Foundations of Fuzzy Set Theory and Fuzzy Logic: A Historical Overview

Klir, George J.

doi:10.1080/03081070108960701

Cited by 28 publications

(5 citation statements)

References 26 publications

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“…A further technical suggestion would be that, given an interest in greater verisimilitude to natural selection, some attention should be shifted from fully explicit techniques toward fuzzier ones, moving even through second-order fuzziness in the direction of vagueness (e.g., [24,25]). More generally, while it is true that in simulations simple rules can generate complicated behavior and forms, we might note that the simulations themselves are the complex frameworks that allow this to happen [26,39], just as the world itself is the complex framework within which natural selection will have to be working.…”

Section: Resultsmentioning

confidence: 99%

Natural Selection in Relation to Complexity

Salthe¹

2008

Artificial Life

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Structural complexity characterizes our representations of dissipative structures. As a mechanistic concept, when referred to natural systems it generates perplexity in the face of logically sound models. Natural selection is a simple mechanistic concept, whose logic is well exemplified in genetic algorithms. While biological traits and functions do appear to have been subjected to selective culling, current neo-Darwinian theory is unable to account for the evolution of traits or functions when many of these are taken as the separate objects of independent fitness functions. Soft selection, acting in a phenotypically holistic manner, does model selection acting upon structurally complex systems with many traits and functions, but does not account for the evolution of specific traits or functions. It is further suggested that selection cannot be other than a weak force in the early, generative stages of complex life histories, and that this is a good thing, preserving their generativity. I conclude that natural selection theory by itself cannot account for increases in structural complexity.

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Section: Resultsmentioning

confidence: 99%

Natural Selection in Relation to Complexity

Salthe¹

2008

Artificial Life

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“…Hence, the question of interpretation is purely theoretical and has no practical significance. This conclusion is not at all unexpected since some researchers hold that probability may be interpreted as a special case of degrees of membership, even if it is still a minority viewpoint in the uncertainty research community [35][36][37]. Ref.…”

Section: Discussionmentioning

confidence: 99%

Using Fuzzy Sets in Surgical Treatment Selection and Homogenizing Stratification of Patients with Significant Chronic Ischemic Mitral Regurgitation

Nikolova¹,

Panayotov²,

Panayotova³

et al. 2019

IJCIS

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We present three (main one and two auxiliary) fuzzy algorithms to stratify observations in homogenous classes. These algorithms modify, upgrade and fuzzify crisp algorithms from our earlier works on a medical case study to select the most appropriate surgical treatment for patients with ischemic heart disease complicated with significant chronic ischemic mitral regurgitation. Those patients can be treated with either surgical revascularization and mitral valve repair (group A) or with isolated surgical revascularization (group B) depending on their health status. The main algorithm results in a fuzzy partition of patients in two fuzzy sets (groups A and B) through identification of their degrees of membership. The resulting groups are highly nonhomogenous, which impedes subsequent proper comparisons. So, the two auxiliary algorithms further stratify each group into two homogenous subgroups with comparatively preserved medical condition (A 1 and B 1) and with comparatively deteriorated medical condition (A 2 and B 2). Those two algorithms perform fuzzy partition of patients from A and B respectively into A 1 , A 2 , B 1 and B 2 by identifying their conditional degrees of membership to those subgroups. We then utilize the product t-norm to calculate the degree of membership of patients to their respective subgroup as an intersection of two fuzzy sets. We demonstrate how to form fuzzy samples for medical parameters for any subgroup. We also compare the performance of the fuzzy algorithms with their preceding crisp version, as well as with eight Bayesian classifiers. We then assess the quality of classification by modified confusion matrices, summarized further into four criteria. The fuzzy algorithms show total superiority over the other methods, and excellent differentiation of typical patients and outliers. On top, only the fuzzy algorithms provide a measure of how typical a patient is to its subgroup. The fuzzy algorithms clearly outline the role of the Heart Team, which is missing in the Bayesian classifiers.

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“…b j -the membership degree of evaluation level l j in the fuzzy set B ~, they are eventually the results of fuzzy comprehensive evaluation. [7] The single index evaluation is the bedrock of the multiple indexes evaluation. In general, the evaluation indexes are determined, so the membership degree can be expressed according to the relation above as:…”

Section: Advanced Materials Research Vols 1030-1032 Membership Degree...mentioning

confidence: 99%

Research on the Risk Assessment in Bridge Construction Stage

2014

AMR

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Foundations of Fuzzy Set Theory and Fuzzy Logic: A Historical Overview

Cited by 28 publications

References 26 publications

Natural Selection in Relation to Complexity

Natural Selection in Relation to Complexity

Using Fuzzy Sets in Surgical Treatment Selection and Homogenizing Stratification of Patients with Significant Chronic Ischemic Mitral Regurgitation

Research on the Risk Assessment in Bridge Construction Stage

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