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V.: Likertscale fuzzy uncertainty from a traditional decision making viewpoint: it incorporates both subjective probabilities and utility information
 In: Proceedings of the Joint World Congress of the International Fuzzy Systems Association and Annual Conference of the North American Fuzzy Information Processing Society IFSA/NAFIPS’2013
"... Abstract—One of the main methods for eliciting the values of the membership function (x) is to use the Likert scales, i.e., to ask the user to mark his or her degree of certainty by an appropriate mark k on a scale from 0 to n and take (x) = k=n. In this paper, we show how to describe this process ..."
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Abstract—One of the main methods for eliciting the values of the membership function (x) is to use the Likert scales, i.e., to ask the user to mark his or her degree of certainty by an appropriate mark k on a scale from 0 to n and take (x) = k=n. In this paper, we show how to describe this process in terms of the traditional decision making. Our conclusion is that the resulting membership degrees incorporate both probability and utility information. It is therefore not surprising that fuzzy techniques often work better than probabilistic techniques – which only take into account the probability of different outcomes. I.
How to Reconcile Physical Theories with the Idea of Free Will: From Analysis of a Simple Model to Interval and Fuzzy Approaches
"... Abstract—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 intuitiv ..."
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Abstract—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 counterintuitive 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 IDEA Intuitively, 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.
Reconstructing an Open Order from Its Closure, with Applications to SpaceTime Physics and to Logic
, 2011
"... In his logical papers, Leo Esakia studied corresponding ordered topological spaces and orderpreserving mappings. Similar spaces and mappings appear in many other application areas such the analysis of causality in spacetime. It is known that under reasonable conditions, both the topology and the ..."
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In his logical papers, Leo Esakia studied corresponding ordered topological spaces and orderpreserving mappings. Similar spaces and mappings appear in many other application areas such the analysis of causality in spacetime. It is known that under reasonable conditions, both the topology and the original order relation � can be uniquely reconstructed if we know the “interior ” ≺ of the order relation. It is also known that in some cases, we can uniquely reconstruct ≺ (and hence, topology) from �. In this paper, we show that, in general, under reasonable conditions, the open order ≺ (and hence, the corresponding topology) can be uniquely determined from its closure �.
Granularity Helps Explain Seemingly Irrational Features of Human Decision Making
"... Starting from wellknown studies by Kahmenan and Tarsky, researchers have found many examples when our decision making – and our decision making – seem to be irrational. In this chapter, we show that this seemingly irrational decision making can be explained if we take into account that human abilit ..."
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Starting from wellknown studies by Kahmenan and Tarsky, researchers have found many examples when our decision making – and our decision making – seem to be irrational. In this chapter, we show that this seemingly irrational decision making can be explained if we take into account that human abilities to process information are limited; as a result, instead of the exact values of different quantities, we operate with granules that contain these values. On several examples, we show that optimization under such granularity restriction indeed leads to observed human decision making. Thus, granularity helps explain seemingly irrational human decision making. 1 Known Examples of Seemingly Irrational Human Decision Making: Formulation of the Problem In the ideal world, people should make perfect decisions. In many reallife situations, we know what is best for us, and we know the exact consequences of each of our actions. In this case, a rational person should select an action that leads to the best possible outcome. This assumption underlies basic (idealized) economic models: in these models, our decision making may hurt others but every person is interesting in selecting a decision which is the best for him/herself.
LIKERTTYPE FUZZY UNCERTAINTY FROM A TRADITIONAL DECISION MAKING VIEWPOINT: HOW SYMMETRY HELPS EXPLAIN HUMAN DECISION MAKING (INCLUDING SEEMINGLY IRRATIONAL BEHAVIOR)
, 2014
"... Abstract. One of the main methods for eliciting the values of the membership function (x) is to use the Likerttype scales, i.e., to ask the user to mark his or her degree of certainty by an appropriate mark k on a scale from 0 to n and take (x) = k=n. In this paper, we show how to describe this pr ..."
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Abstract. One of the main methods for eliciting the values of the membership function (x) is to use the Likerttype scales, i.e., to ask the user to mark his or her degree of certainty by an appropriate mark k on a scale from 0 to n and take (x) = k=n. In this paper, we show how to describe this process in terms of the traditional decision making, and we conclude that the resulting membership degrees incorporate both probability and utility information. It is therefore not surprising that fuzzy techniques often work better than probabilistic techniques (which only take into account the probability of different outcomes). We also show how symmetry helps
Why awe makes people more generous: utility theory can explain recent experiments
 Journal of Uncertain Systems
"... Recent psychological experiments show that the feeling of awe increases people's generosity. In this paper, we show that a usual utilitybased approach to decision making explains this increase. 1 Formulation of the Problem Recent experiment: a brief summary. A recent experiment [13] showed th ..."
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Recent psychological experiments show that the feeling of awe increases people's generosity. In this paper, we show that a usual utilitybased approach to decision making explains this increase. 1 Formulation of the Problem Recent experiment: a brief summary. A recent experiment [13] showed that the feeling of awe increases people’s generosity. Recent experiment: details. To measure a person’s generosity, researchers use a socalled Ultimatum Bargaining Game. In this game, to test a person’s generosity, this person is paired with another person in a simulated situation in which they should share a certain fixed amount of money given to them by the experimenter: • the tested person announces which part of this amount he or she is willing to give to the second person; • if the second person agrees, each of them gets the agreedon amount;
Journal of Uncertain Systems Vol.5, No.x, pp.xx, 2011 Online at: www.jus.org.uk Uncertainty in Partially Ordered Sets as a Natural Generalization of Intervals: Negative Information Is Sufficient, Positive Is Not
, 2010
"... In many reallife applications, we have an ordered set: a set of all spacetime events, a set of all alternatives, a set of all degrees of confidence. In practice, we usually only have a partial information about an element x of this set. This partial information includes positive knowledge: that a ..."
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In many reallife applications, we have an ordered set: a set of all spacetime events, a set of all alternatives, a set of all degrees of confidence. In practice, we usually only have a partial information about an element x of this set. This partial information includes positive knowledge: that a ≤ x or x ≤ a for some known a, and negative knowledge: that a ̸ ≤ a or x ̸ ≤ a for the known a. In the case of a total order, the set of all elements satisfying this partial information is an interval. We show that in the general case of a partial order, the corresponding analogue of an interval is a convex set. We also show that in general, to describe partial knowledge, it is sufficient to have only negative information about x but it is not sufficient to have only positive information.
Why Tensors?
"... Abstract. We show that in many application areas including soft constraints reasonable requirements of scaleinvariance lead to polynomial (tensorbased) formulas for combining degrees (of certainty, of preference, etc.) Partial orders naturally appear in many application areas. One of the main obje ..."
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Abstract. We show that in many application areas including soft constraints reasonable requirements of scaleinvariance lead to polynomial (tensorbased) formulas for combining degrees (of certainty, of preference, etc.) Partial orders naturally appear in many application areas. One of the main objectives of science and engineering is to help people select decisions which are the most beneficial to them. To make these decisions, – we must know people’s preferences, – we must have the information about different events – possible consequences of different decisions, and – since information is never absolutely accurate and precise, we must also have information about the degree of certainty. All these types of information naturally lead to partial orders: – For preferences, a < b means that b is preferable to a. This relation is used in decision theory; see, e.g., [1].
How to Encourage Imperfect Individuals to Care More about Society in General: a UtilityTheory Approach
"... For a society to function efficiently, it is desirable that all members of this society care no only about themselves, but also about the society as a whole, i.e., about all the other individuals from the society. In practice, most people are only capable of caring about a few other individuals. We ..."
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For a society to function efficiently, it is desirable that all members of this society care no only about themselves, but also about the society as a whole, i.e., about all the other individuals from the society. In practice, most people are only capable of caring about a few other individuals. We analyze this problem from the viewpoint of decision theory and show that even with such imperfect individuals, it is possible to make sure that everyone’s decisions are affected by the society as a whole: namely, it is sufficient to make sure that people have emotional attachment to those few individuals who are capable of caring about the society as a whole. As a side effect, our result provides a possible explanation of why the Biblical commandment to love your God encourages ethical behavior.