hayat, Xiao-Peng Yang
2020 Mathematics  
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

Faisal Mehmood, Fu-Gui Shi
2021 Mathematics  
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

Jizhong Shen
2000 Southeast Asian Bulletin of Mathematics  
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

Jizhong Shen
2000 Southeast Asian Bulletin of Mathematics  
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 [page]

1996 Mathematical Reviews  
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  
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 [page]

2001 Mathematical Reviews  
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

Etienne Kerre, Lynn D´eer, Bart Van Gasse
2016 Axioms  
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

Cynthia Vera Glodeanu
2014 Electronical Notes in Theoretical Computer Science  
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

Siegfried Gottwald
2006 Studia Logica: An International Journal for Symbolic Logic  
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

Ginés Moreno, Carlos Vázquez
2014 Journal of Software Engineering and Applications  
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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