A method of constructing fuzzy implications from the FIφ-construction

2021 ◽  
pp. 1-14
Author(s):  
Yifan Zhao ◽  
Kai Li
Keyword(s):  
Specific Property ◽  
New Method ◽  
Aggregation Function ◽  
Fuzzy Implications ◽  
Construction Methods ◽  
Fuzzy Implication ◽  
New Construction

In the recent years, several new construction methods of fuzzy implications have been proposed. However, these construction methods actually care about that the new implication could preserve more properties. In this paper, we introduce a new method for constructing fuzzy implications based on an aggregation function with F (1,  0) =1, a fuzzy implication I and a non-decreasing function φ, called FIφ-construction. Specifically, some logical properties of fuzzy implications preserved by this construction are studied. Moreover, it is studied how to use the FIφ-construction to produce a new implication satisfying a specific property. Furthermore, we produce two new subclasses of fuzzy implications such as UIφ-implications and GpIφ-implications by this method and discuss some additional properties. Finally, we provide a way to generate fuzzy subsethood measures by means of FIφ-implications.

scholarly journals A Method of Generating Fuzzy Implications from n Increasing Functions and n + 1 Negations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 886
Author(s):  
Maria N. Rapti ◽  
Basil K. Papadopoulos
Keyword(s):  
Artificial Intelligence ◽  
Fuzzy Implications ◽  
Fuzzy Implication ◽  
New Construction ◽  
Novel Method ◽  
Increasing Functions ◽  
Increasing Function ◽  
Important Form ◽  
And Robotics ◽  
Exchange Principle

In this paper, we introduce a new construction method of a fuzzy implication from n increasing functions g i : [ 0 , 1 ] → [ 0 , ∞ ) ,   ( g ( 0 ) = 0 ) ( i = 1 , 2 , … , n ,   n   ∈ ℕ ) and n + 1 fuzzy negations N i ( i = 1 , 2 , … , n + 1 ,   n   ∈ ℕ ). Imagine that there are plenty of combinations between n increasing functions g i and n + 1 fuzzy negations N i in order to produce new fuzzy implications. This method allows us to use at least two fuzzy negations N i and one increasing function g in order to generate a new fuzzy implication. Choosing the appropriate negations, we can prove that some basic properties such as the exchange principle (EP), the ordering property (OP), and the law of contraposition with respect to N are satisfied. The worth of generating new implications is valuable in the sciences such as artificial intelligence and robotics. In this paper, we have found a novel method of generating families of implications. Therefore, we would like to believe that we have added to the literature one more source from which we could choose the most appropriate implication concerning a specific application. It should be emphasized that this production is based on a generalization of an important form of Yager’s implications.

scholarly journals A Method of Generating Fuzzy Implications with Specific Properties

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 155 ◽  
Author(s):  
Dimitrios S. Grammatikopoulos ◽  
Basil K. Papadopoulos
Keyword(s):  
New Method ◽  
Fuzzy Implications ◽  
Fuzzy Implication

In this paper we introduce a new method of generating fuzzy implications via known fuzzy implications. We focus on the case of generating fuzzy implications via a fuzzy connective and at least one known fuzzy implication. We present some basic desirable properties of fuzzy implications that are invariant via this method. Furthermore, we suggest some ways of preservation or violation of these properties, based in this method. We show how we can generate not greater or not weaker fuzzy implications with specific properties. Finally, two subclasses of any fuzzy implication arise, the so called T and S subclasses.

scholarly journals The Classification of 7- and 8-dimensional Naturally Reductive Spaces

2019 ◽  
Vol 72 (5) ◽  
pp. 1246-1274 ◽  
Author(s):  
Reinier Storm
Keyword(s):  
New Method ◽  
Structure Theory ◽  
New Construction ◽  
Naturally Reductive

AbstractA new method for classifying naturally reductive spaces is presented. This method relies on a new construction and the structure theory of naturally reductive spaces recently developed by the author. This method is applied to obtain the classification of all naturally reductive spaces in dimension 7 and 8.

CONTRAPOSITIVE SYMMETRY OF DISTRIBUTIVE FUZZY IMPLICATIONS

2002 ◽  
Vol 10 (supp01) ◽  
pp. 135-147 ◽  
Author(s):  
MICHAŁ BACZYŃSKI
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Strong Negation ◽  
Fuzzy Implications ◽  
Fuzzy Implication

Recently, we have examined the solutions of the system of the functional equations I(x, T(y, z)) = T(I(x, y), I(x, z)), I(x, I(y, z)) = I(T(x, y), z), where T : [0, 1]2 → [0, 1] is a strict t-norm and I : [0, 1]2 → [0, 1] is a non-continuous fuzzy implication. In this paper we continue these investigations for contrapositive implications, i.e. functions which satisfy the functional equation I(x, y) = I(N(y), N(x)), with a strong negation N : [0, 1] → [0, 1]. We show also the bounds for two classes of fuzzy implications which are connected with our investigations.

A new class of fuzzy implications. Axioms of fuzzy implication revisited

1998 ◽  
Vol 100 (1-3) ◽  
pp. 267-272 ◽  
Author(s):  
I. Burhan Türkşen ◽  
Vladik Kreinovich ◽  
Ronald R. Yager
Keyword(s):  
New Class ◽  
Fuzzy Implications ◽  
Fuzzy Implication

Next Generation CANDU: Conceptual Design for a Short Construction Schedule

2002 ◽  
Author(s):  
Jerry M. Hopwood ◽  
Ian J. W. Love ◽  
Medhat Elgohary ◽  
Neville Fairclough
Keyword(s):  
Conceptual Design ◽  
Critical Path ◽  
Construction Method ◽  
Phase Iii ◽  
Next Generation ◽  
Project Schedule ◽  
Construction Methods ◽  
New Construction ◽  
Construction Strategy ◽  
Construction Schedule

Atomic Energy of Canada Ltd. (AECL) has very successful experience in implementing new construction methods at the Qinshan (Phase III) twin unit CANDU 6 plant in China. This paper examines the construction method that must be implemented during the conceptual design phase of a project if short construction schedules are to be met. A project schedule of 48 months has been developed for the nth unit of NG (Next Generation) CANDU with a 42 month construction period from 1st Concrete to In-Service. An overall construction strategy has been developed involving paralleling project activities that are normally conducted in series. Many parts of the plant will be fabricated as modules and be installed using heavy lift cranes. The Reactor Building (RB), being on the critical path, has been the focus of considerable assessment, looking at alternative ways of applying the construction strategy to this building. A construction method has been chosen which will result in excess of 80% of internal work being completed as modules or as very streamlined traditional construction. This method is being further evaluated as the detailed layout proceeds. Other areas of the plant have been integrated into the schedule and new construction methods are being applied to these so that further modularization and even greater paralleling of activities will be achieved. It is concluded that the optimized construction method is a requirement, which must be implemented through all phases of design to make a 42 month construction schedule a reality. If the construction methods are appropriately chosen, the schedule reductions achieved will make nuclear more competitive.

New construction of binary and nonbinary quantum stabilizer codes based on symmetric matrices

2019 ◽  
Vol 33 (24) ◽  
pp. 1950274 ◽  
Author(s):  
Duc Manh Nguyen ◽  
Sunghwan Kim
Keyword(s):  
Inner Product ◽  
Symmetric Matrices ◽  
Parity Check ◽  
Stabilizer Codes ◽  
Construction Methods ◽  
Singleton Bound ◽  
New Construction ◽  
Symplectic Inner Product ◽  
Quantum Stabilizer Codes

In this paper, we propose two construction methods for binary and nonbinary quantum stabilizer codes based on symmetric matrices. In the first construction, we use the identity and symmetric matrices to generate parity-check matrices that satisfy the symplectic inner product (SIP) for the construction of quantum stabilizer codes. In the second construction, we modify the first construction to generate parity-check matrices based on the Calderbank–Shor–Stean structure for the construction of quantum stabilizer codes. The binary and nonbinary quantum stabilizer codes whose parameters achieve equality of the quantum singleton bound are investigated with the code lengths ranging from 4 to 12.

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.

Some new construction methods for t-norms on bounded lattices

2019 ◽  
Vol 48 (7) ◽  
pp. 775-791 ◽  
Author(s):  
Ümit Ertuğrul ◽  
M. Nesibe Kesicioğlu ◽  
Funda Karaçal
Keyword(s):  
Construction Methods ◽  
New Construction
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