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

2004 Mathematical Reviews  
We determine all the fuzzy orderings (they contain all the crisp orderings) which make it possible to compare two fuzzy strict lower sections and two fuzzy strict upper sections.  ...  Summary: “Strict lower sections, strict upper sections and open order intervals (strict order intervals) are classical notions asso- ciated to crisp orderings (crisp total preorders).  ... 

Contrapositive symmetrisation of fuzzy implications—Revisited

J. Balasubramaniam
2006 Fuzzy sets and systems (Print)  
Also we have proposed a new contrapositivisation technique, viz., M-contrapositivisation, which is N-compatible independent of the ordering on the negations.  ...  Given a fuzzy implication J , towards imparting contrapositive symmetry to J with respect to a strong negation N two techniques, viz., upper and lower contrapositivisation, have been proposed by Bandler  ...  The author wishes to acknowledge the excellent environment provided by the Department of Mathematics and Computer Sciences, Sri Sathya Sai Institute of Higher Learning, during the period of this work,  ... 
doi:10.1016/j.fss.2006.03.015 fatcat:kvipnubvrratjf5xg7uzmlbn7a

A Linear Algorithm for Polygonal Approximations of Thick Curves [chapter]

Trung Nguyen
2005 Lecture Notes in Computer Science  
The quality of decomposition can be easily controlled by setting two threshold values: the maximum order and the minimum density of the fuzzy segments.  ...  In this paper we suggest a notion of strict fuzzy segment and provide a linear algorithm for recognizing it thanks to a simple property of convex hull.  ...  Acknowledgements The author wishes to express his gratitude to Isabelle Debled-Rennesson for the helpful discussions in the course of the preparation of this paper.  ... 
doi:10.1007/11556121_3 fatcat:blqksd5zrje4bosipalhrdhwiy

Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms and Implications Satisfying the Order Property

Zhudeng Wang
2017 Applied and Computational Mathematics  
Then, we lay bare the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.  ...  We firstly give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation.  ...  Acknowledgements This work is supported by Jiangsu Provincial Natural Science Foundation of China (BK20161313), Science Foundation of Yancheng Teachers University (16YCKLQ006) and the National Natural  ... 
doi:10.11648/j.acm.20170601.13 fatcat:rph2vbrxzfbfzhx2jhmbuvzeum

Existence of Order-Preserving Functions for Nontotal Fuzzy Preference Relations under Decisiveness

Paolo Bevilacqua, Gianni Bosi, Magalì Zuanon
2017 Axioms  
We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space.  ...  Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation.  ...  We say that l (x) (r (x)) is the strict lower section (respectively, strict upper section) associated to x ∈ X, while d (x) (i (x)) is the weak lower section (respectively, weak upper section) associated  ... 
doi:10.3390/axioms6040029 fatcat:u5vhg4j5yfa3xesbdfpatuakni

Interval-valued contractive fuzzy negations

Benjamin Bedregal, Humberto Bustince, Javier Fernandez, Glad Deschrijver, Radko Mesiar
2010 International Conference on Fuzzy Systems  
We relate this to the concept of Lipschitz function. In particular, we prove that the only contractive interval-valued fuzzy negation is the one generated from the standard (Zadeh's) negation.  ...  In this work we consider the concept of contractive interval-valued fuzzy negation, as a negation such that it does increase the length or amplitude of an interval.  ...  In Section III we introduce interval-valued fuzzy sets and interval-valued mappings. In Section IV we present our main results on interval-valued contractive fuzzy mappings.  ... 
doi:10.1109/fuzzy.2010.5584635 dblp:conf/fuzzIEEE/BedregalSFDM10 fatcat:3svktd5ginbxznk2eqs276c66u

New Uncertainty Measure of Rough Fuzzy Sets and Entropy Weight Method for Fuzzy-Target Decision-Making Tables

Huani Qin, Darong Luo
2014 Journal of Applied Mathematics  
In the rough fuzzy set theory, the rough degree is used to characterize the uncertainty of a fuzzy set, and the rough entropy of a knowledge is used to depict the roughness of a rough classification.  ...  Theoretical studies and examples show that the new rough entropy of a rough fuzzy set is suitable.  ...  and Science Project of China.  ... 
doi:10.1155/2014/487036 fatcat:6gdxgokoxfhohkfpw66mgyk7la

A decomposition theorem for T-indistinguishability operators. The continuous strict Archimedean case

D. Boixader, J. Recasens
2012 2012 IEEE International Conference on Fuzzy Systems  
In this paper we study the relationship between the cuts of a T-indistinguishability operator and the t-norm T chosen to define fuzzy transitivity.  ...  The key result is, strict Archimedean t-norms provide equivalence relations as their zero cuts, and that property characterizes such t-norms.  ...  that neither the lower nor the upper bounds for( ) dim E in [4.3.1]can be improved. which form a partition of X.  ... 
doi:10.1109/fuzz-ieee.2012.6250838 dblp:conf/fuzzIEEE/BoixaderR12 fatcat:p7hw5j6kxrea7gp7fl7wobea6a

Ambiguous representations as fuzzy relations between sets

Oleh Nykyforchyn, Dušan Repovš
2011 Fuzzy sets and systems (Print)  
Crisp and L-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced.  ...  It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or L-fuzzy) ambiguous representations is a lattice and a compact Hausdorff Lawson upper semilattice.  ...  Acknowledgments The authors wish to express gratitude to anonymous reviewers and editors for valuable comments, corrections and suggestions.  ... 
doi:10.1016/j.fss.2011.02.007 fatcat:vuqr7jfff5h6bmeyagaog6qexe

Decomposition of the Transitivity for Additive Fuzzy Preference Structures

Susana Díaz, Susana Montes, Bernard De Baets
2009 European Society for Fuzzy Logic and Technology  
We characterize the behaviour with respect to transitivity of the strict preference and indifference relations of any fuzzy preference structure associated to any large preference relation.  ...  Transitivity is a very important property in order to provide coherence to a preference relation. Usually, t-norms are considered to define the transitivity of fuzzy relations.  ...  Acknowledgment The research reported on in this paper has been partially supported by Project FEDER-MEC-MTM2007-61193.  ... 
dblp:conf/eusflat/DiazMB09 fatcat:c6fguhdcebbo5oo6g4xrg2wnxy

Towards a formal theory of fuzzy Dedekind reals

Libor Behounek
2005 European Society for Fuzzy Logic and Technology  
In the framework of Henkin style higher-order fuzzy logic LΠ ω we construct fuzzy real numbers as fuzzy Dedekind cuts over crisp rationals, and show some of their properties provable in LΠ ω .  ...  The definitions of algebraic operations and a theory of fuzzy intervals are sketched.  ...  B100300502 of the Grant Agency of the Academy of Sciences of the Czech Republic.  ... 
dblp:conf/eusflat/Behounek05 fatcat:xtggzssi7bdxrmisxgynjibtee

Constructions of Strict Left (Right)-Conjunctive Left (Right) Semi-Uninorms on a Complete Lattice

Yuan Wang
2017 International Journal of Intelligent Information Systems  
Then we give out the formulas for calculating the upper and lower approximation strict left (right)-conjunctive left (right) semi-uninorms of a binary operation.  ...  In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice.  ...  Acknowledgements This work is supported by Science Foundation of Yancheng Teachers University (16YCKLQ006), the National Natural Science Foundation of China (61379064) and Jiangsu Provincial Natural Science  ... 
doi:10.11648/j.ijiis.20170601.11 fatcat:jvimw5s27nhibjkc42i2qu4rxy

Optimal Solution of Nonlinear Fuzzy Optimization Problem under Linear Order Relation [article]

Umme Salma M. Pirzada
2018 arXiv   pre-print
Multi-variable nonlinear fuzzy optimization problem is considered under linear order relation on fuzzy numbers.  ...  Optimum solution of the fuzzy optimization problem is obtained based on the optimality conditions.  ...  UMP is also thankful to B S Ratanpal (Department of Applied Mathematics, The Maharaja Sayajirao University of Baroda, India) for necessary suggestions.  ... 
arXiv:1802.09909v1 fatcat:lmqwf5xfjbbstm5ztwpgemr4zu

Constructions of Implications Satisfying the Order Property on a Complete Lattice

Yuan Wang
2017 Automation Control and Intelligent Systems  
Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.  ...  In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice.  ...  Acknowledgements This work is supported by Science Foundation of Yancheng Teachers University (16YCKLQ006), the National Natural Science Foundation of China (61379064) and Jiangsu Provincial Natural Science  ... 
doi:10.11648/j.acis.20170501.11 fatcat:m2vyiozqobdvdp47nl7qhzlrce

Rough Atanassov's Intuitionistic Fuzzy Sets Model over Two Universes and Its Applications

Shuqun Luo, Weihua Xu
2014 The Scientific World Journal  
Recently, much attention has been given to the rough set models based on two universes. And many rough set models based on two universes have been developed from different points of view.  ...  We study some important properties of approximation operators and investigate the rough degree in the novel model.  ...  and (̃) are called the lower and upper approximations of fuzzy set̃in ( ), and (̃) and (̃) are called the lower and upper approximations of fuzzy setĩ n ( ), respectively. ( (̃), (̃)) and ( (̃), (̃)) are  ... 
doi:10.1155/2014/348683 pmid:24959609 pmcid:PMC4052704 fatcat:lu6fe2f7fba2bbe7ulqqmjdoey
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