scholarly journals On Algebraic Properties of Inverse Fuzzy Languages

2020 ◽  
pp. 59-66
Author(s):  
Pamy Sebastian ◽  
Varghese Jacob
Keyword(s):  
Inverse Monoid ◽  
Fuzzy Language ◽  
Fuzzy Automaton ◽  
Algebraic Properties

Aims/Objectives: In this paper, we investigate some of the algebraic properties of inverse fuzzy languages. We proved that a fuzzy automaton is inverse if and only if the transition monoid is an inverse monoid. A fuzzy language is an inverse fuzzy language if the minimal fuzzy automaton recognizing that fuzzy language is an inverse fuzzy automaton. We also discuss some more properties of an inverse fuzzy language based on the fact that an inverse monoid is one which is regular and idempotent commute.

The Relationship Among Fuzzy Languages, Upper Sets and Fuzzy Ordered Monoids

2019 ◽  
Vol 15 (02) ◽  
pp. 361-372
Author(s):  
M. K. Dubey ◽  
S. P. Tiwari
Keyword(s):  
Ordered Monoid ◽  
Fuzzy Language ◽  
Fuzzy Automaton ◽  
The Relationship

The concept of recognizability of a fuzzy language by crisp deterministic fuzzy automaton and monoid is well known. The purpose of the present work is to study the recognizability of fuzzy languages by fuzzy ordered monoids. We show that the upper sets of a given fuzzy ordered monoid play a nice role in such studies. Also, we introduce the syntactic fuzzy ordered monoid of an upper set which recognizes this upper set.

Categories of Automata and Languages Based on a Complete Residuated Lattice

2018 ◽  
Vol 14 (03) ◽  
pp. 423-444 ◽  
Author(s):  
Vinay Gautam ◽  
S. P. Tiwari ◽  
Priyanka Pal ◽  
Jayanti Tripathi
Keyword(s):  
Residuated Lattice ◽  
Fuzzy Language ◽  
Fuzzy Automaton ◽  
Complete Residuated Lattice ◽  
Categorical Framework ◽  
Fuzzy Automata

The purpose of this paper is to introduce a new category of fuzzy automata based on complete residuated lattice. We introduce and study the categorical concepts such as product, equalizer and their duals in this category. Finally, we establish a construction of a minimal fuzzy automaton for a given fuzzy language in a categorical framework. The construction of such fuzzy automaton is based on derivative of a given fuzzy language.

scholarly journals Minimization of Hesitant L-Fuzzy Automaton

2021 ◽  
Author(s):  
Marzieh Shamsizadeh ◽  
Mohammad Mehdi Zahedi ◽  
Mohamad Javad Agheli Goki
Keyword(s):  
Time Complexity ◽  
Fuzzy Language ◽  
Fuzzy Automaton ◽  
Fuzzy Automata

Abstract In this paper, we study a new generalization for the notion of fuzzy automata, which we called hesitant L-fuzzy automaton (HLFA). We present the formulations of the mathematics framework for the theory of HLFA. Moreover, we present the concepts of hesitant L-fuzzy behavior and inverse hesitant L-fuzzy behavior recognized by a type of HLFA. After that, for any hesitant L-fuzzy language we present a minimal complete accessible deterministic hesitant L-fuzzy automaton recognizing that. Finally, we present an algorithm, which determines states of the minimal hesitant L-fuzzy automaton and we present the time complexity of the algorithm.

scholarly journals L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1538-1546
Author(s):  
Xin Zhou ◽  
Liangyun Chen ◽  
Yuan Chang
Keyword(s):  
Fuzzy Sets ◽  
Homomorphic Image ◽  
Quotient Algebra ◽  
Algebraic Properties ◽  
Novikov Algebras ◽  
Fuzzy Ideal

Abstract In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal.

On Some Rings of Arithmetical Functions

1999 ◽  
Vol 6 (4) ◽  
pp. 299-306
Author(s):  
D. Bhattacharjee
Keyword(s):  
Arithmetical Functions ◽  
Algebraic Properties

Abstract In this paper we consider several constructions which from a given 𝐵-product *𝐵 lead to another one . We shall be interested in finding what algebraic properties of the ring 𝑅𝐵 = 〈𝐶ℕ, +, *𝐵〉 are shared also by the ring . In particular, for some constructions the rings 𝑅𝐵 and will be isomorphic and therefore have the same algebraic properties.

An algebraic approach to N-soft sets with application in decision-making using TOPSIS

2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Real World ◽  
Algebraic Approach ◽  
Multi Criteria Decision Making ◽  
Commutative Monoids ◽  
Soft Sets ◽  
Algebraic Properties ◽  
Different Types ◽  
Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

scholarly journals New Inner Product Quasilinear Spaces on Interval Numbers

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Hacer Bozkurt ◽  
Yılmaz Yilmaz
Keyword(s):  
Functional Analysis ◽  
Inner Product ◽  
Interval Numbers ◽  
Algebraic Properties ◽  
Interval Space

Primarily we examine the new example of quasilinear spaces, namely, “IRninterval space.” We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependence-independence and basis on quasilinear functional analysis, we obtain some results onIRninterval space related to these concepts. Secondly, we presentIs,Ic0,Il∞, andIl2quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis.

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