Fuzzy sets as named sets

Burgin, Mark; Kuznetsov, V. I.

doi:10.1016/0165-0114(92)90131-m

Cited by 9 publications

(9 citation statements)

References 4 publications

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“…Fuzzy sets differentiate from other set types because they contain elements that present a degree of membership i.e., making it possible to represent the imprecision level in non-numeric variables. Fuzzy relations are a generalization of L-Relations (Burgin and Kuznetsov. 1992) and they assign a membership grade in each set entity as a mapped value between 0 and 1.…”

Section: Fuzzy Sets Theory and Fahp Methodsmentioning

confidence: 99%

Optimizing Microalgal Biomass Feedstock Selection for Nanocatalytic Conversion Into Biofuel Clean Energy, Using Fuzzy Multi-Criteria Decision Making Processes

2021

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Biofuel production from microalgae non-food feedstock is a challenge for strengthening Green energy nowadays. Reviewing the current technology, there is still reluctance in investing towards the production of new algal strains that yield more oil and maximize capital gains. In the current work, the microalgal feedstock selection problem is investigated for increased lipid production and nano-catalytic conversion into clean biofuel. For that purpose, a variety of Fuzzy Multi-Criteria Decision Making processes and a multitude of Optimization criteria spanning to technological, environmental, economic, and social aspects are used. The strains selected for the analysis are Chlorella sp., Schizochytrium sp., Spirulina sp., and Nannochloropsis sp. The methods applied are fuzzy analytic hierarchy process, FTOPSIS (fuzzy technique for the order of preference to the ideal solution), and FCM (fuzzy cognitive mapping). Pairwise comparison matrices were calculated using data from extensive literature review. All aforementioned fuzzy logic methodologies are proven superior to their numeric equivalent under uncertain factors that affect the decision making, such as cost, policy implications, and also geographical and seasonal variation. A major finding is that the most dominant factor in the strain selection is the high lipid content. Moreover, the results indicate that the Chlorella Vulgaris microalgae is ranked as the best choice by the FTOPSIS method followed by the Nannochloropsis strain, and Spirulina Platensis was found to be the last in performance. The best and worst case scenario run with FCM experimentally verify this choice indicating that Chlorella Vulgaris follows this trend of selection mostly with the technological and the economic criteria for both the sigmoid and the hyperbolic tangent deep-learning functions used.

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Section: Fuzzy Sets Theory and Fahp Methodsmentioning

confidence: 99%

Optimizing Microalgal Biomass Feedstock Selection for Nanocatalytic Conversion Into Biofuel Clean Energy, Using Fuzzy Multi-Criteria Decision Making Processes

2021

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“…Where X is the support of X, N is the component of names (reflector) or set of names of X and f is the naming correspondence of X [Burgin 2011[Burgin , 2012.…”

Section: Nearly Readymentioning

confidence: 99%

Methodological Criteria for the Interpretation of Quantum Mechanics

Rocchi

2023

Preprint

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Over a dozen constructions have been proposed to untangle the foundations of quantum mechanics (QM). The authors have spent a lot of energy in establishing formal solutions but, to the best of my knowledge, have not carefully examined the methodological problems that arise before beginning a theoretical construct in QM. This paper argues on the following methodological obstacles: 1. The definitional and computational formulas. 2. The different theories of probability. We have also tried to solve problems 1 and 2, but the complete illustration of this attempt exceeds an article’s length, so this paper is limited to presenting 1 and 2, and discussing the intellectual and formal assumptions that should be necessary to unify the theories of probability.

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“…It is worthy of note that mathematicians introduced the concept of a triple in an abstract category [8]. In essence, such a triple is a triad that consists of three fundamental triads and thus is a triad of the second order [4]. Understanding of the complex nature of the categorical triple made mathematicians to change the name of this structure and now it is always called a monad [9].…”

Section: Named Sets and Fundamental Triadsmentioning

confidence: 99%

“…This shows how it is possible to construct bidirectional named sets using inverse composition of basic named sets [4]. Inverse composition of basic named sets X = (X, f, I) and Y = (Y, g, J) is defined as …”

Section: Named Sets and Fundamental Triadsmentioning

confidence: 99%

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Bidirectional Named Sets as Structural Models of Interpersonal Communication

Burgin

2017

Proceedings of the IS4SI 2017 Summit DIGITALISATION FOR a SUSTAINABLE SOCIETY, Gothenburg, Sweden, 12–16 June 2017.

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Treating communication as information exchange between systems, we employ the most fundamental structure in mathematics, nature and cognition, which is called a named set or a fundamental triad because it has been useful in a variety of areas such as networks and networking, physics, information theory, mathematics, logic, database theory and practice, artificial intelligence, mathematical linguistics, epistemology and methodology of science, to mention but a few. Here we use structural models based on the theory of named sets for description and analysis of interpersonal communication explicating its structural regularities.

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Fuzzy sets as named sets

Cited by 9 publications

References 4 publications

Optimizing Microalgal Biomass Feedstock Selection for Nanocatalytic Conversion Into Biofuel Clean Energy, Using Fuzzy Multi-Criteria Decision Making Processes

Optimizing Microalgal Biomass Feedstock Selection for Nanocatalytic Conversion Into Biofuel Clean Energy, Using Fuzzy Multi-Criteria Decision Making Processes

Methodological Criteria for the Interpretation of Quantum Mechanics

Bidirectional Named Sets as Structural Models of Interpersonal Communication

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