Physical Sciences and Mathematics Commons^™

When Is A Single "And"-Condition Enough?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, there are several possible decisions. Any general recommendation means specifying, for each possible decision, conditions under which this decision is recommended. In some cases, a single "and"-condition is sufficient: e.g., a condition under which a patient is recommended to take aspirin is that "the patient has a fever and the patient does not have stomach trouble". In other cases, conditions are more complicated. A natural question is: when is a single "and"-condition enough? In this paper, we provide an answer to this question.

How To Make Decision Under Interval Uncertainty: Description Of All Reasonable Partial Orders On The Set Of All Intervals, Tiago M. Costa, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to make a decision while for each alternative, we only know the corresponding value of the objective function with interval uncertainty. To help a decision maker in this situation, we need to know the (in general, partial) order on the set of all intervals that corresponds to the preferences of the decision maker. For this purpose, in this paper, we provide a description of all such partial orders -- under some reasonable conditions. It turns out that each such order is characterized by two linear inequalities relating the endpoints of the corresponding intervals, and …

Towards Decision Making Under General Uncertainty, Andrzej Pownuk, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

There exist techniques for decision making under specific types of uncertainty, such as probabilistic, fuzzy, etc. Each of the corresponding ways of describing uncertainty has its advantages and limitations. As a result, new techniques for describing uncertainty appear all the time. Instead of trying to extend the existing decision making idea to each of these new techniques one by one, we attempt to develop a general approach that would cover all possible uncertainty techniques.

In Fuzzy Decision Making, General Fuzzy Sets Can Be Replaced By Fuzzy Numbers, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real decision situations, for each of the alternatives, we only have fuzzy information about the consequences of each action. This fuzzy information can be described by a fuzzy number, i.e., by a membership function with a single local maximum, or it can be described by a more complex fuzzy set, with several local maxima. We show that, from the viewpoint of decision making, it is sufficient to consider only fuzzy numbers. To be more precise, the decisions will be the same if we replace each original fuzzy set with the smallest fuzzy number of all fuzzy numbers of …

Decision Making Under Interval (And More General) Uncertainty: Monetary Vs. Utility Approaches, Vladik Kreinovich

Departmental Technical Reports (CS)

In many situations, e.g., in financial and economic decision making, the decision results either in a money gain (or loss) and/or in the gain of goods that can be exchanged for money or for other goods. In such situations, interval uncertainty means that we do not know the exact amount of money that we will get for each possible decision, we only know lower and upper bounds on this amount. In this case, a natural idea is to assign a fair price to different alternatives, and then to use these fair prices to select the best alternative. In the talk, …

Multi-Expert Multi-Criteria Decision Making, Joel Henderson

Open Access Theses & Dissertations

Expert analysis and decisions are highly valued assets in a wide variety of fields, from social services to grant funding committees. However, the use of experts can be prohibitive due to either lack of availability or cost. As such, it is desirable to be able to replicate such decisions. However, there are many obstacles that impede an accurate simulation of expert decisions. For example, despite looking at the same information, two experts may disagree on the decisions. In addition, a single expert may make inconsistent decisions across similar scenarios.

In this work, we focus on multi-criteria decision making and in …

Note On Fair Price Under Interval Uncertainty, Joshua Mckee, Joe Lorkowski, Thavatchai Ngamsantivong

Departmental Technical Reports (CS)

Often, in decision making situations, we do not know the exact value of a gain resulting from making each decision, we only know the bounds on this gain. To make a reasonable decision under such interval uncertainty, it makes sense to estimate the fair price of each alternative, and then to select the alternative with the highest price. In this paper, we show that the value of the fair price can be uniquely determined from some reasonable requirements: e.g., the additivity requirement, that the fair price of two objects together should be equal to the sum of the fair prices …