INNER PRODUCT BASED ENTROPY IN THE INTUITIONISTIC FUZZY SETTING
International Journal of Uncertainty Fuzziness and Knowledge-Based SystemsPublished 1 June 2006
Ioannis Vlachos, George D. Sergiadis
Citations23
SJR quartileQ3
SJR score0.32
SNIP0.58
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
An entropy formula for intuitionistic fuzzy sets is presented and an entropy measure is derived based on the normalized normalized fuzzy vector.
Abstract
In this paper, an entropy formula for intuitionistic fuzzy sets is presented. The notion of the intuitionistic fuzzy vector is introduced and an entropy measure is derived based on the normalized inner product between intuitionistic fuzzy vectors in the unit intuitionistic fuzzy cube. Some considerations regarding the geometrical representations of intuitionistic fuzzy sets are also stated and a connection between the different notions of entropy in the intuitionistic fuzzy setting is established. Finally, the relation of the proposed entropy measure to the concepts of correlation and informational energy for intuitionistic fuzzy sets is revealed and a new correlation coefficient is introduced.
Keywords
Computer ScienceDecision SciencesMathematics
Fuzzy Sets and SystemsIntuitionistic fuzzy sets
16,153 Citations1986Krassimir Atanassov
Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
European Journal of Operational ResearchFuzzy sets, uncertainty, and information
3,193 Citations1989
The fuzzy sets uncertainty and information is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Information and ControlA definition of a nonprobabilistic entropy in the setting of fuzzy sets theory
2,260 Citations1972Aldo de Luca, S. Termini
A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets.
Studies in fuzziness and soft computingIntuitionistic Fuzzy Sets
1,927 Citations1999Krassimir Atanassov
IEEE Transactions on Systems Man and CyberneticsVague sets
1,649 Citations1993Wen-Bing Gau, Daniel J. Buehrer
A vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of according to the inequality of the following type:
Fuzzy Sets and SystemsDistances between intuitionistic fuzzy sets
1,587 Citations2000Eulalia Szmidt, Janusz Kacprzyk
It is shown that all three parameters describing intuitionistic fuzzy sets should be taken into account while calculating those distances between intuitionistically fuzzy sets.
Fuzzy Sets and SystemsMore on intuitionistic fuzzy sets
1,488 Citations1989Krassimir Atanassov
Two news operators on intuitionistic fuzzy sets are defined and their basic properties are studied to introduce new results on intuitionism fuzzy sets.
Fuzzy Sets and SystemsNew operations defined over the intuitionistic fuzzy sets
917 Citations1994Krassimir Atanassov
Fuzzy Sets and SystemsEntropy for intuitionistic fuzzy sets
907 Citations2001Eulalia Szmidt, Janusz Kacprzyk
It is shown that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities: of F ∩ F c and F ∪ F c .
Fuzzy Sets and SystemsVague sets are intuitionistic fuzzy sets
885 Citations1996Humberto Bustince, P. Burillo
This paper recapitulates the definition given by Atanassov (1983) of intuitionistic fuzzy sets as well as the definition of vague sets given by Gau and Byehrer (1993) and sees that both definitions coincide.
Fuzzy Sets and SystemsEntropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets
792 Citations1996P. Burillo, Humberto Bustince
The distance measure between intuitionistic fuzzy sets is defined and an axiom definition of intuitionist fuzzy entropy is given and a theorem which characterizes it is studied.
Fuzzy Sets and SystemsOperators over interval valued intuitionistic fuzzy sets
753 Citations1994Krassimir Atanassov
Different operators are defined over the interval valued intuitionistic fuzzy sets and their basic properties are studied.
Fuzzy Sets and SystemsDistances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric
620 Citations2003Przemysław Grzegorzewski
New methods for measuring distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets, based on the Hausdorff metric, are suggested.
Information SciencesFuzzy entropy and conditioning
616 Citations1986Bart Kosko
A new nonprobabilistic entropy measure is introduced in the context of fuzzy sets or messages and the theory of subsethood is shown to solve one of the major problems with Bayes-theorem learning and its variants—the problem of requiring that the space of alternatives be partitioned into disjoint exhaustive hypotheses.
International Journal of General SystemsON THE MEASURE OF FUZZINESS AND NEGATION Part I: Membership in the Unit Interval
579 Citations1979Ronald R. Yager
It is suggested that fuzziness can be related to the lack of distinction between a set and its negation and the concept of compatibility is used to develop linguistic measures of fuzziness.
Fuzzy Sets and SystemsEntropy, distance measure and similarity measure of fuzzy sets and their relations
572 Citations1992Xuecheng Liu
The axiom definitions of entropy, distance measure and similarity measure of fuzzy sets are systematically given and basic relations between these measures are discussed.
Fuzzy Sets and SystemsSome operations on intuitionistic fuzzy sets
544 Citations2000Supriya Kumar De, Ranjit Biswas +1 more
Concentration, dilation and normalization of intuitionistic fuzzy sets are defined, which will be useful while dealing with various linguistic hedges like “very”, “more or less” etc. involved in the problems under intuitionism fuzzy environment.
International Journal of General SystemsFUZZINESS VS. PROBABILITY
436 Citations1990Bart Kosko
A new geometric proof of the Subsethood Theorem is given, a corollary of which is that the apparently probabilistic relative frequency nA /N turns out to be the deterministic subsethood S(X, A), the degree to which the sample space X is contained in its subset A.
Fuzzy Sets and SystemsCorrelation of intuitionistic fuzzy sets
337 Citations1991Tadeusz Gerstenkorn, Jacek Mańko
A functional measuring the interrelation of intuitionistic fuzzy sets, the so-called correlation of these sets, is defined and a coefficient of such a correlation is introduced and examined to examine its properties.
Fuzzy Sets and SystemsTerminological difficulties in fuzzy set theory—The case of “Intuitionistic Fuzzy Sets”
303 Citations2005Didier Dubois, Siegfried Gottwald +3 more
This paper is a plea for a clarification of terminology, based on mathematical resemblances and the comparison of motivations between ''intuitionistic fuzzy sets'' and other theories.
Journal of Symbolic LogicIntuitionistic fuzzy logic and intuitionistic fuzzy set theory
280 Citations1984Gaisi Takeuti, Satoko Titani
From a logical standpoint, each logic has its corresponding set theory in which each logical operation is translated into a basic operation for set theory; namely, the relation ⊆ and = on sets are translation of the logical operations → and ↔.
Fuzzy Sets and SystemsDistance measure and induced fuzzy entropy
176 Citations1999Jiulun Fan, Weixin Xie
The relations between fuzzy entropy, fuzzy Hamming distance, divergence measuredefined by Bhandari and Pal (1993), and divergence measure defined in this paper are studied and quite a general conclusion is obtained.
Fuzzy Sets and SystemsCorrelation of intuitionistic fuzzy sets in probability spaces
157 Citations1995Dug Hun Hong, Seok Yoon Hwang
These results give the results of Gerstenkorn and Manko: (1991) and in the case of infinite spaces, also give the correct forms of Yu's (1993) results.
Information SciencesHigher order fuzzy entropy and hybrid entropy of a set
112 Citations1992Nikhil R. Pal, Sankar K. Pal
New entropy measures such as higher order fuzzy entropy and hybrid entropy of a set have been introduced and various properties along with their proofs have been included.
International Journal of Uncertainty Fuzziness and Knowledge-Based SystemsA NOTE ON ENTROPY OF INTUITIONISTIC FUZZY SETS
36 Citations2003Wen‐Liang Hung
Two new formulas of fuzzy entropy induced by distances between two intuitionistic fuzzy sets are given that can be computed easily and give reliable results.