Papers by Prince Williams
Turkish Journal of Electrical Engineering and Computer Sciences
Determining the software quality and release time of the software is an important role of softwar... more Determining the software quality and release time of the software is an important role of software reliability. Software reliability growth models (SRGMs) are applications of software reliability. The change-point is defined as the prominent change in the software testing time, in connection with the quality of a software error occurrence or error-detection phenomenon. As a result, the software reliability growth process, based on the change-point, affects the precision of the software reliability prediction, based on the SRGMs. To find the accurate total expected delivery cost with a suitable warranty period of the software system, a new cost model for the software system with the warranty and changepoint phenomenon is proposed in this paper. The entire expected delivery cost and the reliability of the software system is calculated using the change-point SRGM. The optimal release time is calculated by reducing the overall estimated delivery cost for various desired reliability levels. Based on the proposed warranty cost model and the reliability of the software system, we have derived some optimal release policies. Numerical illustrations and interconnected discussed data are itemized. From the testing outcome, we get software release policies that provide a comprehensive analysis of software based on the total expected delivery cost with a suitable warranty period, desired level of reliability, and changepoint. Moreover, these policies will be helpful for project managers to decide where to stop the testing for customer release at the exact time with a suitable warranty period.
In this paper,we introduce a notion of fuzzy ideals in near-subtraction semigroups and study thei... more In this paper,we introduce a notion of fuzzy ideals in near-subtraction semigroups and study their related properties.
The notion of S-fuzzy left h-ideals in a hemiring is introduced and it's basic properties are... more The notion of S-fuzzy left h-ideals in a hemiring is introduced and it's basic properties are investigated.We also study the homomorphic image and preimage of S-fuzzy left h-ideal of hemirings.Using a collection of left h-ideals of a hemiring, S-fuzzy left h-ideal of hemirings are established.The notion of a finite-valued S-fuzzy left h-ideal is introduced,and its characterization is given.S-fuzzy relations on hemirings are discussed.The notion of direct product and S-product are introduced and some properties of the direct product and S-product of S-fuzzy left h-ideal of hemiring are also discussed.
Software Reliability is one of the key factors in the software development process. Software Reli... more Software Reliability is one of the key factors in the software development process. Software Reliability is estimated using reliability models based on Non Homogenous Poisson Process. In most of the literature the Software Reliability is predicted only in testing phase. So it leads to wrong decision-making concept. In this paper, two Software Reliability concepts, testing and operational phase are studied in detail. Using S-Shaped Software Reliability Growth Model (SRGM) and Exponential SRGM, the testing and operational reliability values are obtained. Finally two reliability values are compared and optimal release time is investigated.
Coupled -structures are introduced, and its application is discussed in BCK/BCIalgebras. The noti... more Coupled -structures are introduced, and its application is discussed in BCK/BCIalgebras. The notions of a coupled -subalgerba, a coupled -ideal and a coupled Cideal are introduced, and their relations are investigated. Characterizations of a coupled -ideal and a coupled C-ideal are discussed. Conditions for a coupled -subalgerba to be a coupled -ideal are considered.
In this paper, we introduce a notion of fuzzy n-ary subgroups with respect to t-conorm(s-fuzzy n-... more In this paper, we introduce a notion of fuzzy n-ary subgroups with respect to t-conorm(s-fuzzy n-ary subgroups) in an n-ary groups (G; f) and have studied their related properties. The main contribution of this paper are studying the properties of s-fuzzy n-ary subgroups over s-level n-ary subgroup of (G; f) , n-ary homomorphism and reta(G; f). Moreover some results of the S-product of s-fuzzy n-ary relations in an n-ary groups (G; f) are also obtained.
Korean Journal of Computational & Applied Mathematics, 2002
... 32(12) (1992), 1763-1773. Prince Williams DR received his M.Sc and M.Phil from Pachiyappa... more ... 32(12) (1992), 1763-1773. Prince Williams DR received his M.Sc and M.Phil from Pachiyappa's College, Chennai. Since 1999 he is doing research(part-time) at Anna University. ... School of Mathematics, Anna University, Chennai 600 025, India e-mail: vivek@@annauniv.edu
Honam Mathematical Journal, 2014
In this paper, we introduce a coupled N-structure which is the generalization of N-structure. Usi... more In this paper, we introduce a coupled N-structure which is the generalization of N-structure. Using this coupled N-structure, we have applied in a subtraction algebra and have introduced the notion of a coupled N-subalgebra, a coupled N-ideal. Also the characterization of coupled N-ideal is presented.
Software reliability is one of the most important characteristics of software quality. Its measur... more Software reliability is one of the most important characteristics of software quality. Its measurement and management technologies employed during the software life-cycle are essential for producing and maintaining quality/reliable software systems. Herein, we discuss a modified approach to calculating the delivery cost of a software product, when warranty is to be provided, with an imperfect debugging phenomenon. Unlike existing cost models, here the strategy was to consider maintenance support given to the customer with an imperfect debugging phenomenon. The optimal release time can be calculated for various reliability levels by minimizing the cost. The delivery cost, reliability of the software system, and the optimal release time were calculated by using an imperfect debugging software reliability growth model. Numerical illustration supports the optimal release policies.
International Mathematical Forum, 2007
In this paper ,we fuzzify the new class of algebraic structure introduced by Kim[5].In this fuzzi... more In this paper ,we fuzzify the new class of algebraic structure introduced by Kim[5].In this fuzzification(called fuzzy KS-semigroups),we introduce the notions of fuzzy sub KS-semigroups,fuzzy KS-ideal,fuzzy KS-p-ideal and investigate some of their related properties.The purpose of this study is to implement the fuzzy set theory and ideal theory in the KS-semigroups.This fuzzification leads to development of new notions over fuzzy KS-semigroups.
In this paper, we introduce the notions of (∈, ∈ ∨ q)-N-ideals and (γ, δ)-N-ideals of subtraction... more In this paper, we introduce the notions of (∈, ∈ ∨ q)-N-ideals and (γ, δ)-N-ideals of subtraction algebras, which are generalization of N-ideals. Some characterization for these generalized N-ideals are derived. Also, we introduce the notions of (∈, ∈ ∨ q)-N-ideals and N-ideals with thresholds of subtraction algebras. The characterization of N-ideals with thresholds by their closed (f, t)-cut ideals over the subtraction algebras X is also established.
Fuzzy Information and Engineering, 2015
The concept of fuzzy ideals is extended by introducing θ-Euclidean fuzzy k-ideals in semirings. I... more The concept of fuzzy ideals is extended by introducing θ-Euclidean fuzzy k-ideals in semirings. In particular, some structural theorems for θ-Euclidean fuzzy k-ideals of a semiring R are proved.
In this paper, we introduce the notions of an interval-valued (∈, ∈ ∨q)-fuzzy subgroups, TG-inter... more In this paper, we introduce the notions of an interval-valued (∈, ∈ ∨q)-fuzzy subgroups, TG-interval-valued (∈, ∈ ∨q)-fuzzy subgroups and investigate some of their related properties. The theory of fuzzy set was first developed by Zadeh [23] and has been applied to many branches in Mathematics. Later fuzzification of the "group" concept into "fuzzy subgroup" was made by Rosenfeld [19]. This work was the first fuzzification of any algebraic structure and thus opened a new direction, new exploration, new path of thinking to mathematicians, engineers, computer scientists and many oth-ers in various tests. To study more about fuzzy subgroups, see [1, 2, 3, 7, 16, 17]. Also, Zadeh [22] have introduced the concept of fuzzy set by an interval-valued fuzzy set (ie., a fuzzy set with an interval-valued membership function) and he con-structed a method of approximate inference using his interval-valued fuzzy sets. The interval-valued fuzzy subgroups were first defined and ...
Mathematica
Using the "belongs to" relation (∈) and quasi-coincidence with rela-tion (q) between fu... more Using the "belongs to" relation (∈) and quasi-coincidence with rela-tion (q) between fuzzy points and fuzzy sets, the new concept of interval-valued (α, β)-fuzzy subgroup is introduced, where α and β are any of {∈, q, ∈ ∨q, ∈ ∧q} with α =∈ ∧q, and related properties are investigated. We provide character-izations of an interval-valued (∈, ∈ ∨q)-fuzzy subgroup and study their related properties. MSC 2010. 20K27, 04A72, 08A72, 20N25. Key words. Interval-valued (∈, ∈ ∨q)-fuzzy subgroup, (∈, ∈)-fuzzy subgroup, (∈, ∈ ∨q)-fuzzy subgroup, (α, β)-fuzzy subgroup. The authors are extremely grateful to the referees for their valuable comments and sug-gestions which have contributed to improve the paper.
International Journal of Fuzzy Systems
In this paper a new generalization of the fuzzy BCK/BCI-algebras of type * (, ) α β are introduce... more In this paper a new generalization of the fuzzy BCK/BCI-algebras of type * (, ) α β are introduced. Then we state and prove some theorems which determine the relationships between these notions and sub algebras of BCK/BCI-algebras. Characterizations of * (, ) α β -interval-valued fuzzy sub algebras in
In this paper, we have introduced the notion of vague Lie ideal and have studied their related pr... more In this paper, we have introduced the notion of vague Lie ideal and have studied their related properties. The cartesian products of vague Lie ideals are discussed. In particular, the Lie homomorphisms between the vague Lie ideals of a Lie algebra and the relationship between the domains and the co-domains of the vague Lie ideals under these Lie homomorphisms are investigated. Mathematics subject classification: 08A72, 17B99, 03E72.
2013 INTERNATIONAL CONFERENCE ON COMPUTING, ELECTRICAL AND ELECTRONIC ENGINEERING (ICCEEE), 2013
The aim of this paper is to investigate using the TOPSIS fuzzy model in the academic advising are... more The aim of this paper is to investigate using the TOPSIS fuzzy model in the academic advising area as an educational management system to advice on probation students to register appropriate number of credit hours to minimize the risk. The most important criteria that could affect the academic advising process are discussed. Accordingly a separate rating table of each alternative and separate weight table of each criterion are described by linguistic terms and expressed by triangular fuzzy numbers. According to the concept of TOPSIS, the closeness coefficients has been calculated to determine the best alternative that could minimize the risk by calculating the distance to both the fuzzy positive ideal solution (FPIS) and the fuzzy negative ideal solution (FNIS) at the same time. Finally, a real case study is shown to highlight the proposed fuzzy system for ranking different alternatives decisions in academic advising activity.
iamm.ac.donetsk.ua
... Some results on fuzzy subsets in gamma-nearrings DR Prince Williams, P. Dheena, KB Latha, E. ... more ... Some results on fuzzy subsets in gamma-nearrings DR Prince Williams, P. Dheena, KB Latha, E. Chandrasekeran (Presented by VV Sharko) ... ISSN 1810 – 3200. c Iнститут математики НАН України Page 2. DR Prince Williams, P. Dheena, KB Latha, E. Chandrasekeran 253 ...
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Papers by Prince Williams