Logic and Foundations Commons^™

Opening The Lantern: The Leiden Declaration, Mark Huber

Journal of Humanistic Mathematics

The Leiden Declaration on Artificial Intelligence and Mathematics provides insight into how mathematicians view their discipline. However, when positioning mathematics against AI, the declaration falls short in recognizing recent advances. This column introduces the reader who might be unfamiliar with these new methods through the formal language Lean and discusses how these new abilities might change the way journals operate.

Riding The Rails Of Reason: A Dialogue On Truth, Logic, And Proof, Surinder Pal Singh Kainth

Journal of Humanistic Mathematics

On a quiet train ride, I found myself in conversation with Noor, an inquisitive teenager with sharp questions about truth, logic, and mathematical proof. As we talked, I used the train itself as a metaphor to explain how mathematical proofs provide certainty, far beyond what repetitive verification alone can offer. Our discussion ranged from common misconceptions about the foundations of logic to the need for clear definitions and axioms. We also touched on fundamental ideas such as the challenges posed by the Axiom of Choice and the limitations revealed by Gödel’s incompleteness theorem.

(R2177) Further Study On Intuitionistic Fuzzy Matrices, S. Sriram, A. Anitha

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a comprehensive study of the distributive law associated with two newly introduced operations addition and multiplication defined on Intuitionistic Fuzzy Matrices (IFMs). The proposed operations are systematically examined to investigate their algebraic properties, with particular emphasis on the behavior of the distributive law under these novel definitions. Furthermore, modal and extended modal operators are employed to establish several theoretical results that reinforce the mathematical foundation of the proposed framework. The validity and practical relevance of these results are further demonstrated through applications in decision-making scenarios, highlighting their effectiveness in addressing complex problems characterized by uncertainty.

(R2170) Delta-Continuous Functions In Interval-Valued Neutrosophic Soft Topological Spaces And An Application Using Distance And Similarity Measures, B. Vijayalakshmi, S. Madhunika

Applications and Applied Mathematics: An International Journal (AAM)

This paper introduces delta-continuous functions in interval-valued neutrosophic soft topological spaces and investigates their fundamental properties. Additionally, delta-irresolute functions are introduced within the same framework. The relationships between these functions and existing function classes are explored. Several theorems, accompanied by illustrative examples, are provided to support the theoretical findings. The study also includes an application of the proposed concepts to distance and similarity measures.

(R2187) Analysis Of Neurological Impairments In Hospitalized Patients Using Cubic Neutrosophic Sets, B. Anitha, M. Lavanya

Applications and Applied Mathematics: An International Journal (AAM)

This study introduces an MCDM-based framework for identifying neurological diseases in hospitalized patients using symptom-based evaluations. A team of interns, guided by the chief doctor, was responsible for determining each patient’s precise condition from the presented neurological symptoms. To enhance diagnostic accuracy, the interns employed the TOPSIS and WASPAS methods to assess and rank the potential disease options. The combined analysis yielded a clear identification of the highest ranked disease for every patient, highlighting the effectiveness of these MCDM techniques in supporting clinical decision making.

Classes Of Analytic Functions Defined By Salagean Derivative Operator Associated With Neutrosophic Generalized Poisson Distribution, Soliu O. Opeyemi Okunola, Olushola Adeyemo, Sayo A. Abidemi Gbangbala, Folorunso I. Isola Akinwale

Neutrosophic Systems with Applications

This study introduces and analyses new subclasses of analytic functions by applying the Salagean derivative operator to the Neutrosophic Generalized Poisson Distribution (NGPD) series. We develop a model where the mean parameter is treated as an interval or set to account for indeterminacy in complex systems. By employing Stirling numbers of the second kind and decreasing factorials, we derive necessary and sufficient coefficient inequalities and inclusion relations for these new subclasses. Numerical results and graphical illustrations demonstrate the sensitivity of these functions to orientation and the neutrosophic parameter, providing a framework for applications in fields like medical imaging and network …

Objections To The Use Of The Axiom Of Choice To Model The Physical World, Kensey Doughtie

Rose-Hulman Undergraduate Mathematics Journal

We look at platonistic mathematics and the application of this perspective in the physical world. We recognize paradoxes within Zermelo–Fraenkel set theory with the axiom of choice (ZFC) that conflict with physical reality, giving us reason to question if the axiom of choice should be so freely applied in theories of the physical world especially since it appears to enable a deterministic perspective. In theories of quantum physics, the axiom of choice is used to assume noncomputable numbers as initial conditions. This is equivalent to assuming a finite system contains an infinite amount of information at an instant in time; …

A Virtual Community Math Circle, Skona Brittain, Sayonita Ghosh Hajra, Steve Heller, Daniel Hodgins, Peter Petto, Gabriella Pinter, Lauren Rose, A. Gwinn Royal, Asmita Sodhi

Journal of Math Circles

The Julia Robinson Mathematics Festival (JRMF) Community Math Circle is free, volunteer-run, and online. We collaborate with JRMF and use their activities in our events. Started during the pandemic, the Community Math Circle continues to thrive. We have about 40 participants attending every month, typically kids aged 6 to 13, teachers, facilitators, and other adults. This article describes how our event is organized, planned, and executed, and how we train facilitators. We will also offer reflections on our successes and challenges.

(R2127) On 2-Absorbing Hesitant Primary Fuzzy Ideals Of Rings, B. Anitha, M. Vidhya

Applications and Applied Mathematics: An International Journal (AAM)

By presenting 2-absorbing hesitant primary fuzzy ideals, we begin the investigation of a generalisation of hesitant primary fuzzy ideals (HPRFI) in rings in this research. The concepts of a weakly completely 2-absorbing hesitant primary fuzzy ideal (WC2-AHPRFI) and a Weakly completely 2-absorbing hesitant fuzzy ideal (WC2-AHFI) are developed, and their structural features and attributes are examined. We introduce the idea of a 2-absorbing hesitant K-fuzzy ideal (2-AHK-FI), 2-absorbing hesitant K-primary fuzzy ideal (2-AHK-PRFI) and examine a few of its characteristics.

(Si15-017) Modeling Construction Project Uncertainty Using Fuzzy Inference And Nature-Inspired Metaheuristic Knowledge-Based Algorithms, M. Kapoor, B. K. Pathak, R. Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Construction projects are influenced by various uncertain factors, including supervisory knowledge, labor expertise, and weather conditions. These uncertain factors have linguistic properties that are challenging to quantify with the help of traditional set theory. To address this, the study applies fuzzy inference systems, specifically the Mamdani fuzzy inference system, to model and evaluate the impact of these uncertainties on construction projects. This fuzzy inference system provides a more nuanced understanding of these factors compared to traditional set theory methods. Experimental results indicate that uncertainties significantly impact construction projects. These findings establish a valuable framework for developing adaptive strategies, enhancing project …

(Si15-067) Ahp And Moora Decision Making Methods On Bipolar Fuzzy Sets, S. Anita Shanthi, R. Preethi

Applications and Applied Mathematics: An International Journal (AAM)

Decision making, in the present contemporary world, has been inherently complicated. Nowadays, the major challenge is the selection of an appropriate option. The arrival of numerous brands and models makes a purchase challenging. Hence, in this paper, four different models of the same branded laptops are considered, for the selection of an appropriate option, using the Analytic Hierarchy Process (AHP) and Multi-Objective Optimization on the basis of Ratio Analysis (MOORA), with bipolar fuzzy sets, which help decision makers arrive at the most logical choice based on their preferences. The bipolar fuzzy Analytic Hierarchy Process efficaciously supports decision making in cases …

A Dualistic Interpretation Of Mathematical Creation Through Art And Argumentation, Sofia Almpani, Petros Stefaneas, Mihir Chakraborty

Journal of Humanistic Mathematics

Creativity, informal reasoning and dynamic exchange of ideas form the pulsating heart of mathematical creation. In this approach, the concept of a mathematical object surpasses conventional boundaries of formal presentation, as they also encompass the intention to prove, significant creative stages within the proving, and the overall experience of prover's journey, which may involve arguments, debates, discovery insights, aesthetic visualizations, and narrative elements. In this paper we present two conceptual frameworks, namely Argumentation-based Proof-Events Calculus (APEC) and Mathematical RUPAs, in order to provide distinct yet interconnected perspectives on informal thinking, knowledge creation, and proving in mathematics. Following the two perspectives, …

Belonging, Lawrence M. Lesser

Journal of Humanistic Mathematics

No abstract provided.

The Making Of Mathematics: An Interview With Carlo Cellucci, Marshall Gordon

Journal of Humanistic Mathematics

Carlo Cellucci is professor emeritus of the Sapienza University of Rome, and has written books on logic, mathematics, and philosophy. In the following interview conducted via back-and-forth email correspondence, he discusses his 2022 book, The Making of Mathematics: Heuristic Philosophy of Mathematics [3], which presents a new paradigm for thinking about, doing, and teaching mathematics.

Discordium Mathematica - A Symphony In Aleph Minor, Vijay Fafat

Journal of Humanistic Mathematics

How did Mathematics arise? Who created it? Why is it subject to Godel’s Incompleteness Theorems? And what does all this have to do with Coleridge’s poem, “Kubla Khan”, and “The Person from Porlock”? Here is a complete mythology of Mathematics set in an epic poetry format, fusing thoughts and verses from Western religions and Eastern mysticism… Those with immense patience and careful reading shall reap the fruit… (best read on a large screen or in printed form)

(R2068) A Study To Assess The Stress On Students Of Higher Education During Covid-19 Using Fuzzy Logic System, Monika Rathore, Uday Raj Singh, Sanjeev Kumar

Applications and Applied Mathematics: An International Journal (AAM)

The COVID-19 pandemic significantly disrupted various sectors, with higher education being one of the most severely affected. Students in higher education faced numerous challenges transitioning to online learning, leading to a surge in mental health issues. The abrupt shift in the mode of education and the inability of many students to adapt exacerbated their mental health struggles. This, in turn, contributed to a notable rise in student suicide rates in India during the pandemic-induced isolation period. Addressing this critical socio-psychological issue requires effective strategies for stress detection and management. The proposed study employed the Online Education Stress Scale (Online ESS) …

(R2087) Modal Operators On Bipolar Intuitionistic Fuzzy Matrices, T. Muthuraji, P. Punitha Elizabeth

Applications and Applied Mathematics: An International Journal (AAM)

Bipolar intuitionistic fuzzy sets are currently a robust area in several industries. Additionally, bipolar intuitionistic fuzzy matrices are a highly regarded topic in many fields including psychology, engineering, qualitative reasoning and multi-criteria decision making. A civilization must deal with negative and positive problems. In this article, we discussed some algebraic properties of modal operators on bipolar intuitionistic fuzzy matrices. Finally, we derive some results of necessity and possibility operators along with Max-Min product.

(R2082) Two New Operations And Extended Modal Operators On Bipolar Pythagorean Fuzzy Matrices, S. Sriram, K. Sivaranjani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, two novel binary operations concerning bipolar Pythagorean fuzzy matrices are delineated. Several algebraic properties, such as commutativity and associativity, are explored. Additionally, extended modal operators for Bipolar Pythagorean fuzzy matrices are introduced. Subsequently, these methodologies are applied to a decision-making scenario wherein a scoring matrix is formulated and alternatives are ranked according to their cumulative score values.

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

(R1986) Neutrosophic Soft Contra E-Continuous Maps, Contra E-Irresolute Maps And Application Using Distance Measure, P. Revathi, K. Chitirakala, A. Vadivel

Applications and Applied Mathematics: An International Journal (AAM)

We introduce and investigate neutrosophic soft contra e-continuous maps and contra e-irresolute maps in neutrosophic soft topological spaces with examples. Also, neutrosophic soft contra econtinuous maps are compared with neutrosophic soft continuous maps, δ-continuous maps, δ- semi continuous maps, δ-pre continuous maps and e∗ continuous maps in neutrosophic soft topological spaces. We derive some useful results and properties related to them. An application in decision making problem using distance measure is given. An example of a candidate selection from a company interview is formulated as neutrosophic soft model problem and the hamming distance measure is applied to calculate the distance …

(R1957) Some Types Of Continuous Function Via N-Neutrosophic Crisp Topological Spaces, A. Vadivel, C. John Sundar

Applications and Applied Mathematics: An International Journal (AAM)

The aim of this article is to introduced a new type of continuous functions such as N-neutrosophic crisp gamma continuous and weakly N-neutrosophic crisp gamma continuous functions in a N-neutrosophic crisp topological space and also discuss a relation between them in a N-neutrosophic crisp topological spaces. We also investigate some of their properties in N-neutrosophic crisp gamma continuous function via N-neutrosophic crisp topological spaces. Further, a contra part of continuity called N-neutrosophic crisp gamma-contra continuous map in a N-neutrosophic crisp topology is also initiated. Finally, an application based on neutrosophic score function of medical diagnosis is examined with graphical representation.

(R1997) Distance Measures Of Complex Fermatean Fuzzy Number And Their Application To Multi-Criteria Decision-Making Problem, V. Chinnadurai, S. Thayalan, A. Bobin

Applications and Applied Mathematics: An International Journal (AAM)

Multi-criteria decision-making (MCDM) is the most widely used decision-making method to solve many complex problems. However, classical MCDM approaches tend to make decisions when the parameters are imprecise or uncertain. The concept of a complex fuzzy set is new in the field of fuzzy set theory. It is a set that can collect and interpret the membership grades from the unit circle in a plane instead of the interval [0,1]. CFS cannot deal with membership and non-membership grades, while complex intuitionistic fuzzy set and complex Pythagorean fuzzy set works only for a limited range of values. The concept of a …

(R1965) Some More Properties On Generalized Double Fuzzy Z Alpha Open Sets, K. Jayapandian, A. Saivarajan, O. Uma Maheswari, J. Sathiyaraj

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new class of sets termed as double fuzzy generalized Z alpha closed sets and double fuzzy generalized Z alpha open sets are introduced with the help of double fuzzy Z alpha open and double fuzzy Z alpha closed sets, respectively. Using these sets double fuzzy generalized Z alpha border, double fuzzy generalized Z alpha exterior and double fuzzy generalized Z alpha frontier of a fuzzy set in double fuzzy topological spaces are introduced. Also, the topological properties and characterizations of these sets and operators are studied. Furthermore, suitable examples have been provided to illustrate the theory.

Self-Reference And Diagonalisation, Joël A. Doat

Journal of Humanistic Mathematics

This poem is an exercise on self-reference and diagonalisation in mathematics featuring Turing’s proof of the undecidability of the halting problem, Cantor’s cardinality argument, the Burali-Forti paradox, and Epimenides' liar paradox.

Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur

Journal of Humanistic Mathematics

Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …

(R1500) Type-I Generalized Spherical Interval Valued Fuzzy Soft Sets In Medical Diagnosis For Decision Making, M. Palanikumar, K. Arulmozhi

Applications and Applied Mathematics: An International Journal (AAM)

In the present communication, we introduce the concept of Type-I generalized spherical interval valued fuzzy soft set and define some operations. It is a generalization of the interval valued fuzzy soft set and the spherical fuzzy soft set. The spherical interval valued fuzzy soft set theory satisfies the condition that the sum of its degrees of positive, neutral, and negative membership does not exceed unity and that these parameters are assigned independently. We also propose an algorithm to solve the decision making problem based on a Type-I generalized soft set model. We introduce a similarity measure based on the Type-I …

(R1958) On Deferred Statistical Convergence Of Fuzzy Variables, Ömer Kişi, Mehmet Gürdal, Ekrem Savaş

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, within framework credibility theory, we examine several notions of convergence and statistical convergence of fuzzy variable sequences. The convergence of fuzzy variable sequences such as the notion of convergence in credibility, convergence in distribution, convergence in mean, and convergence uniformly virtually certainly via postponed Cesàro mean and a regular matrix are researched using fuzzy variables. We investigate the connections between these concepts. Significant results on deferred statistical convergence for fuzzy variable sequences are thoroughly investigated.

(R2022) Mathematical Modelling Of Tuberculosis And Covid-19 Co-Infection In India: A Real Data Analysis On Concomitant Diseases, Vijai Shanker Verma, Harshita Kaushik, Archana Singh Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have proposed an epidemiological model to study the dynamics of two concomitant diseases Tuberculosis (TB) and COVID-19. Here, we have formulated a deterministic compartmental model as an extended form of the classical SIS model. First, the basic reproduction number R₀ is derived and then stability analysis of the model is done. It is observed that the disease-free equilibrium is stable when R₀ is less than one and the endemic equilibrium is stable only when R₀ is greater than one. Numerical simulation is carried out to illustrate the theoretical findings and to study the …

(R1509) Topsis And Vikor Methods For Spherical Fuzzy Soft Set Aggregating Operator Framework, M. Palanikumar, K. Arulmozhi, Lejo J. Manavalan

Applications and Applied Mathematics: An International Journal (AAM)

The Spherical Fuzzy Soft (SFS) set is a generalization of the Pythagorean fuzzy soft set and the intuitionistic fuzzy soft set. We introduce the concept of aggregating SFS decision matrices based on aggregated operations. The techniques for order of preference by similarity to ideal solution (TOPSIS) and viekriterijumsko kompromisno rangiranje (VIKOR) for the SFS approaches are the strong points of multi criteria group decision making (MCGDM), which is various extensions of fuzzy soft sets. We define a score function based on aggregating TOPSIS and VIKOR methods to the SFS-positive and SFS-negative ideal solutions. The TOPSIS and VIKOR methods provide decision-making …

(R1960) Connectedness And Compactness In Fuzzy Nano Topological Spaces Via Fuzzy Nano Z Open Sets, R. Thangammal, M. Saraswathi, A. Vadivel, C. John Sundar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study the notion of fuzzy nano Z connected spaces, fuzzy nano Z disconnected spaces, fuzzy nano Z compact spaces and fuzzy nano Z separated sets in fuzzy nano topological spaces. We also give some properties and theorems of such concepts with connectedness and compactness in fuzzy nano topological spaces.