scholarly journals THE IMPLEMENTATION OF FUZZY-TSUKAMOTO METHOD IN MAKING THE BEST DECISION TO BUY A SMARTPHONE

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Adwitya Rai Paramaartha ◽  
Rikip Ginanjar
Keyword(s):  
Fuzzy Logic ◽  
Real Number ◽  
Truth Values

Smartphone is one of the most important things for people nowadays. The increasing number of products as well as the amount information carried by each brand of smartphone can overload, there are many things to consider before buying a smartphone. Fuzzy logic is a form of many- valued logic in which the truth values of variables may be any real number between 0 and 1. Fuzzy logic is one method to analyze system containing uncertainty. This study aims to use fuzzy logic in helping people make decisions on buying the most suitable smartphone for them by producing an output value that can help the user to determine which smartphone will be purchased based on user’s ideal criteria of a smartphone.

Fuzzy Logic and Mathematics

2017 ◽  
Author(s):  
Radim Belohlavek ◽  
Joseph W. Dauben ◽  
George J. Klir
Keyword(s):  
Fuzzy Logic ◽  
Common Ground ◽  
Fundamental Principle ◽  
Paradigm Shifts ◽  
Human Beings ◽  
Truth Values ◽  
Logical Connectives ◽  
Broad Variety ◽  
And Mathematics ◽  
Truth Degrees

The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—true and false. Each logical system subsumed under FL allows for additional, intermediary truth values, which are interpreted as degrees of truth. These systems are distinguished from one another by the set of truth degrees employed, its algebraic structure, truth functions chosen for logical connectives, and other properties. The book examines from the historical perspective two areas of research on fuzzy logic known as fuzzy logic in the narrow sense (FLN) and fuzzy logic in the broad sense (FLB), which have distinct research agendas. The agenda of FLN is the development of propositional, predicate, and other fuzzy logic calculi. The agenda of FLB is to emulate commonsense human reasoning in natural language and other unique capabilities of human beings. In addition to FL, the book also examines mathematics based on FL. One chapter in the book is devoted to overviewing successful applications of FL and the associated mathematics in various areas of human affairs. The principal aim of the book is to assess the significance of FL and especially its significance for mathematics. For this purpose, the notions of paradigms and paradigm shifts in science, mathematics, and other areas are introduced and employed as useful metaphors.

A Mathematical Setting for Fuzzy Logics

1997 ◽  
Vol 05 (03) ◽  
pp. 223-238 ◽  
Author(s):  
Mai Gehrke ◽  
Carol Walker ◽  
Elbert Walker
Keyword(s):  
Fuzzy Logic ◽  
Propositional Logic ◽  
Normal Forms ◽  
Unit Interval ◽  
Fuzzy Logics ◽  
Real Numbers ◽  
Truth Values ◽  
Finite Algebras ◽  
Finite Algorithms ◽  
Interval Valued

The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and -x=1-x for conjunction, disjunction and negation, respectively, is the standard propositional fuzzy logic. This is shown to be the same as three-valued logic. The propositional logic obtained when the algebra of truth values is the set {(a, b)|a≤ b and a,b∈[0,1]} of subintervals of the unit interval with component-wise operations, is propositional interval-valued fuzzy logic. This is shown to be the same as the logic given by a certain four element lattice of truth values. Since both of these logics are equivalent to ones given by finite algebras, it follows that there are finite algorithms for determining when two statements are logically equivalent within either of these logics. On this topic, normal forms are discussed for both of these logics.

A fuzzy logic with interval truth values

2000 ◽  
Vol 113 (2) ◽  
pp. 161-183 ◽  
Author(s):  
Carl W. Entemann
Keyword(s):  
Fuzzy Logic ◽  
Truth Values

scholarly journals FUZZY TYPE THEORY IN THE ANALYSIS OF ARGUMENTATION

2021 ◽  
pp. 37-47
Author(s):  
Oleg Domanov
Keyword(s):  
Fuzzy Logic ◽  
Type Theory ◽  
Proof Assistant ◽  
Truth Values

The article deals with a fazzy variant of P. Martin-Löf ’s intuitionistic type theory. It presents the overview of fuzzy type theory rules and an example of its application to the analysis of the persuasiveness of argumentation. In the latter, the truth values of fuzzy logic are interpreted as degrees of persuasiveness of statements and arguments. The formalization is implemented in the proof assistant Agda.

Modality and Degrees of Truth

2017 ◽  
Author(s):  
Peter Simons
Keyword(s):  
Fuzzy Logic ◽  
Objective Probability ◽  
Possible World ◽  
Third Way ◽  
Truth Values ◽  
World Theory

This chapter explores a third way in construing modality—rejecting both linguistic accounts and the polycosmism of possible world theory—in the work of Alexis Meinong and Jan Łukasiewicz. Some of Meinong’s non-existent objects are incomplete, so in 1915 he accounts for objective probability (he says possibility) with an idea of degrees of truth: the proposition ‘My draw of a card from the pack tomorrow will be a king’ is neither simply wholly true nor wholly false, regardless of the draw I will actually make tomorrow, but has a degree of truth corresponding to the proportion of kings in a pack, between 0 and 1. Łukasiewicz, inventor of fuzzy logic, visited Meinong in Graz, and in 1913 published his own work on probability, suggesting some propositions are indefinite and have truth values between and 0 and 1; then in 1917 he began to extend this to definite propositions about future contingencies.

scholarly journals Properties of Trapezoid Truth Values in Fuzzy Logic

1999 ◽  
Vol 11 (2) ◽  
pp. 338-346 ◽  
Author(s):  
Kazuhiko OTSUKA ◽  
Masashi EMOTO ◽  
Masao MUKAIDONO
Keyword(s):  
Fuzzy Logic ◽  
Truth Values

Further results on infinite valued predicate logic

1964 ◽  
Vol 29 (2) ◽  
pp. 69-78 ◽  
Author(s):  
L. P. Belluce
Keyword(s):  
Real Number ◽  
Present Author ◽  
Closed Interval ◽  
Abelian Groups ◽  
Predicate Logic ◽  
Real Numbers ◽  
The Real ◽  
Truth Values ◽  
Recursively Enumerable ◽  
Weakened Form

In a previous paper [1] Chang and the present author presented a system of infinite valued predicate logic, the truth values being the closed interval [0, 1] of real numbers. That paper was the result of an investigation attempting to establish the completeness of the system using the real number 1 as the sole designated value. In fact, we fell short of our mark and proved a weakened form of completeness utilizing positive segments, [0, a], of linearly ordered abelian groups as admissible truth values. A result of Scarpellini [8], however, showing that the set of well-formed formulas of infinite valued logic valid (with respect to the sole designated real number 1) is not recursively enumerable indicates the above mentioned result is the best possible.

scholarly journals A Theory of Approximate Reasoning with Type-2 Fuzzy Set

2021 ◽  
Vol 27 (1) ◽  
pp. 9-28
Author(s):  
Sudin Mandal ◽  
Injamam Ul Karim ◽  
Swapan Raha
Keyword(s):  
Fuzzy Logic ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Residuated Lattice ◽  
Approximate Reasoning ◽  
Truth Values ◽  
Logic Structure

In this paper, an attempt is made to study approximate reasoning based on a Type-2 fuzzy set theory. In the process, we have examined the underlying fuzzy logic structure on which the reasoning is formulated. We have seen that the partial/incomplete/imprecise truth-values of elements of a type-2 fuzzy set under consideration forms a lattice. We propose two new lattice operations which ultimately help us to define a residual and thereby making the structure of truth- values a residuated lattice. We have focused upon two typical rules of inference used mostly in ordinary approximate reasoning methodology based on Type-1 fuzzy set theory. Our proposal is illustrated with typical artificial examples.

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