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To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and…

Bilattice-based triangle provides an elegant algebraic structure for reasoning with vague and uncertain information. But the truth and knowledge ordering of intervals in bilattice-based triangle can not handle repetitive belief revisions…

In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…

In this paper we present a propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is…

A new approach for uncertainty management for fuzzy, rule based decision support systems is proposed: The domain expert's knowledge is expressed by a set of rules that frequently refer to vague and uncertain propositions. The certainty of…

Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1],…

We present a unified logical framework for representing and reasoning about both quantitative and qualitative preferences in fuzzy answer set programming, called fuzzy answer set optimization programs. The proposed framework is vital to…

In this paper, we present the interval neutrosophic logics which generalizes the fuzzy logic, paraconsistent logic, intuitionistic fuzzy logic and many other non-classical and non-standard logics. We will give the formal definition of…

This book presents the advancements and applications of neutrosophics. Chapter 1 first introduces the interval neutrosophic sets which is an instance of neutrosophic sets. In this chapter, the definition of interval neutrosophic sets and…

Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable…

Fuzzy optimization deals with the problem of determining 'optimal'solutions of an optimization problem when some of the elements that appear in the problem are not precise. In real situations it is usual to have information, in systems…

The approach described here allows to use the fuzzy Object Based Representation of imprecise and uncertain knowledge. This representation has a great practical interest due to the possibility to realize reasoning on classification with a…

A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework…

Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…

In this paper we analyse the benefits of incorporating interval-valued fuzzy sets into the Bousi-Prolog system. A syntax, declarative semantics and im- plementation for this extension is presented and formalised. We show, by using potential…

Approaches based on computing with words find good applicability in decision making systems. Predominantly finding their basis in type-1 fuzzy sets, computing with words approaches employ type-1 fuzzy sets as semantics of the linguistic…

In medicine one frequently deals with vague information. As a tool for reasoning in this area, fuzzy logic suggests itself. In this paper we explore the applicability of the basic ideas of fuzzy set theory in the context of medical…

A reason maintenance system which extends an ATMS through Mukaidono's fuzzy logic is described. It supports a problem solver in situations affected by incomplete information and vague data, by allowing nonmonotonic inferences and the…

The basic aim of our study is to give a possible model for handling uncertain information. This model is worked out in the framework of DATALOG. At first the concept of fuzzy Datalog will be summarized, then its extensions for…

Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nommonotonic reasoning with plausible reasoning…