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A FUZZY-FUZZY RELATION AND ITS APPLICATION TO THE CLUSTERING TECHNIQUE

Masaaki Miyakoshi, Yoshiharu Sato, Michiaki Kawaguchi
1980 Behaviormetrika  
Fuzzy-Fuzzy relation R on two ordinary non-empty sets X and Y is defined as a fuzzy fuzzy set on their product X X Y, and its membership function ,uR is defined as follows : /R :XXY-[0, l]J.  ...  An F-F relation with convexity for the all the elements of X X Y is called a convex F-F relation, and similarly an F-F relation with normality for all the elements of X X Y is called a normal one.  ... 
doi:10.2333/bhmk.7.8_15 fatcat:7bwmcshx45ccdps6mexdrxjd34

Type 2 Fuzzy Convexity*

Pishtiwan Sabir, Diyar Mohammed
2017 Evaluation Study of Three Diagnostic Methods for Helicobacter pylori Infection  
We also discuss the relationship of type 2 fuzzy convex set with generalized strongly convex fuzzy set and semistrongly convex fuzzy set.  ...  In this paper, we introduce a new notion of fuzzy convexity as a generalization of the other types of convexities, and give some connections between type 2 fuzzy convexity and generalized fuzzy convexity  ...  A fuzzy set ̃ on is quasi-convex if and only if ̃( ) [ ̃( ) ̃( )] , where ( ) , and ( ) . Frequently, we will denote the family of all fuzzy sets in by ( ) and sometimes write ( ̃) instead of ̃( ).  ... 
doi:10.24271/garmian.131 fatcat:2lmwzfxjxje3raoxzrex3xbpqa

Special Types of Fuzzy Relations

S. Nădăban, I. Dzitac
2014 Procedia Computer Science  
The aim of this paper is to present, in an unitary way, some special types of fuzzy relations: affine fuzzy relations, linear fuzzy relations, convex fuzzy relations, M-convex fuzzy relations.  ...  All these fuzzy relations are characterized and we established the inclusions between these classes of fuzzy relations.  ...  Acknowledgments This work was supported in part by research centers: 1) SC Cercetare Dezvoltare Agora (R & D Agora) of Agora University of Oradea and 2) Mathematical Models and Information Systems, Faculty  ... 
doi:10.1016/j.procs.2014.05.301 fatcat:udpbidzkfbd5fijakjjxe5iaqq

Page 4141 of Mathematical Reviews Vol. , Issue 92h [page]

1992 Mathematical Reviews  
Two elementary applications of recession cones are presented: one on the charac- terization of boundedness of convex fuzzy sets, the other on the decomposition of unbounded convex fuzzy sets.” 05 COMBINATORICS  ...  Fuzzy Sets and Systems 44 (1991), no. 1, 57-69. Summary: “We reconsider the generation of convex hulls of fuzzy sets and establish the theory of recession cones for convex fuzzy sets.  ... 

Page 3923 of Mathematical Reviews Vol. , Issue 96g [page]

1996 Mathematical Reviews  
(R-CLUJM; Cluj-Napoca) Degenerate and non-degenerate convex decomposition of finite fuzzy partitions. I. (English summary) Fuzzy Sets and Systems 73 (1995), no. 3, 365-376. Summary: “J. C.  ...  Applications to relational equations, the reduction of relational systems, decision-making with fuzzy binary relations, and to the description of closeable and cutworthy properties of fuzzy objects are  ... 

Page 906 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
(ET-TANTS; Tanta) Some properties of convex fuzzy sets and convex fuzzy cones. (English summary) Fuzzy Sets and Systems 106 (1999), no. 3, 381-386.  ...  In this paper, we study a modified concept called fuzzy convexity by introducing the notions of convex, M-convex and quasiconvex fuzzy sets, cones and hulls.  ... 

Fuzzy Network Analysis for Projects with High Level of Risks – Uncertainty in Time and Structure

Reza Morovatdar, Abdolah Aghaie, Simak Haji Yakhchali
2011 International Journal of Industrial Engineering and Production Research  
Since the convexity and normalization of traditional fuzzy numbers are not satisfied, some corrected algebraic operations are also presented.  ...  In this paper we consider three types of imprecision namely activity duration, activity existence and precedence relation existence which make our general fuzzy project network.  ...  activities, ‫ܧ‬ ෨ is a fuzzy relation on support of ܸ ෨ , and ‫ܦ‬Ԣ is a crisp set of fuzzy activity durations based on support of ܸ ෨ .  ... 
doaj:8e6a49b1d5d94d2298f2032f9892e2a8 fatcat:h72f44cdxneapcvuk7lih3ftmu

A General Framework for Ordering Fuzzy Sets [chapter]

Ulrich Bodenhofer
2002 Studies in Fuzziness and Soft Computing  
Orderings and rankings of fuzzy sets have turned out to play a fundamental role in various disciplines.  ...  The aim of this paper is to present a new framework for comparing fuzzy sets with respect to a general class of fuzzy orderings.  ...  of Upper Austria, and partly at the Fuzzy Logic Laboratorium Linz-Hagenberg which is part of to the Department of Algebra, Stochastics, and Knowledge-Based Mathematical Systems of the Johannes Kepler  ... 
doi:10.1007/978-3-7908-1797-3_17 fatcat:c73mt4gilbfedkcyxjbglltpme

Fuzzy sets

L.A. Zadeh
1965 Information and Control  
The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established.  ...  Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one.  ...  ALGEBRAIC OPERATIONS ON FUZZY SETS In addition to the operations of union and intersection, one can define a number of other ways of forming combinations of fuzzy sets and relating them to one another.  ... 
doi:10.1016/s0019-9958(65)90241-x fatcat:i3qv4jfolrb25dc5qeqrllqli4

The definition of convex fuzzy subset

Xue-Hai Yuan, E.S. Lee
2004 Computers and Mathematics with Applications  
First, by the use of the relations between fuzzy points and fuzzy sets, the definition of a (a, &)-convex fuzzy subset is introduced.  ...  Suppose that 5 is a random set on X. Let A(x) = P({w I x E t(w))), for each x E X. Fuzzy set A is called a falling shadow of the random set < and < is called a cloud on A.  ... 
doi:10.1016/s0898-1221(04)90009-0 fatcat:uj37f5vwxvewjgsxtfaqwjlqym

Fuzzy Detour Convexity and Fuzzy Detour Covering in Fuzzy Graphs

R. Rajeshkumar, Et. al.
2021 Turkish Journal of Computer and Mathematics Education  
It has been proved that for a fuzzy tree there exists a nested chain of sets, where each set is a fuzzy detour convex. Application of fuzzy detour covering and fuzzy detour basis is also presented.  ...  In this paper we establish the notion of fuzzy detour convex sets, fuzzy detour covering, fuzzy detour basis, fuzzy detour number, fuzzy detour blocks and investigate some of their properties.  ...  Umamaheswari presented the notion of fuzzy detourdistance and some of its properties in [1] . Linda and Sunitha extensively studied the notions of -convex sets and its related properties in [3] .  ... 
doi:10.17762/turcomat.v12i2.1898 fatcat:5musje54bnd25fd2lcofzngfsq

Harmonically Convex Fuzzy-Interval-Valued Functions and Fuzzy-Interval Riemann–Liouville Fractional Integral Inequalities

Gul Sana, Muhammad Bilal Khan, Muhammad Aslam Noor, Pshtiwan Othman Mohammed, Yu-Ming Chu
2021 International Journal of Computational Intelligence Systems  
of fuzzy order relation and to investigate this new class via fuzzy-interval Riemann-Liouville fractional operator.  ...  With the help of fuzzy order relation and fuzzyinterval Riemann-Liouville fractional, we derive some integrals inequalities of Hermite-Hadamard (H-H) type and Hermite-Hadamard-Fejér (H-H Fejér) type as  ...  ACKNOWLEDGMENTS The authors would like to thank the Rector, COMSATS University Islamabad, Islamabad, Pakistan, for providing excellent research and academic environments.  ... 
doi:10.2991/ijcis.d.210620.001 fatcat:ok5vwwkm6ze73fwsh6oujfiopa

(L,M) -fuzzy convex structures

Fu-Gui Shi, Zhen-Yu Xiu
2017 Journal of Nonlinear Science and its Applications  
In our definition of (L, M)-fuzzy convex structures, each L-fuzzy subset can be regarded as an L-convex set to some degree.  ...  In this paper, the notion of (L, M)-fuzzy convex structures is introduced. It is a generalization of L-convex structures and M-fuzzifying convex structures.  ...  The first author is supported by the National Natural Science Foundation of China (11371002) and Specialized Research Fund for the Doctoral Program of Higher Education (20131101110048).  ... 
doi:10.22436/jnsa.010.07.25 fatcat:gr4tkrobsbbxvgcngqwzth3giy

Note on fuzzy sets

Robert Lin
2014 Yugoslav Journal of Operations Research  
We present some improvements for the landmark paper of fuzzy sets for distributive law, convex combination and convex fuzzy sets.  ...  Our enhancement will help researcher absorb the original paper of fuzzy sets.  ...  For examples, Brown [1] considered a note on fuzzy sets to obtain some analytical findings on convex fuzzy sets, star-shaped fuzzy sets, and arcwise connected fuzzy sets.  ... 
doi:10.2298/yjor130202010l fatcat:rizclhdgkjbg7bqcpxb5rizpr4

Group Decision Making Problem by General Convexity or Concavity and Aggregation Process

Barbara Pękala
2016 Journal of Automation, Mobile Robotics & Intelligent Systems  
ACKNOWLEDGEMENTS This work was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge of University of Rzeszów, Poland, project RPPK.01.03.00-18-001  ...  Convexity of utility functions is one of the most important aspects connected with the study of geometric properties of not only crisp, but also fuzzy sets and interval-valued fuzzy sets.  ...  Keywords: aggrega on func ons, interval-valued fuzzy sets, S-convexity, T-concavity  ... 
doi:10.14313/jamris_4-2016/32 fatcat:dr3n46v3mbfojgcdev7hpius24
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