Physical Sciences and Mathematics Commons^™

When Is A Single "And"-Condition Enough?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, there are several possible decisions. Any general recommendation means specifying, for each possible decision, conditions under which this decision is recommended. In some cases, a single "and"-condition is sufficient: e.g., a condition under which a patient is recommended to take aspirin is that "the patient has a fever and the patient does not have stomach trouble". In other cases, conditions are more complicated. A natural question is: when is a single "and"-condition enough? In this paper, we provide an answer to this question.

Which Fuzzy Implications Operations Are Polynomial? A Theorem Proves That This Can Be Determined By A Finite Set Of Inequalities, Sebastia Massanet, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To adequately represent human reasoning in a computer-based systems, it is desirable to select fuzzy operations that are as close to human reasoning as possible. In general, every real-valued function can be approximated, with any desired accuracy, by polynomials; it is therefore reasonable to use polynomial fuzzy operations as the appropriate approximations. We thus need to select, among all polynomial operations that satisfy corresponding properties -- like associativity -- the ones that best fit the empirical data. The challenge here is that properties like associativity mean satisfying infinitely many constraints (corresponding to infinitely many possible triples of values), while most …

Logical Inference Inevitably Appears: Fuzzy-Based Explanation, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich, Orsolya Csiszar

Departmental Technical Reports (CS)

Many thousands years ago, our primitive ancestors did not have the ability to reason logically and to perform logical inference. This ability appeared later. A natural question is: was this appearance inevitable -- or was this a lucky incident that could have been missed? In this paper, we use fuzzy techniques to provide a possible answer to this question. Our answer is: yes, the appearance of logical inference in inevitable.

Is Fully Explainable Ai Even Possible: Fuzzy-Based Analysis, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main limitations of many current AI-based decision-making systems is that they do not provide any understandable explanations of how they came up with the produced decision. Taking into account that these systems are not perfect, that their decisions are sometimes far from good, the absence of an explanation makes it difficult to separate good decisions from suspicious ones. Because of this, many researchers are working on making AI explainable. In some applications areas -- e.g., in chess -- practitioners get an impression that there is a limit to understandability, that some decisions remain inhuman -- not explainable. …

Selecting The Most Adequate Fuzzy Operation For Explainable Ai: Empirical Fact And Its Possible Theoretical Explanation, Orsolya Csiszar, Gábor Csiszar, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

A reasonable way to make AI results explainable is to approximate the corresponding deep-learning-generated function by a simple expression formed by fuzzy operations. Experiments on real data show that out of all easy-to-compute fuzzy operations, the best approximation is attained if we use an operation a + b − 0.5 ( limited to the interval [0,1]$. In this paper, we provide a possible theoretical explanation for this empirical result.

Interval-Valued And Set-Valued Extensions Of Discrete Fuzzy Logics, Belnap Logic, And Color Optical Computing, Victor L. Timchenko, Yury P. Kondratenko, Vladik Kreinovich

Departmental Technical Reports (CS)

It has been recently shown that in some applications, e.g., in ship navigation near a harbor, it is convenient to use combinations of basic colors -- red, green, and blue -- to represent different fuzzy degrees. In this paper, we provide a natural explanation for the efficiency of this empirical fact: namely, we show that it is reasonable to consider discrete fuzzy logics, it is reasonable to consider their interval-valued and set-valued extensions, and that a set-valued extension of the 3-values logic is naturally equivalent to the use of color combinations.

Beyond Negation And Excluded Middle: An Exploration To Embrace The Otherness Beyond Classical Logic System And Into Neutrosophic Logic, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

As part of our small contribution in dialogue toward better peace development and reconciliation studies, and following Toffler & Toffler’s War and Antiwar (1993), the present article delves into a realm of logic beyond the traditional confines of negation and the excluded middle principle, exploring the nuances of "Otherness" that transcend classical and Nagatomo logics. Departing from the foundational premises of classical Aristotelian logic systems, this exploration ventures into alternative realms of reasoning, specifically examining Neutrosophic Logic and Klein bottle logic (cf. Smarandache, 2005). The study challenges conventional boundaries and explores the implications of embracing paradoxes and self-reference in logic …

Why People Tend To Overestimate Joint Probabilities, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that, in general, people overestimate the probabilities of joint events. In this paper, we provide an explanation for this phenomenon -- as explanation based on Laplace Indeterminacy Principle and Maximum Entropy approach.

Hail Detection Using Dual Polarization Weather Radar, Alfonso Ladino Rincon

English Language Institute

This poster highlights how active remote sensors such as weather radar are completely useful for hail detection given its feature and the information they produce. Hail detection is already well studied by the atmospheric scientific community and dual polarimetric variables values for hail signature are presented according to those advances. Then, a supervised classification technique is showed to illustrated how machine learning can be integrated to radar information for automatic hail detection. However, this fuzzy logic algorithm has the capability to distinguish between meteorological and non-meteorological echoes. This automatic information might help forecasters from National Weather Services – NWS to …

Fine-Grained Sentiment Analysis For Measuring Customer Satisfaction Using An Extended Set Of Fuzzy Linguistic Hedges, Asad Khattak, Waqas Tariq Paracha, Muhammad Zubair Asghar, Nosheen Jillani, Umair Younis, Furqan Khan Saddozai, Ibrahim A. Hameed

All Works

© 2020 The Authors. Published by Atlantis Press SARL. In recent years, the boom in social media sites such as Facebook and Twitter has brought people together for the sharing of opinions, sentiments, emotions, and experiences about products, events, politics, and other topics. In particular, sentiment-based applications are growing in popularity among individuals and businesses for the making of purchase decisions. Fuzzy-based sentiment analysis aims at classifying customer sentiment at a fine-grained level. This study deals with the development of a fuzzy-based sentiment analysis by extending fuzzy hedges and rule-sets for a more efficient classification of customer sentiment and satisfaction. …

An Empirical Evaluation Of The Inferential Capacity Of Defeasible Argumentation, Non-Monotonic Fuzzy Reasoning And Expert Systems, Lucas Rizzo, Luca Longo

Articles

Several non-monotonic formalisms exist in the field of Artificial Intelligence for reasoning under uncertainty. Many of these are deductive and knowledge-driven, and also employ procedural and semi-declarative techniques for inferential purposes. Nonetheless, limited work exist for the comparison across distinct techniques and in particular the examination of their inferential capacity. Thus, this paper focuses on a comparison of three knowledge-driven approaches employed for non-monotonic reasoning, namely expert systems, fuzzy reasoning and defeasible argumentation. A knowledge-representation and reasoning problem has been selected: modelling and assessing mental workload. This is an ill-defined construct, and its formalisation can be seen as a reasoning …

Historia De Las Teorías Neutrosóficas Y Sus Aplicaciones (Actualizado), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Historia de las Teorías Neutrosóficas y sus Aplicaciones (actualizado)

Fuzziness-Based Active Learning Framework To Enhance Hyperspectral Image Classification Performance For Discriminative And Generative Classifiers, Muhammad Ahmad, Stanislav Protasov, Adil Mehmood Khan, Rasheed Hussain, Asad Masood Khattak, Wajahat Ali Khan

All Works

© 2018 Ahmad et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Hyperspectral image classification with a limited number of training samples without loss of accuracy is desirable, as collecting such data is often expensive and time-consuming. However, classifiers trained with limited samples usually end up with a large generalization error. To overcome the said problem, we propose a fuzziness-based active learning framework (FALF), in which we implement the idea of selecting optimal …

Fuzzy Logic-Based Guaranteed Lifetime Protocol For Real-Time Wireless Sensor Networks, Babar Shah, Farkhund Iqbal, Ali Abbas, Ki Il Kim

All Works

© 2015 by the authors; licensee MDPI, Basel, Switzerland. Few techniques for guaranteeing a network lifetime have been proposed despite its great impact on network management. Moreover, since the existing schemes are mostly dependent on the combination of disparate parameters, they do not provide additional services, such as real-time communications and balanced energy consumption among sensor nodes; thus, the adaptability problems remain unresolved among nodes in wireless sensor networks (WSNs). To solve these problems, we propose a novel fuzzy logic model to provide real-time communication in a guaranteed WSN lifetime. The proposed fuzzy logic controller accepts the input descriptors energy, …

How Success In A Task Depends On The Skills Level: Two Uncertainty-Based Justifications Of A Semi-Heuristic Rasch Model, Joe Lorkowski, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The more skills a student acquires, the more successful this student is with the corresponding tasks. Empirical data shows that the success in a task grows as a logistic function of skills; this dependence is known as the Rasch model. In this paper, we provide two uncertainty-based justifications for this model: the first justification provides a simple fuzzy-based intuitive explanation for this model, while the second -- more complex one -- explains the exact quantitative behavior of the corresponding dependence.

Postmodern Fuzzy System Theory: A Deconstruction Approach Based On Kabbalah, Gabriel Burstein, Constantin Virgil Negoita, Menachem Kranz

Publications and Research

Modern general system theory proposed a holistic integrative approach based on input-state-output dynamics as opposed to the traditional reductionist detail based approach. Information complexity and uncertainty required a fuzzy system theory, based on fuzzy sets and fuzzy logic. While successful in dealing with analysis, synthesis and control of technical engineering systems, general system theory and fuzzy system theory could not fully deal with humanistic and human-like intelligent systems which combine technical engineering components with human or human-like components characterized by their cognitive, emotional/motivational and behavioral/action levels of operation. Such humanistic systems are essential in artificial intelligence, cognitive and behavioral science …

New Operations Over Interval Valued Intuitionistic Hesitant Fuzzy Set, Florentin Smarandache, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Recently, another suitable means were defined by Zhiming Zhang [1], called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and vagueness, and which is more powerful than the hesitant fuzzy sets. In this paper, four new operations are introduced on interval-valued intuitionistic hesitant fuzzy sets and several important properties are also studied.

Algebraic Structures On Fuzzy Unit Square And Neutrosophic Unit Square, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors build algebraic structures on fuzzy unit semi open square UF = {(a, b) | a, b  [0, 1)} and on the fuzzy neutrosophic unit semi open square UN = {a + bI | a, b  [0, 1)}. This study is new and we define, develop and describe several interesting and innovative theories about them. We cannot build ring on UN or UF. We have only pseudo rings of infinite order. We also build pseudo semirings using these semi open unit squares. We construct vector spaces, S-vector spaces and strong pseudo special vector space using …

Complete Description Of Idempotent Hedges In Fuzzy Logic, Jaime Nava

Departmental Technical Reports (CS)

In describing expert knowledge, it is often important to properly take into account hedges} like "very", "somewhat", etc. In particular, fuzzy logic provides a consistent way of describing hedges. For some of the hedges, a repetition changes the meaning: e.g., "very very small" is smaller than "very small". However, other hedges -- like "somewhat" -- are idempotent, in the sense that repeating this hedge twice does not change the meaning. In this paper, we provide a complete description of such idempotent hedges.

Why Trapezoidal And Triangular Membership Functions Work So Well: Towards A Theoretical Explanation, Aditi Barua, Lalitha Snigdha Mudunuri, Olga Kosheleva

Departmental Technical Reports (CS)

In fuzzy logic, an imprecise ("fuzzy") property is described by its membership function μ(x), i.e., by a function which describes, for each real number x, to what degree this real number satisfies the desired property. In principle, membership functions can be of different shape, but in practice, trapezoidal and triangular membership functions are most frequently used. In this paper, we provide an interval-based theoretical explanation for this empirical fact.

Computing With Words: Towards A New Tuple-Based Formalization, Olga Kosheleva, Vladik Kreinovich, Ariel Garcia, Felipe Jovel, Luis A. Torres Escobedo, Thavatchai Ngamsantivong

Departmental Technical Reports (CS)

An expert opinion describes his or her opinion about a quantity by using imprecise ("fuzzy") words from a natural language, such as "small", "medium", "large", etc. Each of these words provides a rather crude description of the corresponding quantity. A natural way to refine this description is to assign degrees to which the observed quantity fits each of the selected words. For example, an expert can say that the value is reasonable small, but to some extent it is medium. In this refined description, we represent each quantity by a tuple of the corresponding degrees.

Once we have such a …

Minimization Of Average Sensitivity As A Method Of Selecting Fuzzy Functions And Operations: Successes And Limitations, Riya George, Suresh Subramanian, Alejandro Vega, Olga Kosheleva

Departmental Technical Reports (CS)

Fuzzy logic is an extension of the standard 2-valued logic -- with two possible truth values 0 ("false") and ("true") -- to values (degrees of certainty) represented by arbitrary numbers from the interval [0,1]. One of the main challenges in fuzzy logic is that we need to extend the usual logical operations from the set {0,1} to the entire interval, and there are many possible extensions. One promising technique for selecting a reasonable extension is to take into account that the fuzzy degrees of certainty are themselves only known with uncertainty; so, it makes sense to select an operation which …

Estimation Of Performance Indices For The Planning Of Sustainable Transportation Systems, Alexander Paz, Pankaj Maheshwari, Pushkin Kachroo, Sajjad Ahmad

Civil and Environmental Engineering and Construction Faculty Research

In the context of sustainable transportation systems, previous studies have either focused only on the transportation system or have not used a methodology that enables the treatment of incomplete, vague, and qualitative information associated with the available data. This study proposes a system of systems (SOS) and a fuzzy logic modeling approach. The SOS includes the Transportation, Activity, and Environment systems. The fuzzy logic modeling approach enables the treatment of the vagueness associated with some of the relevant data. Performance Indices (PIs) are computed for each system using a number of performance measures. The PIs illustrate the aggregated performance of …

Fuzzy Linguistic Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Artificial Intelligence: Soon To Be The World’S Greatest Intelligence, Or Just A Wild Dream?, Edward R. Kollett

Academic Symposium of Undergraduate Scholarship

The purpose of the paper was to examine the field of artificial intelligence. In particular, the paper focused on what has been accomplished towards the goal of making a machine that can think like a human, and the hardships that researchers in the field has faced. It also touched upon the potential outcomes of success. Why is this paper important? As computers become more powerful, the common conception is that they are becoming more intelligent. As computers become more integrated with society and more connected with each other, people again believe they are becoming smarter. Therefore, it is important that …

An Optical Machine Vision System For Applications In Cytopathology, Jonathan Blackledge, Dmitry Dubovitskiy

Articles

This paper discusses a new approach to the processes of object detection, recognition and classification in a digital image focusing on problem in Cytopathology. A unique self learning procedure is presented in order to incorporate expert knowledge. The classification method is based on the application of a set of features which includes fractal parameters such as the Lacunarity and Fourier dimension. Thus, the approach includes the characterisation of an object in terms of its fractal properties and texture characteristics. The principal issues associated with object recognition are presented which include the basic model and segmentation algorithms. The self-learning procedure for …

A Fuzzy-Based Approach For Partner Selection In Multi-Agent Systems, Fenghui Ren, Minjie Zhang, Quan Bai

Faculty of Informatics - Papers (Archive)

Traditional negotiation approaches pay intensive attention to decision making models in order to reach the optimal agreements, while placing insufficient efforts on the problem of partner selection. In this paper, a fuzzy-based approach for partner selection in multi-agent systems is proposed. By employing both the fuzzy logic and the extended dual concern model, agents can adapt their individual behaviors for partner selection in negotiation. The proposed approach has three merits, which are: (1) both the agent’s own benefit and its potential partners’ benefits are considered for partner selection in negotiation; (2) by employing the extended dual concern model, agents’ attitudes …

A Fuzzy Logic Controller For Autonomous Wheeled Vehicles, Mohamed Trabia, Linda Z. Shi, Neil Eugene Hodge

Mechanical Engineering Faculty Research

Autonomous vehicles have potential applications in many fields, such as replacing humans in hazardous environments, conducting military missions, and performing routine tasks for industry. Driving ground vehicles is an area where human performance has proven to be reliable. Drivers typically respond quickly to sudden changes in their environment. While other control techniques may be used to control a vehicle, fuzzy logic has certain advantages in this area; one of them is its ability to incorporate human knowledge and experience, via language, into relationships among the given quantities. Fuzzy logic controllers for autonomous vehicles have been successfully applied to address various …

A Fuzzy Approach For Detecting Anomalous Behaviour In E-Mail Traffic, Mark Jynhuey Lim, Michael Negnevitsky, Jacky Hartnett

Australian Digital Forensics Conference

This paper investigates the use of fuzzy inference for detection of abnormal changes in email traffic communication behaviour. Several communication behaviour measures and metrics are defined for extracting information on the traffic communication behaviour of email users. The information from these behaviour measures is then combined using a hierarchy of fuzzy inference systems, to provide an abnormality rating for overall changes in communication behaviour of suspect email accounts. The use of fuzzy inference is then demonstrated with a case study investigating the email traffic behaviour of a person’s email accounts from the Enron email corpus.

Fuzzy And Neutrosophic Analysis Of Women With Hiv/Aids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Fuzzy theory is one of the best tools to analyze data, when the data under study is an unsupervised one, involving uncertainty coupled with imprecision. However, fuzzy theory cannot cater to analyzing the data involved with indeterminacy. The only tool that can involve itself with indeterminacy is the neutrosophic model. Neutrosophic models are used in the analysis of the socio-economic problems of HIV/AIDS infected women patients living in rural Tamil Nadu. Most of these women are uneducated and live in utter poverty. Till they became seriously ill they worked as daily wagers. When these women got admitted in the hospital …