In our contemporary world, where crime prevails, the expeditious conduct of criminal investigatio... more In our contemporary world, where crime prevails, the expeditious conduct of criminal investigations stands as an essential pillar of law and order. However, these inquiries often grapple with intricate complexities, particularly uncertainties stemming from the scarcity of reliable evidence, which can significantly hinder progress. To surmount these challenges, the invaluable tools of crime linkage and psychological profiling of offenders have come to the forefront. The advent of Intuitionistic Fuzzy Sets (IFS) has proven pivotal in navigating these uncertain terrains of decision-making, and at the heart of this lies the concept of similarity measure-an indispensable tool for unraveling intricate problems of choice. While a multitude of similarity measures exists for gauging the likeness between IFSs, our study introduces a novel generalized similarity measure firmly rooted in the IFS framework, poised to surpass existing methods with enhanced accuracy and applicability. We then extend the horizon of practicality by employing this pioneering similarity measure in the domain of clustering for crime prediction-a paramount application within the realm of law enforcement. Furthermore, we venture into the domain of psychological profiling, a potent avenue that has the potential to significantly fortify the arsenal of crime investigations. Through the application of our proposed similarity measure, we usher in a new era of efficacy and insight in the pursuit of justice. In sum, this study not only unveils a groundbreaking similarity measure within the context of an Intuitionistic fuzzy environment but also showcases its compelling applications in the arena of criminal investigation, marking a significant stride toward swifter and more informed decisions in the realm of law and order.
Beni-Suef University Journal of Basic and Applied Sciences, Apr 24, 2023
Background The concept of Pythagorean fuzzy sets (PFSs) is an utmost valuable mathematical framew... more Background The concept of Pythagorean fuzzy sets (PFSs) is an utmost valuable mathematical framework, which handles the ambiguity generally arising in decision-making problems. Three parameters, namely membership degree, non-membership degree, and indeterminate (hesitancy) degree, characterize a PFS, where the sum of the square of each of the parameters equals one. PFSs have the unique ability to handle indeterminate or inconsistent information at ease, and which demonstrates its wider scope of applicability over intuitionistic fuzzy sets. In the present article, we opt to define two nonlinear distances, namely generalized chordal distance and non-Archimedean chordal distance for PFSs. Most of the established measures possess linearity, and we cannot incorporate them to approximate the nonlinear nature of information as it might lead to counter-intuitive results. Moreover, the concept of non-Archimedean normed space theory plays a significant role in numerous research domains. The proficiency of our proposed measures to overcome the impediments of the existing measures is demonstrated utilizing twelve different sets of fuzzy numbers, supported by a diligent comparative analysis. Numerical examples of pattern recognition and medical diagnosis have been considered where we depict the validity and applicability of our newly constructed distances. In addition, we also demonstrate a problem of suitable medicine selection for COVID-19 so that the transmission rate of the prevailing viral pandemic could be minimized and more lives could be saved. Although the issues concerning the COVID-19 pandemic are very much challenging, yet it is the current need of the hour to save the human race. Furthermore, the justifiable structure of our proposed distances and also their feasible nature suggest that their applications are not only limited to some specific research domains, but decision-makers from other spheres as well shall hugely benefit from them and possibly come up with some further extensions of the ideas.
International Journal of Fuzzy System Applications
The Entropy measure of an intuitionistic fuzzy set (IFS) plays a significant role in decision mak... more The Entropy measure of an intuitionistic fuzzy set (IFS) plays a significant role in decision making sciences, for instance, medical diagnosis, pattern recognition, criminal investigation, etc. The inadequate nature of an entropy measure may lead to some invalid results. Therefore, it is significant to use an efficient entropy measure for studying various decision-making problems under IFS environment. This paper first proposes a novel similarity measure for IFS. Based on the proposed similarity measure, an advanced entropy measure is defined with a different axiomatic approach. This axiomatic approach allows us to measure an IFS's entropy with the help of a similarity measure. To show the efficiency of the proposed similarity measure, a comparative study is performed with the existing similarity measures. Some structural linguistic variables are taken as examples to show the validity and consistency of the proposed entropy measure along with the existing entropy measures. Final...
Havoc, brutality, economic breakdown, and vulnerability are the terms that can be rightly associa... more Havoc, brutality, economic breakdown, and vulnerability are the terms that can be rightly associated with COVID-19, for the kind of impact it is having on the whole world for the last two years. COVID-19 came as a nightmare and it is still not over yet, changing its form factor with each mutation. Moreover, each unpredictable mutation causes more severeness. In the present article, we outline a decision support algorithm using Generalized Trapezoidal Intuitionistic Fuzzy Numbers (GTrIFNs) to deal with various facets of COVID-19 problems. Intuitionistic fuzzy sets (IFSs) and their continuous counterparts, viz., the intuitionistic fuzzy numbers (IFNs), have the flexibility and effectiveness to handle the uncertainty and fuzziness associated with real-world problems. Although a meticulous amount of research works can be found in the literature, a wide majority of them are based mainly on normalized IFNs rather than the more generalized approach, and most of them had several limitations. Therefore, we have made a sincere attempt to devise a novel Similarity Measure (SM) which considers the evaluation of two prominent features of GTrIFNs, which are their expected values and variances. Then, to establish the superiority of our approach we present a comparative analysis of our method with several other established similarity methods considering ten different profiles of GTrIFNs. The proposed SM is then validated for feasibility and applicability, by elaborating a Fuzzy Multicriteria Group Decision Making (FMCGDM) algorithm and it is supportedby a suitable illustrative example. Finally, the proposed SM approach is applied to tackle some significant concerns due to COVID-19. For instance, problems like the selection of best medicine for COVID-19 infected patients; proper healthcare waste disposal technique; and topmost government intervention measures to prevent the COVID-19 spread, are some of the burning issues which are handled with our newly proposed SM approach.
International Journal of Advanced Research in Computer Science, Apr 30, 2017
Multi Criteria Decision Making (MCDM) is the process to find the best alternatives among a set of... more Multi Criteria Decision Making (MCDM) is the process to find the best alternatives among a set of available alternatives in presence of various conflicting criteria. In this paper MCDM method is presented using α-cut approach and it is observed that α-cut approach is general enough to deal with MCDM methods. Here first fuzzy numbers have been assigned to quantify different qualitative criteria of alternatives and then their α-cut values are evaluated and then performed some arithmetic operation to order ranking of the alternatives. Finally, a decision making problem is carried out with different case studies by using different shapes of fuzzy numbers.
Recent Advances in Intelligent Information Systems and Applied Mathematics, 2020
In medical science it is said that prevention is better than cure. Nowadays, medical science has ... more In medical science it is said that prevention is better than cure. Nowadays, medical science has been developed in such a way that almost all of the disease are becoming near to curable. Though, we should prevent the diseases by knowing the exact reason for disease. But, to find the exact reasons for any disease are a critical task and the cause may vary person to person. In this paper we are trying to develop a methodology using hesitant triangular fuzzy number to detect cause for diseases. In this paper, a new concept of expected value for hesitant triangular fuzzy number has been developed. Also, a numerical example has been worked out to show the usability of the methodology.
International Journal of Mathematics Trends and Technology, 2016
It is observed that over the last few decades the rate of crime using fire arms is increasing ver... more It is observed that over the last few decades the rate of crime using fire arms is increasing very rapidly. The criminal activity where fire arm is used for committing murder or suicide is very critical to investigate in the absence of eye witness. When eye witness is not found the investigation is performed totally depending upon the evidences found on the crime scene. To carry out these types of investigation a model has been designed using fuzzy multi-criteria decision making (FMCDM) to reduce the uncertainty factor which comes into play most of the time. This paper highlights and discusses how to help reconstruction of crime scene using FMCDM depending upon physical properties of bloodstain evidences and wounds.
Journal of Ambient Intelligence and Humanized Computing, 2021
Multicriteria Decision Making (MCDM) has a huge role to play while ruling out one suitable altern... more Multicriteria Decision Making (MCDM) has a huge role to play while ruling out one suitable alternative among a pool of alternatives governed by predefined multiple criteria. Some of the factors like imprecision, lack of information/data, etc., which are present in traditional MCDM processes have showcased their lack of efficiency and hence eventually it has paved the ways for the development of Fuzzy multicriteria decision making (FMCDM). In FMCDM processes, the decision makers can model most of the real-life phenomena by fuzzy information-based preferences. The availability of a wide literature on similarity measure (SM) emphasizes the vital role of SM of generalized fuzzy numbers (GFNs) to conduct accurate and precise decision making in FMCDM problems. Despite having few advantages, most of the existing approaches possessed a certain degree of counter intuitiveness and discrepancies. Thus, we have attempted to propose a novel SM for generalized trapezoidal fuzzy numbers (GTrFNs) which could deliberately overcome the impediments associated with the earlier existing approaches. Moreover, a meticulous comparative study with the existing approaches is also presented. This paper provides us with an improved method to obtain the similarity values between GTrFNs and the proposed SM consists of calculating the prominent features of fuzzy numbers such as expected value and variance. We use fourteen different sets of GTrFNs, to compare the fruition of the present approach with the existing SM approaches. Furthermore, to show the utility and applicability of our proposed measure, we illustrate few practical scenarios such as the launching of an electronic gadget by a company, a problem of medical diagnosis and finally, a proper anti-virus mask selection in light of the recent COVID-19 pandemic. The obtained results with our proposed SM, for the mentioned FMCDM problems, are analytically correct and they depict the efficiency and novelty of the present article.
This chapter attempts to initiate a novel generalized semielliptic intuitionistic fuzzy number (G... more This chapter attempts to initiate a novel generalized semielliptic intuitionistic fuzzy number (GSEIFN) along with basic arithmetic operations on GSEIFNs. Furthermore, an advanced ranking method for GSEIFN is proposed. In the end, a multicriteria decision-making problem has been carried out by using the proposed GSEIFN and the ranking approach to exhibit the legality and applicability.
INTERNATIONAL CONFERENCE ON RECENT TRENDS IN APPLIED MATHEMATICAL SCIENCES (ICRTAMS-2020), 2021
Uncertainty is an inescapable components of any types of problems of real world, commonly occurs ... more Uncertainty is an inescapable components of any types of problems of real world, commonly occurs owing to lack of knowledge, imprecision, partial information etc. To deal with such uncertainty a new notion called uncertainty theory, comprises of possibility, necessity and credibility measures, can be explored. In this connection, the present paper tries to trash out a very intricate fuzzy variable called parabolic fuzzy variables (PFVs).Furthermore, it is proposed to study comprising measures of uncertainty theory. Afterwards, effort has been made to present expected value, variance, rational upper bound and comparison of all measures along with properties are carried out between the two existing notion of PFVs. In this study it is encountered that based on fuzziness that first type of PFV contains more uncertainty than the other type.
Aim: To devise an effective structural failure analysis approach under uncertainty. Background: I... more Aim: To devise an effective structural failure analysis approach under uncertainty. Background: In reliability evaluation, plenty of factors are uncertain, or sometimes, spontaneously represented via linguistic expressions, and as a consequence, the traditionalist appraisal methods cannot capably handle the ambiguity and vagueness that occurs in reliability assessment components. Subsequently, this leads to the problem of tremendous computationally multifaceted and scanty correctness. Objective: To overcome the limitations and to develop efficiency as well as accuracy in structural failure evaluation techniques, an attempt has been made to devise a novel structural reliability assessment method via credibility distribution. Methods: To get rid of the problems of massive computationally difficult and inadequate precision, an algorithm has been devised using credibility sampling. To exhibit the novelty, validity, and applicability of the present approach, some structural failure asses...
Imprecision or uncertainty is an integral component of medical decision making. This paper attemp... more Imprecision or uncertainty is an integral component of medical decision making. This paper attempts to bring out medical decision making using arithmetic of parabolic fuzzy numbers by preparing a list of potential symptoms of a patient. Furthermore, ranking of parabolic fuzzy number is defined. Finally, the present study seeks to find out the accurate problem of the patient through the listed symptoms and an effort has been made to address the issue via the arithmetic and ranking of PFNs.
Multicriteria decision making (MCDM) is an important process to select best alternative among a s... more Multicriteria decision making (MCDM) is an important process to select best alternative among a set of alternatives based on preassigned multiple criteria. Presence of uncertainty due to lack of information/data, imprecision, vagueness etc. classical MCDM process becomes more complex and inappropriate. To overcome such types of situations, different types of fuzzy sets are explored and consequently fuzzy multicriteria decision making (FMCDM) was developed. In FMCDM problems, similarity measure of generalized fuzzy numbers plays crucial role in making appropriate decision by choosing best alternative. A handful number of work done on similarity measures are confronted in literature. Even though some advantages of these existing works are encountered, most of the works have impediments. In this regard, an attempt has been made to devise a similarity measure (SM) of GFNs with same or unequal height. It is observed that the proposed SM has the capability to overcome the deficiencies of the available earlier approaches and outplays in all the environments. To showcase the novelty and efficiency of the present SM comparative studies have been performed. Moreover, FMCDM problem has been solved under this setting and found that results obtained by this approach confronts human intuitions and analytical output.
Transactions of A. Razmadze Mathematical Institute, 2018
In this paper, decomposition theorems of picture fuzzy set (PFS) have been proved. (⍺,δ,β)cut of ... more In this paper, decomposition theorems of picture fuzzy set (PFS) have been proved. (⍺,δ,β)cut of picture fuzzy set have been defined and some of its properties are studied. Later on extension principle for PFS has been defined and studied some of its properties. Finally, picture fuzzy arithmetic based on extension principle has been performed.
The Open Cybernetics & Systemics Journal, 2018
When patient(s) approach to a medical expert to explain their problems, they often explain their ... more When patient(s) approach to a medical expert to explain their problems, they often explain their conditions through vague linguistic expression . Medical expert needs to prepare a list of potential symptoms for the particular diseases of the patients based on their vague linguistic statements. Together with the vagueness in medical documents and imprecise information gathered for decision making makes the medical experts' job more complex. Due to the occurrence of uncertainty in medical decision making exploitation of the Fuzzy Set (FST) is required. Generally in literature, type-I fuzzy set, Intuitionistic Fuzzy Sets (IFSs), Interval Valued Fuzzy Sets (IVFSs), and Picture Fuzzy Sets (PFSs) are extensively applied in medical decision making.
The Open Cybernetics & Systemics Journal, 2018
Uncertainty is an integral part of decision-making process which arises due to the lack of knowle... more Uncertainty is an integral part of decision-making process which arises due to the lack of knowledge, data or information. Initially fuzzy set theory (FST) was used to handle this type of uncertainty. Later, intuitionistic fuzzy set (IFS) was developed to encounter uncertainty in a more specific manner. However, it is observed that due to the existence of different types of uncertainties, the membership function (MF) of IFS itself is uncertain and consequently, the concept of interval-valued intuitionistic fuzzy sets (IVIFS) came into the picture. But IVIFS is also not capable of handling uncertainty. To overcome the limitations of the existing IVIFS, generalized interval valued intuitionistic fuzzy sets (GIVIFS) have been defined and it has been observed that it has utmost applicability in real world situations as the parameter height characterises the degree of buoyancy of judgment of decision maker in a very specific compartment.
The objective of this paper is to devise a new technique to combine generalized interval valued f... more The objective of this paper is to devise a new technique to combine generalized interval valued fuzzy numbers (GIVFNs)based on average width of fuzzy set concept. The effectiveness and applicability of the proposed technique are illustrated with an example.
International Journal of Computer Applications, 2012
Uncertainty parameters in risk assessment can be modeled by different ways viz. probability distr... more Uncertainty parameters in risk assessment can be modeled by different ways viz. probability distribution, possibility distribution, belief measure, depending upon the nature and availability of the data. Different transformations exist for converting expression of one form of uncertainty to another form. In this paper, we reviewed the consistency principles as given by different researchers. Then we have carried out dose assessment using probability-possibility transformation satisfying consistency conditions.
International Journal of Computer Applications, 2012
Dempster-Shafer Theory (DST) of Evidence is a powerful and flexible mathematical tool for handlin... more Dempster-Shafer Theory (DST) of Evidence is a powerful and flexible mathematical tool for handling uncertainty, impreciseness, and incomplete information. It can be used when both epistemic and aleatory uncertainties are present in the problem under consideration. The fundamental and important object of this theory of evidence is the primitive function called basic probability assignment (bpa). In the absence of empirical data, experts in related fields provide necessary information (bpa). However how to obtain BPA is still an open issue. In this paper, we propose methods to determine BPA when only the minimum, maximum and most likely values of the parameter are known. An example is illustrated to demonstrate and check the efficiency of the proposed methods. We have also developed an extended version of uncertainty measurement in evidence theory in order to calculated total uncertainty in the body of evidence obtained by the proposed methods.
International Journal of Computer Applications, 2012
Risk assessment is a popular and important tool in decision making process. Risk assessment is ge... more Risk assessment is a popular and important tool in decision making process. Risk assessment is generally performed using models and model is a function of some parameters which are usually affected by uncertainty. Here, we consider that model parameters are affected by epistemic uncertainty. To represent epistemic uncertainty in general triangular fuzzy number or trapezoidal fuzzy numbers are used. In this paper, we study Gaussian fuzzy number to represent epistemic type uncertainty and try to fuse with triangular fuzzy numbers and also risk assessment is carried out under fuzzy environment.
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Papers by Palash Dutta