scholarly journals A New Model of Fuzzy Logic: Monadic Monoidal T-Norm Based Logic

2022 ◽  
Author(s):  
Saeide Zahiri ◽  
Arsham Borumand Saeid
Keyword(s):  
Fuzzy Logic ◽  
Representation Theorem ◽  
Completeness Theorem ◽  
Subdirectly Irreducible ◽  
New Model ◽  
Basic Properties ◽  
Subdirect Representation ◽  
Ams Classification ◽  
Monadic Filters

Abstract In this article, we introduce the variety of monadic MTL-algebras as MTL-algebras equipped with two monadic operators. After a study of the basic properties of this variety, we define and investigate monadic filters in monadic MTL-algebras. By using the notion of monadic filters, we prove the subdirect representation theorem of monadic MTL-algebras and characterize simple and subdirectly irreducible monadic MTL-algebras. Moreover, present monadic monoidal t-norm based logic (MMT L), a system of many valued logic capturing the tautologies of monadic MTL-algebras and prove a completeness theorem.AMS Classification: 08A72, 03G25, 03B50, 03C05.

Monadic NM-algebras

2019 ◽  
Vol 27 (6) ◽  
pp. 812-835
Author(s):  
Juntao Wang ◽  
Pengfei He ◽  
Yanhong She
Keyword(s):  
Representation Theorem ◽  
Predicate Logic ◽  
Algebraic Semantics ◽  
Subdirectly Irreducible ◽  
Approximation Spaces ◽  
Rough Approximation ◽  
Subdirect Representation ◽  
Algebraic Foundation ◽  
The Relationship ◽  
Monadic Filters

Abstract In this paper, we investigate universal and existential quantifiers on NM-algebras. The resulting class of algebras will be called monadic NM-algebras. First, we show that the variety of monadic NM-algebras is algebraic semantics of the monadic NM-predicate logic. Moreover, we discuss the relationship among monadic NM-algebras, modal NM-algebras and rough approximation spaces. Second, we introduce and investigate monadic filters in monadic NM-algebras. Using them, we prove the subdirect representation theorem of monadic NM-algebras, and characterize simple and subdirectly irreducible monadic NM-algebras. Finally, we present the monadic NM-logic and prove its (chain) completeness with respect to (strong) monadic NM-algebras. These results constitute a crucial first step for providing an algebraic foundation for the monadic NM-predicate logic.

A completeness theorem for higher order logics

2000 ◽  
Vol 65 (2) ◽  
pp. 857-884 ◽  
Author(s):  
Gábor Sági
Keyword(s):  
Set Theory ◽  
Representation Theorem ◽  
Completeness Theorem ◽  
Higher Order ◽  
Algebraic Solution ◽  
Algebraic Proof ◽  
Relation Algebras ◽  
Cylindric Algebras ◽  
Strong Representation ◽  
Algebraic Counterpart

AbstractHere we investigate the classes of representable directed cylindric algebras of dimension α introduced by Németi [12]. can be seen in two different ways: first, as an algebraic counterpart of higher order logics and second, as a cylindric algebraic analogue of Quasi-Projective Relation Algebras. We will give a new, “purely cylindric algebraic” proof for the following theorems of Németi: (i) is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain a strong representation theorem for if one chooses an appropriate (non-well-founded) set theory as foundation of mathematics. These results provide a purely cylindric algebraic solution for the Finitization Problem (in the sense of [11]) in some non-well-founded set theories.

scholarly journals Global Dynamics of a Prey-Predator Model with Antipredator Behavior and Two Predators

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Chentong Li ◽  
Yingying Zhang ◽  
Jinhu Xu ◽  
Yicang Zhou
Keyword(s):  
Antipredator Behavior ◽  
Periodic Oscillation ◽  
Global Dynamics ◽  
Boundedness Of Solutions ◽  
New Model ◽  
Basic Properties ◽  
Predator Model ◽  
Existence Of Equilibria ◽  
Insight Into ◽  
Positivity And Boundedness

In this work, we establish a new model of one prey and two predators with antipredator behavior. The basic properties on the positivity and boundedness of solutions and the existence of equilibria are established. Through analyzing the global dynamics, we find that there exist some values of the parameters such that one of the predators can be driven into being extinct by another. Furthermore, the coexistence of the three species is investigated which shows that the antipredator behavior makes the species coexist by periodic oscillation. The results give a new insight into the influence of antipredator behavior in nature selection.

A New Model to Distinguish Railhead Defects Based on Set-Membership Type-2 Fuzzy Logic System

2020 ◽  
Author(s):  
Eduardo P. de Aguiar ◽  
Thiago E. Fernandes ◽  
Fernando M. de A. Nogueira ◽  
Daniel D. Silveira ◽  
Marley M. B. R. Vellasco ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Logic System ◽  
New Model ◽  
Set Membership ◽  
Logic System

scholarly journals New Approaches to Seismic Microzonation Modelling of Ground Shaking Using Direct Characteristics of Influencing Criteria: Case Study of Bam City, Iran

2018 ◽  
Author(s):  
Reza Hassanzadeh ◽  
Mehdi Honarmand ◽  
Mahdieh Hossienjani Zadeh ◽  
Farzin Naseri
Keyword(s):  
Fuzzy Logic ◽  
Analytic Hierarchy Process ◽  
Rural Areas ◽  
Seismic Microzonation ◽  
Kappa Statistics ◽  
Analytic Hierarchy ◽  
Ground Shaking ◽  
New Model ◽  
New Approaches ◽  
Hierarchy Process

Abstract. This paper proposes a new model in evaluating seismic microzonation of ground shaking by considering direct characteristics of influencing criteria and dealing with uncertainty of modelling through production of fuzzy membership functions for each criterion. The relevant criteria were explored by reviewing previous literature and interviewing 10 specialized experts. Analytic Hierarchy Process (AHP) and Fuzzy Logic (FL) methods were applied in order to define priority rank of each criteria and to fuzzify sub-criteria of each criterion by interviewing 10 experts, respectively. Applying Fuzzy Logic method to deal with uncertainties of sub criteria of each criterion and using direct characteristics of each criterion are the new approaches in designing a new model. The criteria and sub-criteria were combined in GIS to develop a model for assessing microzonation of ground shaking in the study area of Bam city, Iran. The model’s output shows high to very high ground shaking levels were happened in central, east, and northeast to north part of the area. The validation results based on overall accuracy and Kappa statistics showed 80 % to 82 % accuracy, 0.74 and 0.75 Kappa indicating a good fit to the model's output. This model assists planners and decision makers to produce seismic microzonation of ground shaking to be incorporated in designing new development plans of urban and rural areas, and to facilitate making informed decision regarding safety measures of existing buildings and infrastructures. Keywords: Seismic Microzonation, Site Effects, Ground Shaking, Spatial Modelling, Analytic Hierarchy Process, Fuzzy Logic and GIS.

ARITHMETIC MEAN BASED COMPENSATORY FUZZY LOGIC

2011 ◽  
Vol 10 (02) ◽  
pp. 231-243 ◽  
Author(s):  
AGUSTINA BOUCHET ◽  
JUAN IGNACIO PASTORE ◽  
RAFAEL ESPIN ANDRADE ◽  
MARCEL BRUN ◽  
VIRGINIA BALLARIN
Keyword(s):  
Fuzzy Logic ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Arithmetic Mean ◽  
Original Model ◽  
Logic Model ◽  
Boolean Logic ◽  
New Model ◽  
Original Definition ◽  
Continuous Operators

Fuzzy Logic is a multi-valued logic model based on fuzzy set theory, which may be considered as an extension of Boolean Logic. One of the fields of this theory is the Compensatory Fuzzy Logic, based on the removal of some axioms in order to achieve a sensitive and idempotent multi-valued system. This system is based on a quadruple of continuous operators: conjunction, disjunction, order and negation. In this work we present a new model of Compensatory Fuzzy Logic based on a different set of operators, conjunction and disjunction, than the ones used in the original definition, and then prove that this new model satisfies the required axioms. As an example, we present an application to decision-making, comparing the results against the ones based on the original model.

Quasi-discriminator varieties

2014 ◽  
Vol 24 (03) ◽  
pp. 375-411 ◽  
Author(s):  
Francesco Paoli ◽  
Antonio Ledda ◽  
Tomasz Kowalski ◽  
Matthew Spinks
Keyword(s):  
Fuzzy Logic ◽  
General Concept ◽  
Discriminator Variety ◽  
Algebraic Characterization ◽  
Basic Properties ◽  
Discriminator Varieties ◽  
Lattice Of Subvarieties

We generalize the notion of discriminator variety in such a way as to capture several varieties of algebras arising mainly from fuzzy logic. After investigating the extent to which this more general concept retains the basic properties of discriminator varieties, we give both an equational and a purely algebraic characterization of quasi-discriminator varieties. Finally, we completely describe the lattice of subvarieties of the pure pointed quasi-discriminator variety, providing an explicit equational base for each of its members.

scholarly journals Tense θ-valued Moisil propositional logic

2010 ◽  
Vol 5 (5) ◽  
pp. 642 ◽  
Author(s):  
Carmen Chiriţă
Keyword(s):  
Representation Theorem ◽  
Propositional Logic ◽  
Propositional Calculus ◽  
Completeness Theorem ◽  
Logical System ◽  
Tense Operators

In this paper we study the tense θ-valued Moisil propositional calculus, a logical system obtained from the θ-valued Moisil propositional logic by adding two tense operators. The main result is a completeness theorem for tense θ-valued Moisil propositional logic. The proof of this theorem is based on the representation theorem of tense θ-valued Łukasiewicz-Moisil algebras, developed in a previous paper.

scholarly journals Very true operators on MTL-algebras

2016 ◽  
Vol 14 (1) ◽  
pp. 955-969 ◽  
Author(s):  
Jun Tao Wang ◽  
Xiao Long Xin ◽  
Arsham Borumand Saeid
Keyword(s):  
Representation Theorem ◽  
Subdirectly Irreducible ◽  
Mv Algebra ◽  
Left And Right ◽  
Soundness And Completeness ◽  
Gödel Algebra

AbstractThe main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.

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