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Intersection of Yager's implications with QL and D-implications

Sebastia Massanet, Joan Torrens
2012 International Journal of Approximate Reasoning  
In particular, we solve an open problem related to the characterization of those implications that are both QL-implications and f -generated implications with f (0) < ∞, fully determining the expression  ...  The intersection of the different classes of implications is one of the most popular topics nowadays due to the large number of construction methods of these operators.  ...  However, since it is a ϕ-conjugate of an f -generated implication with f (0) < ∞, using Theorem 20, it satisfies (LI) with (T P ) ϕ . Consequently, we should have that T P = (T P ) ϕ . So,  ... 
doi:10.1016/j.ijar.2011.11.001 fatcat:dl5vdwkiyreafca5mdsokioe3u

Robustness of f- and g-generated Fuzzy (Co)Implications: The Yager's (Co)Implication Case Study

Renata Reiser, Rosana Zanotelli, Simone Costa, Luciana Foss, Benjamin Bedregal
2016 Electronical Notes in Theoretical Computer Science  
Starting with an evaluation of the sensitivity in representable fuzzy negations, we apply the results in the Yager's classes of fuzzy implications called the f -and g-generated fuzzy implications.  ...  This paper studies the robustness of intuitionistic fuzzy implications in fuzzy reasoning based on Atanassov's intuitionistic fuzzy logic.  ...  the Yager's implication classes, the f -and g-generated implications [24] , focusing on their pointwise components obtained by the projections related to membership and non-membership functions.  ... 
doi:10.1016/j.entcs.2016.09.013 fatcat:mhjtsxlwzjbflcwpzlc3vjgbfy

Monotonicity of SISO Fuzzy Relational Inference Mechanism with Yager's Class of Fuzzy Implications [chapter]

Sayantan Mandal, Balasubramaniam Jayaram
2013 Lecture Notes in Computer Science  
Here we show monotonicity of an FRI with Yager's class of fuzzy implications which do not form a residuated lattice structure on [0, 1].  ...  Monotonicity of a Fuzzy Relational Inference (FRI) mechanism has been studied in the literature with implicative form of a rule base where the implication comes from a residuated lattice structure.  ...  FRI with Yager's Class of Fuzzy Implications In this work, we consider the Relational inference mechanism, where the fuzzy implication is f -implication, one of the Yager's classes of fuzzy implications  ... 
doi:10.1007/978-3-642-45062-4_79 fatcat:aujcrkbc2nblvcr7mgxsebnrzu

Yager's new class of implications Jf and some classical tautologies

J. Balasubramaniam
2007 Information Sciences  
Along the lines of J f implications, a new class of implications called h-generated implications, J h , has been proposed and the interplay between these two types of implications has been discussed.  ...  Recently, Yager (Info Sci, Vol 167, pp.193 -216, 2004) has introduced a new class of fuzzy implications, denoted J f , called the f -generated implications and has discussed some of their desirable properties  ...  Outline of this work Firstly, by discussing the four different general forms of distributive equations we show that the Yager's class of f -generated implications does have more solutions for one of them  ... 
doi:10.1016/j.ins.2006.08.006 fatcat:4ldqf2rhgfeyfj3rhy2w5ni6uq

Constructing non-functionally expressible fuzzy implications

Sebastia Massanet, Gaspar Mayor, Joan Torrens
2013 Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology  
This article discusses a new method for the construction of non-functionally expressible fuzzy implications.  ...  Now, we first perform an aggregation of the inputs and then an implication function between the aggregated values.  ...  Now, let us briefly study the Yager's implications. There are two classes of Yager's implications, namely, f -and g-generated implications.  ... 
doi:10.2991/eusflat.2013.34 dblp:conf/eusflat/MassanetMT13 fatcat:f64wct2eejdingiy2sectyk7tm

Bandler-Kohout Subproduct with Yager's Classes of Fuzzy Implications [chapter]

Sayantan Mandal, Balasubramaniam Jayaram
2012 Communications in Computer and Information Science  
In this work we discuss the BKS relational inference system with the fuzzy implication interpreted as the Yager's classes of implications, which do not form a residuated structure on [0, 1].  ...  Note that, to the best of the authors' knowledge, this is the first attempt at studying the suitability of an FRI where the operations come from a non-residuated structure.  ...  Bandler-Kohout Subproduct with Yager's class of fuzzy implications In this work, we consider the BKS inference mechanism, where the fuzzy implication is one of the Yager's classes of implications.  ... 
doi:10.1007/978-3-642-31715-6_41 fatcat:b4gv7xppzbdtnjv4qhqmvtb2ne

Bandler–Kohout Subproduct With Yager's Classes of Fuzzy Implications

Sayantan Mandal, Balasubramaniam Jayaram
2014 IEEE transactions on fuzzy systems  
In this work we discuss the BKS relational inference system with the fuzzy implication interpreted as the Yager's classes of implications, which do not form a residuated structure on [0, 1].  ...  Note that, to the best of the authors' knowledge, this is the first attempt at studying the suitability of an FRI where the operations come from a non-residuated structure.  ...  Bandler-Kohout Subproduct with Yager's class of fuzzy implications In this work, we consider the BKS inference mechanism, where the fuzzy implication is one of the Yager's classes of implications.  ... 
doi:10.1109/tfuzz.2013.2260551 fatcat:tr5gkdwqijh23pf7z7ogoeunjy

Bijective transformations of fuzzy implications – An algebraic perspective

Nageswara Rao Vemuri, Balasubramaniam Jayaram
2016 Fuzzy sets and systems (Print)  
In this context, they obtained a bijective transformation which ultimately led to hitherto unknown representations of the Yager's families of fuzzy implications, viz., f -, g-implications.  ...  In [Representations through a Monoid on the set of Fuzzy Implications, Fuzzy Sets and Systems, 247, 51-67], Vemuri and Jayaram proposed a monoid structure on the set of fuzzy implications, which is denoted  ...  Recently, Vemuri and Jayaram, in [9] , proposed the following transformation and obtained hitherto unknown representations of two families of fuzzy implications, viz., the Yager's f -and g-implications  ... 
doi:10.1016/j.fss.2015.08.003 fatcat:t6bxoxqhsndlleyx6gk6q3x3my

Study of Two Families of Generalized Yager's Implications for Describing the Structure of Generalized (h,e)-Implications

Raquel Fernandez-Peralta, Sebastia Massanet, Arnau Mir
2021 Mathematics  
These two families can be interpreted as particular cases of the (f,g) and (g,f)-implications, which are two families of fuzzy implication functions that generalize the well-known f and g-generated implications  ...  We determine when this family fulfills some of the main additional properties of fuzzy implication functions and we obtain a representation theorem that describes the structure of a generalized (h,e)-implication  ...  In [21] , a similar approach to provide a generalization of Yager's f -implications was considered.  ... 
doi:10.3390/math9131490 fatcat:hcvzmakx7nhrpogmn27t367txi

Page 6720 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
A solution is given to the following open problem: “When do two families of fuzzy possi- ble valuations produce the same fuzzy implication relation?’  ...  Moreover, we show that it is possible to embed both structures in the class of fuzzy closure systems by a lattice dual monomorphism between semilattices.  ... 

Page 3791 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
the set of all infinitely A-distributive implications on L in detail, and point out that three classes of fundamental fuzzy implications and Yager’s implication on [0,1] are all infinitely A-distributive  ...  Given a function of k-valued logic represented by a polynomial, we must decide whether it belongs to a certain precomplete class of linear functions.  ... 

Representations through a monoid on the set of fuzzy implications

Nageswara Rao Vemuri, Balasubramaniam Jayaram
2014 Fuzzy sets and systems (Print)  
Based on these equivalence classes, we obtain a hitherto unknown representation of the two main families of fuzzy implications, viz., the f -and g-implications.  ...  To this end, we propose a binary operation, denoted by , which makes (I, ) a non-idempotent monoid.  ...  In Section 5, after introducing the Yager's families of f -and g-implications, we explore and illustrate that the equivalence classes obtained allow us to provide the much needed representations of these  ... 
doi:10.1016/j.fss.2014.02.014 fatcat:bir4btybgncyxeristi2awxmna

New measures of similarity based on fuzzy implications

Erick González-Caballero, Susana Díaz, Rafael Espín, Susana Montes
2017 Journal of Intelligent & Fuzzy Systems  
We propose a definition of proximity between two fuzzy finite sets by using the previous operators and we study when this type of operators satisfy the formal definition of similarity.  ...  An important problem in fuzzy theory is how to determine if two elements are similar or not. There are different definitions to measure how similar or close are elements.  ...  partially supported by the Spanish Ministerio de Economía y Competitividad under Project TIN2014-59543-P and EUREKA SD project (agreement number 2013-2591), that is supported by the Erasmus Mundus programme of  ... 
doi:10.3233/jifs-16861 fatcat:y3lwu6bg5bfbvjvjlzet77i5wa

The ⊛-composition of fuzzy implications: Closures with respect to properties, powers and families

Nageswara Rao Vemuri, Balasubramaniam Jayaram
2015 Fuzzy sets and systems (Print)  
Some algebraic aspects of (I, ) had already been explored and hitherto unknown representation results for the Yager's families of fuzzy implications were obtained in [Representations through a Monoid on  ...  This study shows that the -composition carries over many of the desirable properties of the original fuzzy implications to the generated fuzzy implications and further, due to the associativity of the  ...  equations related to fuzzy implications, viz., the law of importation and contrapositive symmetry.  ... 
doi:10.1016/j.fss.2014.10.004 fatcat:lvyazqo3g5aynmf6v474icdexy

A GIS-integrated fuzzy rule-based inference system for land suitability evaluation in agricultural watersheds

T.V. Reshmidevi, T.I. Eldho, R. Jana
2009 Agricultural Systems  
A large amount of information related to the crop land suitability can be conveyed through linguistic terms.  ...  The model has been applied to a subwatershed of Gandheshwari area in West Bengal (India).  ...  of Technology Bombay, and is gratefully acknowledged.  ... 
doi:10.1016/j.agsy.2009.04.001 fatcat:qa7yqxcagrfi3ngua2hwudhmje
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