Vilas Kharat

Semiprime Ideals and Separation Theorems for Posets

The concept of a semiprime ideal in a poset is introduced. The relations between the semiprime (prime) ideals of a poset and the ideals of the set of all ideals of the poset are established. A result analogous to Separation Theorem is obtained in respect of semiprime ideals. Further, a generalization of Stone’s Separation Theorem for posets is obtained in respect of prime ideals. Some counterexamples are also given.

Fuzzy Logic-Based Formalisms for Gynecology Disease Diagnosis

Abstract The very basis of the present article is the fact that the medical knowledge consisting of clinical presentation, diagnosis, and treatment of a disease is with imprecision and uncertainty. The overall approach in gynecological disease diagnosis could be divided into three distinct stages, and this was confirmed by seven experienced gynecologists. Stage 1 refers to an initial screening process in order to arrive at a single disease diagnosis for the patients, which is based only on the subjective information provided by patients to the physician. In stage 2, the patient who has not received a single diagnostic label in stage 1 is further investigated for a single disease diagnosis using past history criteria. If stage 2 fails to arrive at a single disease diagnosis for a patient, then physical examination and various tests like imaging tests, blood tests, etc., are conducted, and the test results are processed in stage 3. In stage 1, we have revisited fuzzy relational calculus and mathematically evaluated the perceptions of the domain experts (gynecologists) with respect to 31 gynecological diseases. The paper also presents the research findings with a case study focused on stage 2 using a type 1 fuzzy inference system. Out of 226 patients, 50 are correctly diagnosed for a single disease and 147 for multiple diseases in stage 1. The paper concludes that fuzzy relational calculus is an effective method as an “initial screening” process to arrive at a single disease diagnosis. We have identified 29 out of 226 patients satisfying past history criteria to achieve a single disease diagnosis by stage 2. Investigations for stage 3 are in progress.

Efficient Virtual Machine Placement with Energy Saving in Cloud Data Center

Cloud data centers provide computing infrastructure as a service to their customers on pay per use basis. In virtualized data centers CPU, RAM, storage and bandwidth are allotted to a Virtual Machine (VM) from pool of shared resources. An autonomic consolidation of VMs on appropriate Physical Machine (PM) by achieving performance and saving cost is the key challenge for virtualized data centers. This paper presents a self-organizing and multi-objective approach for autonomic consolidation of VMs. The proposed approach does the initial placement of VMs in appropriate PM of cloud data centre which addresses different issues altogether such as maximum resource requirement during setup of VMs, future demand of free resources at peak load, improving the performance and energy saving by keeping idle PMs at offline state. The performance of the proposed algorithm is evaluated by simulating a data center with randomly generated resource capacities of PMs and resource requirement of VMs. Experiment results of proposed technique are also compared with standard algorithms of VM consolidation such as first-first, next-fit and random-selection on two dimensions of resources-CPU and RAM.

Fuzzy description of air quality: a case study

The methods suggested by US -EPA for computation of air quality indices do not include experts knowledge. There exists aleotary uncertainty in the pollution parametric data and the epistemic uncertainty in describing the pollutants by the domain experts in linguistic terms such as good, very good, etc. Fuzzy logic based formalism presented in this paper can model two types of uncertainties, and finally straightway describe air quality in linguistic terms with a degree of certainty attached to each term. The case study relates to the assessment of the status of ambient air quality in Pune city at the defined air quality monitoring stations, using fuzzy logic based formalism. The comparison of the results obtained using the conventional method of computing air quality index and the proposed fuzzy logic based method is an integral part of the paper.

On n-normal posets

A poset Q is called n-normal, if its every prime ideal contains at most n minimal prime ideals. In this paper, using the prime ideal theorem for finite ideal distributive posets, some properties and characterizations of n-normal posets are obtained.

Reducibility in Finite Posets

A notion of reducibility in finite posets is studied. Deletable elements in upper semimodular posets are characterized. Though it is known that the class of upper semimodular lattices is reducible, we construct an example of an upper semimodular poset that is not reducible. Reducibility of pseudocomplemented posets is studied.

Evidence Theory and Fuzzy Relational Calculus in Estimation of Health Effects Due to Air Pollution

Abstract. With an overall objective of establishing association between air pollutants and incidence of respiratory diseases, the environmental professionals and medical practitioners have made significant contribution, using statistical mechanics in modelling epidemiological data, population characteristics, and pollution parameters. Broadly speaking, the studies have shown that the increase in vehicular traffic has been one of the causes of respiratory diseases. However, the WHO Centre for Environment and Health, Europe in its 2005 document states: “There is little evidence for a causal relationship between asthma prevalence/incidence and air pollution in general, though the evidence is suggestive of a causal association between the prevalence/incidence of asthma symptoms and living in close proximity to traffic”. Decision making process in a real world is invariably based on perceptions which are expressed in words or may be in numeric terms and not in probability terms. In the paper, we made an attempt to model the perceptions of experienced pulmonologists in arriving at their combined degree of belief/plausibility/ignorance for all the possible combinations of identified respiratory diseases, using evidence theory and fuzzy relational calculus without collecting sizeable parametric data accumulated over a period of years. Tightening pollution norms by the regulatory authorities is an overall objective of the global efforts on greenhouse gases (GHS) reduction in general, and air pollution mitigation in particular. The concept of solar battery operated electric vehicles (SBOEV) for road transport is advocated, initially for two/three wheelers, and extending it to four wheelers, especially in the developing countries.

Efficacy of Fuzzy-Stat Modelling in Classification of Gynaecologists and Patients

Abstract Fuzzy logic-based inference systems depend on the domain experts’ perceptions, which are intrinsically imprecise/vague/fuzzy. The perceptions of more than one expert are needed in the decision-making process. Therefore, there is a need to study the similarity between the experts using a mathematical framework. Classical mathematical models simulating the medical diagnostic process are usually either logical or probabilistic, wherein the concept of partial belief is not considered. Except in a few cases, binary logic is too unrealistic to apply to medical diagnosis. Another important factor in medical science is the patient-symptom relationship, which influences the disease diagnosis. In summary, the following two issues stand out: (i) Do experts agree with one another in arriving at the same diagnostic labels? (ii) Based on the symptom-patient relationship, can patients be classified? The authors have tried to explore the possibility of using fuzzy similarity measures and also Gower’s coefficient in classifying gynaecologists and patients. The comparative evaluation infers that the efficacy of two-valued binary logic-based Gower’s coefficient is low.

Fuzzy logic application in gynecology: A case study

In medical diagnosis, the descriptions of disease entities use linguistic expressions that are inherently imprecise/vague/ fuzzy/ambiguous which form the scaffold of the medical knowledge of a physician. In our view, overall approach in gynecological disease diagnosis could be divided in three distinct stages. Stage 1 refers to initial screening process in order to arrive at a single disease diagnosis for the patients, and based only on the subjective information provided by patients to the physician. In stage 2, the patient who has not received a single diagnostic label in stage 1, is further investigated for single disease diagnosis using the parameter past history. If stage 2 fails to arrive at a single disease diagnosis for a patient then physical examination and various tests like imaging tests, blood tests, etc. are conducted and the test results are processed in stage 3. The paper presents the research findings with a case study focused only on stage 2 using type 1 fuzzy inference system. We have identified 29 out of 226 patients satisfying past history criteria to achieve single disease diagnosis wherein in stage 1, 50 patients were correctly diagnosed.

On the second spectrum of lattice modules

Abstract The second spectrum Specs(M) is the collection of all second elements of M. In this paper, we study the topology on Specs(M), which is a generalization of the Zariski topology on the prime spectrum of lattice modules. Besides some properties, Specs(M) is characterized and the interrelations between the topological properties of Specs(M) and the algebraic properties of M, are studied.