Wyniki wyszukiwania - BazTech

1

A new method for decision making problems with redundant and incomplete information based on incomplete soft sets: From crisp to fuzzy

Xia Sisi, Chen Lin, Liu Siya, Yang Haoran

International Journal of Applied Mathematics and Computer Science

|

2022

|

Vol. 32, no. 4

657--669

EN

This research is focused on decision-making problems with redundant and incomplete information under a fuzzy environment. Firstly, we present the definition of incomplete fuzzy soft sets and analyze their data structures. Based on that, binary relationships between each pair of objects and the “restricted/relaxed AND” operations in the incomplete fuzzy soft set are discussed. After that, the definition of incomplete fuzzy soft decision systems is proposed. To reduce the inconsistency caused by the redundant information in decision making, the significance of the attribute subset, the reduct attribute set, the optimal reduct attribute set and the core attribute in incomplete fuzzy soft decision systems is also discussed. These definitions can be applied in an incomplete fuzzy soft set directly, so there is no need to convert incomplete data into complete one in the process of reduction. Then a new decision-making algorithm based on the above definitions can be developed, which can deal with redundant information and incomplete information simultaneously, and is independent of some unreliable assumptions about the data generating mechanism to forecast the incomplete information. Lastly, the algorithm is applied in the problem of regional food safety evaluation in Chongqing, China, and the corresponding comparison analysis demonstrates the effectiveness of the proposed method.

2

An incomplete soft set and its application in MCDM problems with redundant and incomplete information

Xia Sisi, Yang Haoran, Chen Lin

International Journal of Applied Mathematics and Computer Science

|

2021

|

Vol. 31, no. 3

417--430

EN

Multiple criteria decision making (MCDM) problems in practice may simultaneously contain both redundant and incomplete information and are difficult to solve. This paper proposes a new decision-making approach based on soft set theory to solve MCDM problems with redundant and incomplete information. Firstly, we give an incomplete soft set a precise definition. After that, the binary relationships of objects in an incomplete soft set are analyzed and some operations on it are provided. Next, some definitions regarding the incomplete soft decision system are also given. Based on that, an algorithm to solve MCDM problems with redundant and incomplete information based on an incomplete soft set is presented and illustrated with a numerical example. The results show that our newly developed method can be directly used on the original redundant and incomplete data set. There is no need to transform an incomplete information system into a complete one, which may lead to bad decision-making due to information loss or some unreliable assumptions about the data generating mechanism. To demonstrate its practical applications, the proposed method is applied to a problem of regional food safety evaluation in Chongqing, China.

3

Universal (and Existential) Nulls

Grahne Gösta, Moallemi Ali

Fundamenta Informaticae

|

2019

|

Vol. 167, nr 4

287--321

EN

Incomplete Information research is quite mature when it comes to so called existential nulls, where an existential null is a value stored in the database, representing an unknown object. For some reason universal nulls, that is, values representing all possible objects, have received almost no attention. We remedy the situation in this paper, by showing that a suitable finite representation mechanism, called Star Cylinders, handling universal nulls can be developed based on the Cylindric Set Algebra of Henkin, Monk and Tarski. We provide a finitary version of the cylindric set algebra, called Cylindric Star Algebra, and show that our star-cylinders are closed under this algebra. Moreover, we show that any First Order Relational Calculus query over databases containing universal nulls can be translated into an equivalent expression in our cylindric star-algebra, and vice versa. All cylindric star-algebra expressions can be evaluated in time polynomial in the size of the database. The representation mechanism is then extended to Naive Star Cylinders, which are star-cylinders allowing existential nulls in addition to universal nulls. For positive queries (with universal quantification), the well known naive evaluation technique can still be applied on the existential nulls, thereby allowing polynomial time evaluation of certain answers on databases containing both universal and existential nulls. If precise answers are required, certain answer evaluation with universal and existential nulls remains in coNP. Note that the problem is coNP-hard, already for positive existential queries and databases with only existential nulls. If inequalities ¬(xi ≈ x j) are allowed, reasoning over existential databases is known to be ∏2p -complete, and it remains in ∏ 2pwhen universal nulls and full first order queries are allowed.

4

On Desirable Semantics of Functional Dependencies over Databases with Incomplete Information

Badia A., Lemire D.

Fundamenta Informaticae

|

2018

|

Vol. 158, nr 4

327--352

EN

Codd’s relational model describes just one possible world. To better cope with incomplete information, extended database models allow several possible worlds. Vague tables are one such convenient extended model where attributes accept sets of possible values (e.g., the manager is either Jill or Bob). However, conceptual database design in such cases remains an open problem. In particular, there is no canonical definition of functional dependencies (FDs) over possible worlds (e.g., each employee has just one manager). We identify several desirable properties that the semantics of such FDs should meet including Armstrong’s axioms, the independence from irrelevant attributes, seamless satisfaction and implied by strong satisfaction. We show that we can define FDs such that they have all our desirable properties over vague tables. However, we also show that no notion of FD can satisfy all our desirable properties over a more general model (disjunctive tables). Our work formalizes a trade-off between having a general model and having well-behaved FDs.

5

A refined and asymptotic analysis of optimal stopping problems of Bruss and Weber

Louchard G.

Mathematica Applicanda

|

2017

|

Vol. 45, No. 2

95--118

EN

The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific kind. The Bruss-Weber problems we consider center around the following model: Let X1, X2,…,Xn be a sequence of independent and identically distributed random variables which can take three values: {+1,−1, 0}. The goal is to maximize the probability of stopping on a value +1 or −1 appearing for the last time in the sequence. We study related problems both in discrete and continuous time settings, with known or unknown number of observations, and known and unknown probability measure. In particular, so called x-strategy with incomplete information is taken into consideration. Our contribution in the present paper is a refined analysis of several problems in this class and a study of the asymptotic behaviour of solutions. We also present simulations of the corresponding complete selection algorithms.

PL

Klasyczny problem sekretarki został uogólniony na przestrzeni lat w kilku kierunkach. W niniejszym artykule ograniczamy nasze zainteresowanie do tych uogólnień, które mają związek z bardziej ogólnym problemem zatrzymania na ostatniej obserwacji określonego rodzaju. Problemy Brussa-Webera, które rozważamy, koncentrują się wokół następującego modelu: Obserwowany jest ciąg niezależnych zmiennych losowych o tym samym rozkładzie przyjmujących trzy wartosci: +1; −1; 0. Celem jest maksymalizacja prawdopodobieństwa zatrzymania na wartości +1 lub −1 pojawiającej się po raz ostatni w sekwencji. Badamy pokrewne problemy zarówno z czasem dyskretnym, jak i ciągłym, ze znaną lub nieznaną liczbą obserwacji oraz znanym i nieznanym rozkładem. W szczególności bierze się pod uwagę tak zwaną strategię z niepełną informacją. Nowością w niniejszej pracy jest udoskonalona analiza kilku problemów w tej klasie oraz badanie asymptotycznego zachowania się rozwiązań. Prezentujemy również symulacje odpowiednich kompletnych algorytmów wyboru.

6

Apriori-Based Rule Generation in Incomplete Information Databases and Non-Deterministic Information Systems

Sakai H., Wu M., Nakata M.

Fundamenta Informaticae

|

2014

|

Vol. 130, nr 3

343--376

EN

This paper discusses issues related to incomplete information databases and considers a logical framework for rule generation. In our approach, a rule is an implication satisfying specified constraints. The term incomplete information databases covers many types of inexact data, such as non-deterministic information, data with missing values, incomplete information or interval valued data. In the paper, we start by defining certain and possible rules based on non-deterministic information. We use their mathematical properties to solve computational problems related to rule generation. Then, we reconsider the NIS-Apriori algorithm which generates a given implication if and only if it is either a certain rule or a possible rule satisfying the constraints. In this sense, NIS-Apriori is logically sound and complete. In this paper, we pay a special attention to soundness and completeness of the considered algorithmic framework, which is not necessarily obvious when switching from exact to inexact data sets. Moreover, we analyze different types of non-deterministic information corresponding to different types of the underlying attributes, i.e., value sets for qualitative attributes and intervals for quantitative attributes, and we discuss various approaches to construction of descriptors related to particular attributes within the rules' premises. An improved implementation of NIS-Apriori and some demonstrations of an experimental application of our approach to data sets taken from the UCI machine learning repository are also presented. Last but not least, we show simplified proofs of some of our theoretical results.

7

Negatywna informacja w języku regułowym 4QL

Małuszyński J., Szałas A.

Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki

|

2013

|

nr 9

7--14

EN

Problematyka negatywnej informacji w językach regułowych jest zasadnicza z punktu widzenia dużej liczby aplikacji. Była ona rozważana w rozszerzeniach języków zapytań w dedukcyjnych bazach danych, opartych na wnioskowaniach niemonotonicznych, początkowo wynikających z założenia o zamkniętym świecie CWA (Closed World Assumption). W wielu zastosowaniach, w tym związanych z Semantycznym Internetem i robotyką, założenie CWA nie jest właściwe i zwykle przyjmuje się w nich założenie o świecie otwartym OWA (Open World Assumption). W niniejszym artykule omawiamy nowe podejście do tego problemu, przedstawione w [2] [3] [4], gdzie zaproponowaliśmy język regułowy 4QL w stylu Datalogu, jednak bez ograniczeń na wystąpienie negacji. Język ma architekturę warstwową. Najniższe warstwy 4QL, oparte na OWA, są w pełni monotoniczne. W celu zmniejszenia stref niewiedzy/sprzeczności w [2] [3] wprowadzono proste konstrukcje pozwalające na wyrażanie mechanizmów wnioskowań niemonotonicznych, w tym umożliwiających rozwiązywanie sprzeczności, użycie lokalnych domknięć świata (a więc także CWA) oraz różnych form wnioskowań przez domniemania. Obliczanie zapytań w 4QL ma złożoność wielomianową ze względu na rozmiar bazy danych.

XX

The problem of negative information in rule languages is crucial in many applications. It has been addressed in extensions of query languages in deductive databases, based on nonmonotonic logics initially derived from the Closed World Assumption (CWA). In many applications, including Semantic Web technologies and robotics systems, CWA is not necessarily applicable and developments in these fields usually follow the Open World Assumption (OWA). In this paper we summarize a novel approach to the problem reported in [2] [3] [4], where we proposed a DATALOG-like language 4QL with unrestricted negation. The language supports a layered architecture. The monotonic layer of 4QL, based on OWA, is fully monotonic. To reduce the unknown/inconsistent zones, in [2] [3] we have introduced simple constructs which allow one to express various mechanisms of nonmonotonic reasoning. In particular, this provides means for application-specific disambiguation of inconsistent information, the use of Local CWA (thus also CWA, if needed), and various forms of default reasoning. Query evaluation in 4QL is still tractable as regards its data complexity.

8

Estimation of nonlinear models' parameters of machine tool supporting systems using incomplete vibration tests data

Berczyński S., Gutowski P., Kravtsov Y., Chodźko M.

Advances in Manufacturing Science and Technology

|

2011

|

Vol. 35, nr 3

5-18

EN

An algorithm of reconstruction nonlinear motion equations of machine tool supporting system dynamic models, on the basis of incomplete information about an object is presented in this paper. This information is obtained from experimental tests in the form of time response characteristics of an object to a given excitation. Tested models are developed in the rigid finite elements method convention supplemented by slideway joint modeling option. The effectiveness of the algorithm has been verified by means of simulated identification of selected parameters of the knee - column slideway joint nonlinear model of universal milling machine.

PL

W pracy przedstawiono algorytm rekonstrukcji nieliniowych równań ruchu modeli układów nośnych obrabiarek na podstawie niepełnej informacji o obiekcie uzyskiwanej z badań doświadczalnych w postaci przebiegów czasowych odpowiedzi obiektu na zadane wymuszenie. Badane modele tworzone są w konwencji metody sztywnych elementów skończonych uzupełnionej o opcję modelowania prowadnic. Efektywność algorytmu zweryfikowano poprzez symulowaną identyfikację wybranych parametrów nieliniowego modelu połączenia prowadnicowego wspornik-korpus frezarki uniwersalnej.