Mani A.

• Ph.d, M.Sc, B.Sc., PGD,
• Senior Member at International Rough Set Society

Antichain based semantics for general rough sets was introduced recently by the present author. In her paper two different semantics, one for general rough sets and another for general approximation spaces over quasi-equivalence relations, were developed. These semantics are improved and studied further from a lateral algebraic logic and an algebra...

This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the boo...

In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and variants were recently introduced by the present author as an optimal framework for anti-chain based algebraic sem...

Rough sets are used in numerous knowledge representation contexts, and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalizations of graded and variable precision rough sets are investigated by the present author from the pe...

Several types of ethnomathematics are studied in the literature, and they come with their own questions, problems of representation, and classification. Approximate reasoning or rather reasoning over vaguely defined entities (real or abstract), and uncertain information is natural to ethnomathematics, and human interactions. The main issue is one o...

The collective concept of clean rough randomness (C-rough randomness), with the explicit purpose of handling meaning in vague and dynamic contexts of rough reasoning (and therefore meaningful artificial intelligence and machine learning), is recently introduced by the present author. These ideas are applied to propose validation methods for soft an...

Granular rough sets (GRST) from axiomatic algebraic perspective perspectives are potentially capable of solving the problem of meaning in AI (specifically generative AI) through the following specific interrelated methodologies: 1. Representations of dependence between subsets of attributes by other subsets of attributes (and a related new theory o...

Anthropomorphic perspectives are frequently used to represent or misrepresent information concerning living, and non-living entities, particularly in sociology, biology, and artificial intelligence. Formal models of related approximate reasoning patterns are of natural interest, given the research trends in the last-mentioned area. In this research...

The concepts of precision, and accuracy are domain and problem dependent. The simplified numeric hard and soft measures used in the fields of statistical learning, many types of machine learning, and binary or multiclass classification problems are known to be of limited use for understanding the meaningfulness of models or their relevance. Arguabl...

This talk is intended to cover aspects of research on applications of mereological methods and general rough sets to problems in education research due to the present author. Specifically, her talk features a broad introduction to mereology, and applications to modeling students' and teachers' languages of discourse, and STEM. Further research dire...

The concepts of precision, and accuracy are domain and problem dependent. The simplified numeric hard and soft measures used in the fields of statistical learning, many types of machine learning, and binary or multiclass classification problems are known to be of limited use for understanding the meaningfulness of models or their relevance. Arguabl...

It is known that LBTQIA+ people experience much harassment, discrimination, and marginalization in the STEM ecosystem in India. This talk is about issues in policymaking and related interventions in the light of their lived experiences, and related theoretical insights. [Note: Some of the slides were used in the invited talk].

The concept of clean rough randomness (C-rough randomness), with the explicit purpose of handling meaning in vague and dynamic contexts of rough reasoning (and therefore meaningful artificial intelligence and machine learning), is recently introduced by the present author. These ideas are applied to propose validation methods for soft and hard clus...

(Full Version of my ICME-15 Slides: I used about 23 slides in my talk.) Abstract: Mereology is the study of parts, wholes, related predicates and predications. While the subject finds wide application in specialized areas, it has not been explored in matching depth in education research, and specifically in mathematics education. A recent paper, d...

MR4461095 03-02 03B52 03G27 08C20 Bonzio, Stefano (I-CAGL-MI) ; Paoli, Francesco (I-CAGL-PPQ) ; Pra Baldi, Michele (E-CSIC-AI) FLogics of variable inclusion. Trends in Logic—Studia Logica Library, 59. Springer, Cham, [2022],

Up-directed rough sets are introduced and studied by the present author in earlier papers. This is extended by her in two different granular directions in this research, with a surprising algebraic semantics. The granules are based on ideas of generalized closure under up-directedness that may be read as a form of weak consequence. This yields appr...

A teacher's knowledge base consists of knowledge of mathematics content, knowledge of student epistemology, and pedagogical knowledge. It has severe implications on the understanding of student's knowledge of content, and the learning context in general. The necessity to formalize the different content knowledge in approximate senses is recognized...

Concepts of precision are used in different contexts in various senses. While every case has re- lated structural properties associated, only some are justifiably quantifiable in terms of real num- bers. For example, an ancient Egyptian limestone sculpture may be said to be precisely sculpted with great skill using simple tools. The idea of precisi...

A number of generalizations of stochastic and information-theoretic randomness are known in the literature. In earlier research, it is shown by the present author and others that probabilistic methods are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore meaningful AIML) [1, 2]. Based on these, new...

Five of my recent reviews for AMS Mathematical Reviews.

In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional meaning that go beyond structural conjunction and disjunction as in the theory of \(*\)-norms and associated implic...

In this research, new concepts of existential granules that determine themselves are invented, and are characterized from algebraic, topological, and mereological perspectives. Existential granules are those that determine themselves initially, and interact with their environment subsequently. Examples of the concept, such as those of granular ball...

Mereology is the study of parts, wholes, related predicates and predications. While the subject finds wide application in specialized areas, it has not been explored in matching depth in education research, and specifically in mathematics education. A recent paper, due to the present author, explores potential areas of development for STEAM, in gen...

In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional meaning that go beyond structural conjunction and disjunction as in the theory of $*$-norms and associated implicat...

In this research, new concepts of existential granules that determine themselves are invented, and are characterized from algebraic, topological, and mereological perspectives. Existential granules are those that determine themselves initially, and interact with their environment subsequently. Examples of the concept, such as those of granular ball...

In this research, new concepts of existential granules that determine themselves are invented, and are characterized from algebraic, topological, and mereological perspectives. Existential granules are those that determine themselves initially, and interact with their environment subsequently. Examples of the concept, such as those of granular ball...

In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional meaning that go beyond structural conjunction and disjunction as in the theory of $*$-norms and associated implicat...

Several methods of approximate reasoning are known, and many remain to be discovered across domains. Some are tied to reasoning with uncertainty. The developments over the last fifty years or so in the development of approximate reasoning methods, and their application across multiple STEM domains, suggest that it is necessary to introduce them ear...

Extended abstract: Several methods of approximate reasoning are known, and many remain to be discovered across domains. Some are tied to reasoning with uncertainty. The developments over the last fifty years or so in the development of approximate reasoning methods, and their application across multiple STEM domains, suggest that it is necessary to...

A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable artificial intelligence and machine learning). In this research, new concepts of rough randomness that are neit...

A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable artificial intelligence and machine learning). In this research, new concepts of rough randomness that are neit...

Rough sets are used in a number of knowledge representation contexts, and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalizations of graded and variable precision rough sets are investigated by the present author from the...

A phenomenon is stochastically random if it has probabilistic regularity in the absence of other types of regularity [1]. On the other hand, a sequence is algorithmically random if and only if no computational agent recognizes it as possessing some rare property (that is, properties valid over a set of measure zero that could be tested in a suffici...

The concept of rational discourse is typically determined by subjective, normative, and rule based constraints in the context under consideration. It is typically determined by related ontologies, and coherence between associated concepts employed in the discourse. Classical rough approximations, and variants of variable precision rough sets (VPRS)...

Up-directed rough sets are introduced and studied by the present author in earlier papers. This is extended by her in two different granular directions in this research, with a surprising algebraic semantics. The granules are based on ideas of generalized closure under up-directedness that may be read as a form of weak consequence. This yields appr...

Up-directed rough sets are introduced and studied by the present author in earlier papers. This is extended by her in two different granular directions in this research, with a surprising algebraic semantics. The granules are based on ideas of generalized closure under up-directedness that may be read as a form of weak consequence. This yields appr...

Up-directed rough sets are introduced and studied by the present author in earlier papers. This is extended by her in two different granular directions in this research, with a surprising algebraic semantics. The granules are based on ideas of generalized closure under up-directedness that may be read as a form of weak consequence. This yields appr...

Rational approximations are introduced and studied in granular graded sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between granularity, parthood perspective and approximations used in the context. In addition, a framework is introduced by...

Mereology is widely applied in STEAM and philosophy. However, serious applications tend to be restricted to specialist groups or the nature of applications is too focused. In addition, methodologies associated do not percolate to school or college-level classroom discourses in a clear way. This is worrying because mereology can be used for effectiv...

Rational approximations are introduced and studied in granular graded sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between granularity, parthood perspective and approximations used in the context. In addition, a framework is introduced by...

Compositionality is essential for reducing the complexity of AIML models. This is naturally related to knowledge representation and granularity. These, in turn, can be done in different ways. Also, approximate reasoning and decision-making essentially involve knowledge representation and granularity. In the talk, the following topics will be review...

The concept of rational discourse is typically determined by subjective, normative, and rule based constraints in the context under consideration. It is typically determined by related ontologies, and coherence between associated concepts employed in the discourse. Classical rough approximations, and variants of variable precision rough sets (VPRS)...

In this research, directed and parthood relations are studied in the context of general rough sets. This extends earlier work on directed approximation spaces. The relations are also specialized to representations of general parthood that are upper-directed, reflexive and anti-symmetric for a better behaved groupoidal semantics over the set of roug...

A number of numeric measures like rough inclusion functions (RIFs) are used in general rough sets and soft computing. But these are often intrusive by definition, and amount to making unjustified assumptions about the data. The contamination problem is also about recognizing the domains of discourses involved in this, specifying errors and reducing...

Of the many generalizations of rough sets in the literature, graded rough sets are among the most controversial. When approached from a pointwise perspective, these are closely related to graded modal logic. In this research, a few granular generalizations are proposed by the present author. Some mistakes in the literature are rectified, and defina...

In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realized in a situation (and therefore in a semantics). \emph{It is well-known that...

In this research a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realized in a situation (and therefore in a semantics). It is well-known that of the...

A number of numeric measures like rough inclusion functions (RIFs) are used in general rough sets and soft computing. But these are often intrusive by definition, and amount to making unjustified assumptions about the data. The contamination problem is also about recognizing the domains of discourses involved in this, specifying errors and reducing...

Diversity-friendly and inclusive practices, in the Indian context, are hindered by a spectrum of issues ranging from machinations of the patriarchy sustained by systems of microaggressions, policies disconnected from stakeholders, missing support systems, unscientific colonial mindset of people, hubris of societal norms, and ineffective policies am...

This is the much extended version of my IFSA-EUSFLAT'2021 paper.

It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the present research, a proposal based on mereological principles is advanced towards solving aspects of the problem by...

It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the present research, a proposal based on mereological principles is advanced towards solving aspects of the problem by...

In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realized in a situation (and therefore in a semantics). \emph{It is well-known that...

Tabular representation of information can be traced to ancient times. They were and are used in a wide variety of ways. While every table is essentially a list, their interpretation varies from the simpler to the very complex. This aspect is explored in some detail by the present author. Based on the considerations, she suggests a number of ways of...

Concepts of granules and granular computing have evolved from a number of perspectives over the last few decades. In this short expository paper, the present author discusses aspects of Zadeh’s contributions to a specific form of granular computing especially in the contexts of fuzzy sets, computing with words, and AI. Further she mentions new area...

Education research is a relatively young field with a history that goes back to about 100 years or so. Work done in various parts of the world has contributed to a better understanding of the complexity of associated problems, and their related social context. But most teachers and academics are not aware of methodologies and issues in teaching, an...

It is well-known that concepts of cluster validity and associated rationale are far from being satisfactory from multiple perspectives. Indices are usually controversial. The scope of a model based approach from a statistical, mereo-topological, graph-theoretical, neural network or soft perspective, for example, is apparently limited by methodologi...

In this research a general theoretical framework for abstract clustering is proposed from a philosophical perspective of increasing semantic assumptions over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realize...

Post publication review of the following papers: 1. MR3958325 03G27 03C05 03D15 08B05 Moraschini, Tommaso (CZ-AOS-IC) On the complexity of the Leibniz hierarchy. (English summary) Ann. Pure Appl. Logic 170 (2019), no. 7, 805–824. 2. MR4027123 03E72 Wu, Hsien-Chung (RC-NKNU-M) Generalized extension principle for non-normal fuzzy sets. (English summ...

The book is intended to introduce general rough methods from a relatively philosophical perspective to researchers in the field of education.

The purpose of this book is to serve as an advanced introduction to issues of gender diversity in STEM education, pedagogical practices, and related research areas.

In the context of education research, a concept inventory is an instrument (that consists of a number of multiple-choice questions) designed to test the understanding of concepts (and possibly the reasons for failure to understand) by learners. Subject to a few caveats they are known to be somewhat effective in non student centric learning environm...

A number of low and high-level models of general rough sets can be used to represent knowledge. Often binary relations between attributes or collections thereof have deeper properties related to decisions, inference or vision that can be expressed in ternary functional relationships (or groupoid operations) – this is investigated from a minimalist...

A number of nonequivalent perspectives on granular computing are known in the literature, and many are in states of continuous development. Further, related concepts of granules and granulations may be incompatible in many senses. This expository paper is intended to explain basic aspects of these from a critical perspective, their range of applica...

In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general parthood that are upper-directed, reflexive and antisymmetric for a better behaved groupoidal semantics over...

A number of low and high-level models of general rough sets can be used to represent knowledge. Often binary relations between attributes or collections thereof have deeper properties related to decisions, inference or vision that can be expressed in ternary functional relationships (or groupoid operations)-- this is investigated from a minimalist...

In the context of education research, a concept inventory is an instrument (that consists of a number of multiple-choice questions) designed to test the understanding of concepts (and possibly the reasons for failure to understand) by learners. Subject to a few caveats they are known to be somewhat effective in non student centric learning environm...

Microaggressions are small, subtle, often subconscious actions that marginalize people in oppressed groups including women. Sue (1973) defined it as brief and commonplace daily verbal, behavioral, or environmental indignities, whether intentional or unintentional, that communicate hostile, derogatory, or negative racial slights and insults. It can...

It is well-known that the participation of women in STEM disciplines at higher levels has been relatively bad across multiple demographics. The situation is due to systemic discrimination that has been and is couched in different ways in and outside the academia. The proof of systemic discrimination is in actualizations that span cultural practices...

Call for Participation https://www.fedcsis.org/2020/fvrm

It is well-known that lesbians, trans and queer women face considerable discrimination, exclusion, stigmatization, and abuse in India. That is over and above the misogyny and discrimination faced by women in the patriarchal country. LGBTQIA people were also criminalized by law till recently. In spite of all the oppression and discrimination, lesbia...

This is an extended version of https://www.researchgate.net/publication/329043829_Granularity_and_Generalized_Inclusion_Functions_-_Their_Variants_and_Contamination

Theories of rough mereology have originated from diverse semantic considerations from contexts relating to study of databases, to human reasoning. These ideas of origin, especially in the latter context, are intensely complex. In this research, the semantics of rough contact relations are studied in detail. Rough mereologies are also situated in re...

[See ArXiv for newer version http://arxiv.org/abs/1811.06560 ] Granular operator spaces and variants had been introduced and used in theoretical investigations on the foundations of general rough sets by the present author over the last few years. In this research, higher order versions of these are presented uniformly as partial algebraic systems....

Theories of rough mereology have originated from diverse semantic considerations from contexts relating to study of databases, to human reasoning. These ideas of origin, especially in the latter context, are intensely complex. In this research, concepts of rough contact relations are introduced and rough mereologies are situated in relation to gene...

It is well-known that lesbians, trans and queer women face considerable discrimination, exclusion, stigmatization, and abuse in India. That is over and above the misogyny and discrimination faced by women in the patriarchal country. LGBTQIA people were also criminalized by law till recently. In spite of all the oppression and discrimination, lesbia...

Theories of rough mereology have originated from diverse semantic considerations from contexts relating to study of databases, to human reasoning. These ideas of origin, especially in the latter context, are intensely complex. In this research, concepts of rough contact relations are introduced and rough mereologies are situated in relation to gene...

Exclusion definitely affects a women’s mathematics. Some classification of the factors that shape the unique features associated can definitely be specified. On the basis of these considerations I propose a new partial theoretical model for accessing the connection between a woman's attitude towards and practice of research in mathematics, and the...

Special Session cum Workshop on "Generalized Rough Inclusion, Graded Inclusion, Granularity and Related Topics" at IJCRS'2019, Debrecen, Hungary

Study of concepts of dependence in general rough sets had been initiated by the present author in some of her recent papers. These have been compared with possible concepts of dependence in generalized probability theory and a new deviant probability framework has also been the result of such an approach. In this research, the mereological content...

The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of translating between the methodologies and possibilities in the identification of concepts. Comparison of ideas...

In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and variants were recently introduced by the present author as an optimal framework for anti-chain based algebraic sem...

Granular operator spaces and variants had been introduced and used in theoretical investigations on the foundations of general rough sets by the present author over the last few years. In this research, higher order versions of these are presented uniformly as partial algebraic systems. They are also adapted for practical applications when the data...

Rough inclusion functions (RIFs) are known by many other names in formal approaches to vagueness, belief, and uncertainty. Their use is often poorly grounded in factual knowledge or involve wild statistical assumptions. The concept of contamination introduced and studied by the present author across a number of her papers, concerns mixing up of inf...

The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of translating between the methodologies and possibilities in the identification of concepts. Comparison of ideas...

Granules are the building blocks of concepts of different types in soft computing and rough sets in particular. These granules can be defined in ways that are related to computing or reasoning strategies associated. In this broad perspective, at least three concepts of granular computing have been studied in the literature. The axiomatic approach i...

In this research chapter, dualities and representations of various kinds associated with the semantics of rough sets are explained, critically reviewed, new proofs have been proposed, open problems are specified and new directions are suggested. Some recent duality results in the literature are also adapted for use in rough contexts. New results ar...

The problem of formalizing rationality of reasoning in AI is mostly handled from the perspective of formal epistemology and modal logics associated with multi agent systems that refer concepts of common knowledge. These differ significantly from ideas of instrumental rationality that is concerned with rationality for a purpose. Many approaches in A...

My talk at WMaC-II

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the inverse problem. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present aut...

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the inverse problem. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present aut...

Beamer Slides of my paper in Special Session on Foundations of Rough Sets, Vagueness and Mereology at IJCRS’2017