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Square Root Of "Not": A Major Difference Between Fuzzy And Quantum Logics, Vladik Kreinovich, Ladislav J. Kohout, Eunjin Kim
Square Root Of "Not": A Major Difference Between Fuzzy And Quantum Logics, Vladik Kreinovich, Ladislav J. Kohout, Eunjin Kim
Departmental Technical Reports (CS)
Many authors have mentioned the similarity between quantum logic and fuzzy logic. In this paper, we show that, in spite of this similarity, these logics are not identical. Specifically, we emphasize that while quantum logic has a special ``square root of not'' operation which is very useful in quantum computing, fuzzy logic lacks such an operation.
Which Fuzzy Logic Is The Best: Pragmatic Approach (And Its Theoretical Analysis), Vladik Kreinovich, Hung T. Nguyen
Which Fuzzy Logic Is The Best: Pragmatic Approach (And Its Theoretical Analysis), Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
In this position paper, we argue that when we are looking for the best fuzzy logic, we should specify in what sense the best, and that we get different fuzzy logics as ``the best'' depending on what optimality criterion we use.
Towards More Realistic (E.G., Non-Associative) And- And Or-Operations In Fuzzy Logic, Vladik Kreinovich
Towards More Realistic (E.G., Non-Associative) And- And Or-Operations In Fuzzy Logic, Vladik Kreinovich
Departmental Technical Reports (CS)
No abstract provided.
On Efficient Representation Of Expert Knowledge By Fuzzy Logic: Towards An Optimal Combination Of Granularity And Higher-Order Approaches, Hung T. Nguyen, Vladik Kreinovich
On Efficient Representation Of Expert Knowledge By Fuzzy Logic: Towards An Optimal Combination Of Granularity And Higher-Order Approaches, Hung T. Nguyen, Vladik Kreinovich
Departmental Technical Reports (CS)
A natural approach to designing an intelligent system is to incorporate expert knowledge into this system. One of the main approaches to translating this knowledge into computer-understandable terms is the approach of fuzzy logic. It has led to many successful applications, but in several aspects, the resulting computer representation is somewhat different from the original expert meaning. Two related approaches have been used to make fuzzy logic more adequate in representing expert reasoning: granularity and higher-order approaches. Each approach is successful in some applications where the other approach did not succeed so well; it is therefore desirable to combine these …
Non-Associative Operations, Bernadette Bouchon-Meunier, Vladik Kreinovich, Hung T. Nguyen
Non-Associative Operations, Bernadette Bouchon-Meunier, Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
How is fuzzy logic usually formalized? There are many seemingly reasonable requirements that a logic should satisfy: e.g., since A&B and B&A are the same, the corresponding and-operation should be commutative. Similarly, since A&A means the same as A, we should expect that the and-operation should also satisfy this property, etc. It turns out to be impossible to satisfy all these seemingly natural requirements, so usually, some requirements are picked as absolutely true (like commutativity or associativity), and others are ignored if they contradict to the picked ones. This idea leads to a neat mathematical theory, but the analysis of …
Towards More Realistic (E.G., Non-Associative) And- And Or-Operations In Fuzzy Logic, Jesus Martinez, Leopoldo Macias, Ammar Esper, Jesus Chaparro, Vick Alvarado, Scott A. Starks, Vladik Kreinovich
Towards More Realistic (E.G., Non-Associative) And- And Or-Operations In Fuzzy Logic, Jesus Martinez, Leopoldo Macias, Ammar Esper, Jesus Chaparro, Vick Alvarado, Scott A. Starks, Vladik Kreinovich
Departmental Technical Reports (CS)
How is fuzzy logic usually formalized? There are many seemingly reasonable requirements that a logic should satisfy: e.g., since A&B and B&A are the same, the corresponding and-operation should be commutative. Similarly, since A&A means the same as A, we should expect that the and-operation should also satisfy this property, etc. It turns out to be impossible to satisfy all these seemingly natural requirements, so usually, some requirements are picked as absolutely true (like commutativity or associativity), and others are ignored if they contradict to the picked ones. This idea leads to a neat mathematical theory, but the analysis of …
Multi-Criteria Optimization - An Important Foundation Of Fuzzy System Design, Hung T. Nguyen, Vladik Kreinovich
Multi-Criteria Optimization - An Important Foundation Of Fuzzy System Design, Hung T. Nguyen, Vladik Kreinovich
Departmental Technical Reports (CS)
In many real-life design situations, there are several different criteria that we want to optimize, and these criteria are often in conflict with each other. Traditionally, such multi-criteria optimization situations are handled in an ad hoc manner, when different conflicting criteria are artificially combined into a single combination objective that is then optimized. The use of unnatural ad hoc tools is clearly not the best way of describing a very natural aspect of human reasoning. Fuzzy logic describes a much more natural way of handling multi-criterion optimization problems: when we cannot maximize each of the original conflicting criteria 100%, we …