Fuzzy Set Theory in Medical Diagnosis

Adlassnig, Klaus-Peter

doi:10.1109/tsmc.1986.4308946

Cited by 347 publications

(152 citation statements)

References 14 publications

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“…(2)) is generally a non-convex set, which can be completely determined by one maximum solution and a finite number of minimum solutions. The fuzzy relation equations are used in many problems such as medical diagnosis [2], system analysis [6], decision-making [3], Fuzzy control [7], Fuzzy modelling [8], and in psychology, economics, sociology, and especially Fuzzy arithmetic [7], [9].…”

Section: Minimizementioning

confidence: 99%

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A New Algorithm for Optimization of the Fuzzy Relation Equation With Maxalgebraic Sum Composition

Zharfi¹,

Mirzazadeh²

2011

The South African Journal of Industrial Engineering

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This paper considers an optimization problem with a linear objective function under the constraints expressed by a system of fuzzy relation equations using max-as (Algebraic Sum) composition. First, some properties of minimal solutions of the system with fuzzy relation equations and max-as composition are shown. Then, a new algorithm for solving the optimization problem is derived. The numerical examples have been provided to illustrate the theoretical results. OPSOMMINGHierdie artikel bestudeer 'n optimiseringsprobleem met 'n lineêre doelwitfunksie en wasige randvoorwaardes met 'n algebraïese somsamestelling. Aanvanklik word sommige eienskappe van die minimale oplossings van die wasige vergelykings en die algebraïese samestelling getoon. Daarna word 'n nuwe algoritme vir die oplossing van die optimiseringsprobleem afgelei. Numeriese voorbeelde word voorsien om die teoretiese resultate te ondersteun.

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Section: Minimizementioning

confidence: 99%

“…The resolution of the fuzzy relation in Eq. (2) is an interesting and ongoing research topic [1], [2], [3], [4], [5]. Many different equations are based on a specific composition.…”

Section: Introductionmentioning

confidence: 99%

A New Algorithm for Optimization of the Fuzzy Relation Equation With Maxalgebraic Sum Composition

Zharfi¹,

Mirzazadeh²

2011

The South African Journal of Industrial Engineering

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“…Its design and construction was initiated in the early 80's at the Medical University of Vienna by K.P. Adlassnig -see [1], [2], [3] or [4] for more on the origins and design of CADIAG-2.…”

Section: Introductionmentioning

confidence: 99%

“…The vast majority of them are binary (i.e., they relate single medical entities) and only such rules are considered in this paper. The one that follows is an example of a binary rule of CADIAG-2 (taken from [3]):…”

Section: Introductionmentioning

confidence: 99%

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The Consistency of the CADIAG-2 Knowledge Base: A Probabilistic Approach

Klinov

Parsia

Parra³

2010

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. The paper presents the methodology and the results of checking consistency of the knowledge base of CADIAG-2, a large-scale medical expert system. Such knowledge base consists of a large collection of rules representing knowledge about various medical entities (symptoms, signs, diseases...) and relationships between them. The major portion of the rules are uncertain, i.e., they specify to what degree a medical entity is confirmed by another medical entity or a combination of them. Given the size of the system and the uncertainty it has been challenging to validate its consistency. Recent attempts to partially formalise CADIAG-2's knowledge base into decidable Gödel logics have shown that, on that formalisation, CADIAG-2 is inconsistent. In this paper we verify this result with an alternative, more expressive formalisation of CADIAG-2 as a set of probabilistic conditional statements and apply a state-of-the-art probabilistic logic solver to determine satisfiability of the knowledge base and to extract conflicting sets of rules. As CADIAG-2 is too large to be handled out of the box we describe an approach to split the knowledge base into fragments that can be tested independently and prove that such methodology is complete (i.e., is guaranteed to find all conflicts). With this approach we are able to determine that CADIAG-2 contains numerous sets of conflicting rules and compute all of them for a slightly relaxed version of the knowledge base.

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2020

A Modern Introduction to Fuzzy Mathematics

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Fuzzy Set Theory in Medical Diagnosis

Cited by 347 publications

References 14 publications

A New Algorithm for Optimization of the Fuzzy Relation Equation With Maxalgebraic Sum Composition

A New Algorithm for Optimization of the Fuzzy Relation Equation With Maxalgebraic Sum Composition

The Consistency of the CADIAG-2 Knowledge Base: A Probabilistic Approach

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