scholarly journals Inconsistency Management from the Standpoint of Possibilistic Logic

2015 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 15-30 ◽  
Author(s):  
Didier Dubois ◽  
Henri Prade
Keyword(s):  
Fuzzy Sets ◽  
Lower Bounds ◽  
Propositional Logic ◽  
Information Sources ◽  
Possibility Theory ◽  
Human Knowledge ◽  
Possibilistic Logic ◽  
Inconsistency Management ◽  
The Rich ◽  
Theory Framework

Uncertainty and inconsistency pervade human knowledge. Possibilistic logic, where propositional logic formulas are associated with lower bounds of a necessity measure, handles uncertainty in the setting of possibility theory. Moreover, central in standard possibilistic logic is the notion of inconsistency level of a possibilistic logic base, closely related to the notion of consistency degree of two fuzzy sets introduced by L. A. Zadeh. Formulas whose weight is strictly above this inconsistency level constitute a sub-base free of any inconsistency. However, several extensions, allowing for a paraconsistent form of reasoning, or associating possibilistic logic formulas with information sources or subsets of agents, or extensions involving other possibility theory measures, provide other forms of inconsistency, while enlarging the representation capabilities of possibilistic logic. The paper offers a structured overview of the various forms of inconsistency that can be accommodated in possibilistic logic. This overview echoes the rich representation power of the possibility theory framework.

GRAPHOID PROPERTIES OF QUALITATIVE POSSIBILISTIC INDEPENDENCE RELATIONS

2005 ◽  
Vol 13 (01) ◽  
pp. 59-96 ◽  
Author(s):  
NAHLA BEN AMOR ◽  
SALEM BENFERHAT
Keyword(s):  
Bayesian Networks ◽  
Possibility Theory ◽  
Uncertain Reasoning ◽  
Joint Distributions ◽  
The World ◽  
Theory Framework ◽  
Independence Relations

Independence relations play an important role in uncertain reasoning based on Bayesian networks. In particular, they are useful in decomposing joint distributions into more elementary local ones. Recently, in a possibility theory framework, several qualitative independence relations have been proposed, where uncertainty is encoded by means of a complete pre-order between states of the world. This paper studies the well-known graphoid properties of these qualitative independences. Contrary to the probabilistic independence, several qualitative independence relations are not necessarily symmetric. Therefore, we also analyze the symmetric counterparts of graphoid properties (called reverse graphoid properties).

scholarly journals An Exhaustive Study of Possibility Measures of Interval-Valued Intuitionistic Fuzzy Sets and Application to Multicriteria Decision Making

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Fatma Dammak ◽  
Leila Baccour ◽  
Adel M. Alimi
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multicriteria Decision Making ◽  
Possibility Theory ◽  
Intuitionistic Fuzzy Sets ◽  
Decision Matrix ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Exhaustive Study ◽  
Interval Valued

This work is interested in showing the importance of possibility theory in multicriteria decision making (MCDM). Thus, we apply some possibility measures from literature to the MCDM method using interval-valued intuitionistic fuzzy sets (IVIFSs). These measures are applied to a decision matrix after being transformed with aggregation operators. The results are compared between each other and concluding remarks are drawn.

scholarly journals Characterizing and extending answer set semantics using possibility theory

2014 ◽  
Vol 15 (1) ◽  
pp. 79-116 ◽  
Author(s):  
KIM BAUTERS ◽  
STEVEN SCHOCKAERT ◽  
MARTINE DE COCK ◽  
DIRK VERMEIR
Keyword(s):  
Possibility Theory ◽  
Combinatorial Problems ◽  
The Body ◽  
Uncertain Information ◽  
Possibilistic Logic ◽  
Possibility Distributions ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Answer Set

AbstractAnswer Set Programming (ASP) is a popular framework for modelling combinatorial problems. However, ASP cannot be used easily for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, whereas this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.

A Fuzzy Logic Trail Finding Algorithm Trained With Human Knowledge

2002 ◽  
Author(s):  
Charles Kinney ◽  
Dean B. Edwards
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Classical Logic ◽  
Fuzzy Logic System ◽  
Human Knowledge ◽  
Relationship Of ◽  
The Relationship ◽  
Logic System

This paper presents a method for developing a fuzzy logic trail finding algorithm using a technique called embedding human knowledge. The trail finding algorithm was trained to find the pixels in images that closely resemble those that were classified as belonging to a forest trail by a human analyst. The relationship of the fuzzy logic system to a classical logic system is discussed as a method for training the fuzzy sets to mimic a human. The results show that the method outlined in this paper reduced the error in the fuzzy logic system by 99%. More generally, this method can be applied to many different situations to find features in images quickly and effectively.

Fuzzy-Based Techniques in Human-Like Processing of Social Network Data

2015 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 1-14 ◽  
Author(s):  
Lotfi A. Zadeh ◽  
Ali M. Abbasov ◽  
Shahnaz N. Shahbazova
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Fuzzy Sets ◽  
Possibility Theory ◽  
Linguistic Terms ◽  
Social Network Data ◽  
Processing Data ◽  
Source Of Information ◽  
Analysis Of Social Networks ◽  
Theory Of Fuzzy Sets

Social networks have gained a lot attention. They are perceived as a vast source of information about their users. Variety of different methods and techniques has been proposed to analyze these networks in order to extract valuable information about the users – things they do and like/dislike. A lot of effort is put into improvement of analytical methods in order to grasp a more accurate and detailed image of users. Such information would have an impact on many aspects of everyday life of people – from politics, via professional life, to shopping and entertainment. The theory of fuzzy sets and systems, introduced in 1965, has the ability to handle imprecise and ambiguous information, and to cope with linguistic terms. The theory has evolved into such areas like possibility theory and computing with words. It is very suitable for processing data in a human-like way, and providing the results in a human-oriented manner. The paper presents a short survey of works that use fuzzy-based technologies for analysis of social networks. We pose an idea that fuzzy-based techniques allow for introduction of humancentric and human-like data analysis processes. We include here detailed descriptions of a few target areas of social network analysis that could benefit from applications of fuzzy sets and systems methods.

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