Fábio Romeu de Carvalho

A Simplified Version of the Fuzzy Decision Method and its Comparison with the Paraconsistent Decision Method

Two recent non‐classical logics have been used to make decision: fuzzy logic and paraconsistent annotated evidential logic Et. In this paper we present a simplified version of the fuzzy decision method and its comparison with the paraconsistent one.Paraconsistent annotated evidential logic Et, introduced by Da Costa, Vago and Subrahmanian (1991), is capable of handling uncertain and contradictory data without becoming trivial. It has been used in many applications such as information technology, robotics, artificial intelligence, production engineering, decision making etc.Intuitively, one Et logic formula is type p(a, b), in which a and b belong to [0, 1] (real interval) and represent respectively the degree of favorable evidence (or degree of belief) and the degree of contrary evidence (or degree of disbelief) found in p. The set of all pairs (a; b), called annotations, when plotted, form the Cartesian Unitary Square (CUS). This set, containing a similar order relation of real number, comprises a networ...

Decision Making Method Based on Paraconsistent Annotated Logic and Statistical Method: a Comparison

Presently, there are new kinds of logic capable of handling uncertain and contradictory data without becoming trivial. Decision making theories based on these logics have shown to be powerful in many aspects regarding more traditional methods based on Statistics. In this paper we intend to outline a first study for a decision making theory based on Paraconsistent Annotated Evidential Logic Eτ (Paraconsistent Decision Method (PDM)) and classical Statistical Decision Method (SDM). Some discussion is presented below.

Calculation Program for the Paraconsistent Decision Method (PDM’S CP)

In this chapter, we detail in the EXCEL program the Calculation Program for Paraconsistent Decision Method. It ranges from expert’s opinion to built the database, obtention of resulting for favorable and unfavorable evidences for each factor (parameters), consideration of a group of experts, applying maximization and minimization operations, and obtention of resulting center of gravity (global analysis). Also, it includes the para-analyzer algorithm, and it is given numerous examples and exercises.

The Decision Making Process

In this chapter, we are concerned with presenting a decision-making technique based on the paraconsistent annotated evidential logic Eτ. An expert system is presented that applies this technique. The main algorithm underlying the proposal is the para-analyzer algorithm. The proposal can handle a database containing fuzzy, inconsistent, and incomplete (paracomplete) information. It also includes objective and / or subjective data.

Paraconsistent Annotated Evidential Logic Eτ

In this chapter we present the paraconsistent annotated evidential logic Eτ, a particular case of the annotated logics. We give special attention to its associated lattice by providing it with concepts that make up the decision states.

Complementary Reading: An Example from Everyday Life

In this chapter we present an illustrative example of maximization and minimization operations.

Comparison Between the Paraconsistent Decision Method (PDM) and the Statistical Decision Method (EDM)

In this chapter we present a comparative study between the method studied in this book, the method based on the paraconsistent logic and the traditional statistical method.

An Overview of More Applications

Annotated logics have shown fruitful in many aspects. An overview of more applications of such logical systems are discussed in this chapter. Annotated logics has a well-defined syntactical counterpart as well as a semantic which the logic is sound and complete (when the associated lattice is finite; otherwise is still an open problem). Their composition as 2- sorted logic in which one variable has a mathematical structure (lattice) has allowed a smooth hardware implementation as well as logical programming.

Paraconsistent Annotated Logic in Viability Analysis: an Approach to Product Launching

In this paper we present an application of the Para‐analyzer, a logical analyzer based on the Paraconsistent Annotated Logic Pτ, introduced by Da Silva Filho and Abe in the decision‐making systems. An example is analyzed in detail showing how uncertainty, inconsistency and paracompleteness can be elegantly handled with this logical system.As application for the Para‐analyzer in decision‐making, we developed the BAM — Baricenter Analysis Method. In order to make the presentation easier, we present the BAM applied in the viability analysis of product launching.Some of the techniques of Paraconsistent Annotated Logic have been applied in Artificial Intelligence, Robotics, Information Technolgy (Computer Sciences), etc..