Type 2 fuzzy sets for knowledge representation and inferencing
Published 27 November 2002
Robert John
Citations24
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
The various approaches to knowledge representation and inferencing are discussed, with worked examples, and some of the applications of type 2 sets are reported.
Abstract
Type 2 fuzzy sets allow for linguistic grades of membership thus assisting in knowledge representation. They also offer improvement on inferencing with type 1 sets. The various approaches to knowledge representation and inferencing are discussed, with worked examples, and some of the applications of type 2 sets are reported.
Keywords
Computer ScienceDecision Sciences
Information SciencesThe concept of a linguistic variable and its application to approximate reasoning-III
12,148 Citations1975L. A. Zadeh
Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
Information SciencesThe concept of a linguistic variable and its application to approximate reasoning—I
12,036 Citations1975Lotfi A. Zadeh
It is shown that probabilities, too, can be treated as linguistic variables with values such as likely, very likely, unlikely, etc.
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.
Fuzzy Sets and SystemsInterval valued fuzzy sets based on normal forms
1,078 Citations1986İ.B. Türkşen
It is shown that the proposed representation exists for certain families of the conjugate pairs of t-norms and t-conorms and resolves some of the difficulties associated with particular interpretations of conjunction, disjuntion, and implication in fuzzy set theories.
Information and ControlSome properties of fuzzy sets of type 2
776 Citations1976M. Mizumoto, Kokichi Tanaka
This paper investigates the algebraic structures of fuzzy grades under the operations of join ⊔, meet ⊓, and negation ┐ which are defined by using the extension principle, and shows that convex fuzzy grades form a commutative semiring and normal convex fuzzies form a distributive lattice under ⊢ and ⊡.
International Journal of Approximate ReasoningNN-driven fuzzy reasoning
581 Citations1991Hideyuki Takagi, Isao Hayashi
A new fuzzy reasoning that can solve two problems of conventional fuzzy reasoning by combining an artificial neural network (NN) and fuzzy reasoning is proposed, capable of automatic determination of inference rules and adjustment according to the time-variant reasoning environment because of the use of NN in fuzzy reasoning.
Fuzzy Sets and SystemsMeasurement of membership functions and their acquisition
275 Citations1991İ.B. Türkşen
Fuzzy Sets and SystemsFuzzy sets and type 2 under algebraic product and algebraic sum
242 Citations1981M. Mizumoto, Kokichi Tanaka
This paper investigates the algebraic properties of fuzzygrades under the operations of algebraic product and algebraic sum which can be defined by using the concept of the extension principle and shows that fuzzy grades under these operations do not form such algebraic structures as a lattice and a semiring.
Journal of CyberneticsFUZZY SUBSETS OF TYPE II IN DECISIONS
181 Citations1980Ronald R. Yager
The construction of an ideal decision function from its approximation in terms of other decision functions is interested, and fuzzy subsets of type II, those with linguistic grades of membership, are investigated.
International Journal of Intelligent SystemsSome comments on interval valued fuzzy sets
145 Citations1998Mai Gehrke, Carol Walker +1 more
This article presents a framework for fuzzy set theory in which fuzzy values are intervals, and shows how this framework can be applied to discrete-time set theory.
International Journal of Man-Machine StudiesThe IF THEN ELSE statement and interval-valued fuzzy sets of higher type
141 Citations1981Ellen Hisdal
It is concluded that increased fuzziness in a description means increased ability to handle inexact information in a logically correct manner.
Fuzzy Sets and SystemsAn interval-valued fuzzy inference method— Some basic properties
110 Citations1989Marian B. Gorzałczany
This paper presents a short analysis of formal properties of the interval-valued fuzzy inference method described in [5], concerned with the so-called good-mapping property (GMP) and α-good-mappers property (α-GMP).
International Journal of Intelligent SystemsSome comments on interval valued fuzzy sets
109 Citations1996Mai Gehrke, Carol L. Walker +1 more
Fuzzy Sets and SystemsApplication of fuzzy sets of type 2 to the solution of fuzzy equations systems
106 Citations1988Michael Wagenknecht, K. Hartmann
The situation that the outputs of an object are modelled by fuzzy sets of Type 2, which enables us to define solutions for fuzzy outputs of Type 1, when classical solution concepts may fail.
International Journal of Uncertainty Fuzziness and Knowledge-Based SystemsInterval-Valued Degrees of Belief: Applications of Interval Computations to Expert Systems and Intelligent Control
104 Citations1997Hung T. Nguyen, Владик Крейнович +1 more
This paper describes applications of interval-valued degree of belief computations to expert systems and to intelligent control.
Fuzzy Sets and SystemsFuzzy normal forms
94 Citations1995İ.B. Türkşen
The fuzzy normal forms, generated by crisp operators over fuzzy sets that correspond to max-min-standard-complement De Morgan triple, are shown to be equivalent to the classical normal forms of two-valued logic.
Computers & Electrical EngineeringFuzzy interval control of mobile robots
73 Citations1996Kung C. Wu
The FIC represents an adaptive FLC whose input-output relation is no longer deterministic and is designed for the applications in which limited or uncertain expert's experience is available and provides a practical implementation of a type 2 FLC to real applications.
International Journal of Approximate ReasoningFour methods of approximate reasoning with interval-valued fuzzy sets
67 Citations1989İ.B. Türkşen
Fuzzy Sets and SystemsGenerating fuzzy membership functions: A monotonic neural network model
49 Citations1994Shouhong Wang
This paper suggests that neural networks which use the back propagation learning algorithm under monotonic function constraints can be used in generating fuzzy membership functions.
Fuzzy Sets and SystemsInterval-valued fuzzy sets representation on multiple antecedent fuzzy S-implications and reasoning
24 Citations1992İ.B. Türkşen, Yuan Tian
It is suggested that modification functions utilized in Approximation Analogical Reasoning (AAR) be determined in such a way that consequents deduced by AAR fall within the bounds of the reasoning.
Proceedings of 6th International Fuzzy Systems ConferenceType 2 fuzzy sets and neuro-fuzzy clustering of radiographic tibia images
19 Citations2002Robert John, P.R. Innocent +1 more
The results indicate that the approach outperforms a type 1 approach, for certain tibia problems, and that the type 2 solution assisted the expert in analysing a set of images that he/she was unable to classify originally.
Fuzzy Sets and SystemsHigher level fuzzy numbers arising from fuzzy regression models
16 Citations1990Phil Diamond
MLE can be interpreted as an estimation procedure which transforms randomness into higher levels of fuzziness, when all fuzzy numbers are triangular and the Ei are uniformly distributed.
Interval valued fuzzy sets and fuzzy measures
14 Citations2002İ.B. Türkşen
Interval valued fuzzy set generated by fuzzy disjunctive and conjunctive normal forms are proposed to be a model of type II fuzzy sets to represent the second order semantic uncertainty realized by the combination of two or more fuzzy, vague, linguistic concepts by linguistic connectives.
How to avoid congestion in computer networks
7 Citations2002Scott A. Starks, Владик Крейнович +1 more
A fuzzy control technique is used to transform individuals' words into an efficient control strategy that gets a congestion control technique that is much better than the fractional linear approach.
Fuzzy interval approach to computations on the internet and information super highway
6 Citations2002Dana Tolbert, Jenna Corbin
F fuzzy intervals are proposed to use fuzzy intervals (i.e., membership functions with interval values) as a tool that would help to extract the desired dependency from the experimentally observed times.