Towards more realistic (e.g., non-associative) AND- and OR-operations in fuzzy logic

Martinez, Joe L.; Macias, Lucasantiago Henze; Esper, A.; Chaparro, Javier Dorado; Alvarado, V.; Starks, Scott A.; Крейнович, Владик

doi:10.1109/icsmc.2001.972880

Cited by 4 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Usually, it is also required that the t-norm is associative. However, our results do not need associativity, so they are valid for non-associative andoperations as well; such non-associative operations are sometimes used to more adequately describe human reasoning; see, e.g., [2,3,5,7,9]. • S is the set of all x ∈ X for which the function…”

Section: Bellman-zadeh Approach To Optimization Under Fuzzy Constraintsmentioning

confidence: 97%

Algebraic Product is the only T-norm for Which Optimization Under Fuzzy Constraints is Scale-Invariant

Figueroa–García

Ceberio

Kreinovich

2017

Studies in Systems, Decision and Control

View full text Add to dashboard Cite

Abstract. In many practical situations, we need to optimize under fuzzy constraints. There is a known Bellman-Zadeh approach for solving such problems, but the resulting solution, in general, depends on the choice of a not well-defined constant M . We show that this dependence disappears if we use an algebraic t-norm (and-operation) f & (a, b) = a · b, and we also prove that the algebraic product is the only t-norm for which the corresponding solution is independent on M .

show abstract

Section: Bellman-zadeh Approach To Optimization Under Fuzzy Constraintsmentioning

confidence: 97%

Algebraic Product is the only T-norm for Which Optimization Under Fuzzy Constraints is Scale-Invariant

Figueroa–García

Ceberio

Kreinovich

2017

Studies in Systems, Decision and Control

View full text Add to dashboard Cite

show abstract

“…In [4], [13], [19], [22], [23], [34], it is argued that if we represent such ternary operations directly, then we may get a more adequate representation of expert uncertainty.…”

Section: Discussionmentioning

confidence: 99%

How to reconcile physical theories with the idea of free will: From analysis of a simple model to interval and fuzzy approaches

Urenda

Kosheleva

2008

2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence)

View full text Add to dashboard Cite

Most modern physical theories are formulated in terms of differential equations. As a result, if we know exactly the current state of the world, then this state uniquely determines all the future events including our own future behavior. This determination seems to contradict the intuitive notion of a free will, according to which we are free to make decisions decisions which cannot be determined based on the past locations and velocities of the elementary particles. In quantum physics, the situation is somewhat better in the sense that we cannot determine the exact behavior, but we can still determine the quantum state, and thus, we can determine the probabilities of different behaviors which is still inconsistent with our intuition.This inconsistency does not mean, of course, that we can practically predict our future behavior; however, in view of many physicists and philosophers, even the theoretical inconsistency is somewhat troubling. Some of these researchers feel that it is desirable to modify physical equations in such a way that such a counter-intuitive determination would no longer be possible.In this paper, we analyze the foundations for such possible theories, and show that on the level of simple mechanics, the formalization of a free will requires triple interactions while traditional physics is based on pairwise interactions between the particles. I. FREE WILL: A NATURAL IDEAIntuitively, most of us believe that we are able to make conscientious decisions, i.e., that we have free will. If we walk to a corner, then we can turn right or cross the street.The commonsense belief is that it is not possible to predict beforehand what exactly a person will do. II. THERE SEEMS TO BE NO FREE WILL IN CLASSICAL MECHANICS (AND IN CLASSICAL PHYSICS IN GENERAL)In contrast to the common sense belief, in classical physics, e.g., in classical mechanics where Newton's equa- IV. CAN WE RECONCILE PHYSICS WITH FREE WILL?The possibility to predict every single detail of our behavior (even theoretically) is so contrary to our intuition that it is natural to ask: is it possible to modify physical equations in such a way that there will be room for free will? V. IS QUANTUM PHYSICS AN ANSWER?At rst glance, it may look as if this problem disappears in quantum physics. Indeed, in quantum mechanics, due toHeisenberg's principle, we cannot exactly predict both the location and the velocity of a particle, we can only predict In terms of human behavior, this means that we cannot predict whether a person turns or not, but we can predict (at least theoretically) the probability that a person turns right.This also does not seem to be consistent with common sense. VI. THE PROBLEM OF FREE WILL IN PHYSICS HAS BEEN ACTIVELY STUDIED IN PHILOSOPHYThe seeming disconnect between physics and the intuitive notion of a free will has been actively studied in philosophy, especially by philosophers and physicists interested in foundations of

show abstract

“…If the difference is below the natural resolution level, then, from the practical point of view, the above operations are as good as associative ones. The following is true[2,20]: max a;b;c jf & ðf & ða; bÞ; cÞ À f & ða; f & ðb; cÞÞj ¼ jf _ ðf _ ða; bÞ; cÞ À f _ ða; f _ ðb; cÞÞj ¼ 1 9 :…”

mentioning

confidence: 99%

“…W-00016 from the U.S-Czech Science and Technology Joint Fund. This grant was partly sponsoring several publications [11,12,20,29,30,55,56,58,59], and it also provided financial support for the Czech-US Seminar on Current Trends in Soft Computing.…”

mentioning

confidence: 99%

Research on advanced soft computing and its applications

Novák

Perfilieva

Nguyen

et al. 2004

Soft Computing - A Fusion of Foundations, Methodologies and App

Self Cite

View full text Add to dashboard Cite

The main objective for the research presented in this special issue is to advance theoretical basis in soft computing, for the purpose of improving applications. Why is this theoretical research needed? Because soft computing in general (and intelligent control and decision making in particular) are, in many aspects, still an art. To make this methodology easier to apply, we must use the experience of successful applications of fuzzy control, decision making or classification and extract formal rules that would capture this experience. To be able to do that efficiently, we must understand why some versions of soft computing methodology turned out to be more successful in some practical situations and less successful in others. In other words, to advance the practical success of soft computing methodology, we need further theoretical analysis of soft computing -analysis targeted at enhancing its application abilities.

show abstract

Towards more realistic (e.g., non-associative) AND- and OR-operations in fuzzy logic

Cited by 4 publications

References 9 publications

Algebraic Product is the only T-norm for Which Optimization Under Fuzzy Constraints is Scale-Invariant

Algebraic Product is the only T-norm for Which Optimization Under Fuzzy Constraints is Scale-Invariant

How to reconcile physical theories with the idea of free will: From analysis of a simple model to interval and fuzzy approaches

Research on advanced soft computing and its applications

Contact Info

Product

Resources

About