Lakshmana Gomathi Nayagam Velu

National Institute of Technology Tiruchirappalli | nit-t · Department of Mathematics

Zadeh introduced fuzzy sets to study imprecision in real life after which many variants of fuzzy sets have been developed in literature. In this paper, new variants of fuzzy sets named Hybrid fuzzy sets and Hybrid intuitionistic fuzzy sets have been defined based on some real life scenarios where conventional fuzzy sets are not applicable for deali...

The article aims to investigate the distance measure between any two conventional type trapezoidal-valued intuitionistic fuzzy sets (CTrVIFSs) whose membership and non-membership grades of an element are expressed as conventional trapezoidal intuitionistic fuzzy numbers (CTrIFN). Using the proposed distance measure, the similarity measure of CTrVIF...

The notion of fuzzy subsets was first introduced by Zadeh in 1965, and was later extended to intuitionistic fuzzy subsets by Atanassov in 1983. Since the inception of fuzzy set theory, we have encountered a number of generalizations of sets, one of which is neutrosophic sets introduced by Smarandache [15]. Later neutrosophic sets was generalized in...

L.A. Zadeh (1965) proposed the concept of fuzzy subsets, which was later expanded to include intuitionistic fuzzy subsets by K.Atanassov (1983). We have come across several generalisations of sets since the birth of fuzzy sets theory, one of which is Florentine Smarandache [15] introduced the neutrosophic sets as a major category. Many real-life de...

Zadeh introduced fuzzy sets to study imprecision in real life after which many generalizations have been developed in literature. Fuzzy numbers is the major research area of study because of its needfulness for modeling qualitative and imprecise continuous transitions. Most of the time, data involved in multi-criteria decision making (MCDM) will be...

Conventional trapezoidal intuitionistic fuzzy numbers (CTrIFNs) are used in the literature to handle many real-life problems with imprecise information. However, the CTrIFNs are not the real generalization of interval-valued intuitionistic fuzzy numbers (IVIFNs) and triangular intuitionistic fuzzy numbers (TIFNs). This study discusses the non-conve...

In this article, we introduce the notion of \((\alpha -\beta )\)-level spaces by considering the concept of fuzzy bitopological space (shortly, fbts). We also define the fuzzy bitopological \((\alpha -\beta )\)-Hausdorff space and, with the help of \((\alpha -\beta )^{*}\)-disjoint sets, the idea of fuzzy bitopological \((\alpha -\beta )^{*}\)-Haus...

Numerous real-life problems depend on incomplete and implausible information. To overcome the enigma and obscurity, Zadeh promoted fuzzy set theory in the year 1965. After introducing fuzzy set theory, many researchers have made numerous developments in engineering and medicine. Different ranking principles on trapezoidal fuzzy numbers are establis...

Most of the engineering applications depend on incomplete and imprecise information which are represented by nonlinear mathematical functions for defining membership and nonmembership functions in intuitionistic fuzzy setup. Shuyang Li and Hongxing Li have studied the approximation of conventional intuitionistic fuzzy numbers in which the membershi...

Numerous research papers and several engineering applications have proved that the fuzzy set theory is an intelligent effective tool to represent complex uncertain information. In fuzzy multi-criteria decision-making (fuzzy MCDM) methods, intelligent information system and fuzzy control-theoretic models, complex qualitative information are extracte...

Zadeh introduced fuzzy set theory in the year 1965 to overcome the enigma and obscurity in the real world problems. The underlying power of fuzzy sets is that linguistic / qualitative variables can be used along with quantitative variables to represent continuous imprecise concepts. The continuous anagram concepts need to be modeled by continuous f...

A collection of vertices in different connected graphs embraces a wholesome shift into a new collection with the properties of the couplets monophonic and dominating sets. The new collection of vertices and associated invariant with the new behavior of connected graphs are called as connected monophonic dominating set (cmd-set) and connected monoph...

The concept of fuzzy numbers has been generalized to intuitionistic fuzzy interval numbers (IFINs) to solve problems with imprecision in the information modeling. Similarity measure is an important tool to measure the degree of resemblance between any two objects in real-life situations and is applied in many areas such as decision making, image pr...

Zadeh introduced theory of fuzzy sets in 1965 as generalization of crisp sets to represent uncertain, incomplete, imprecise and inconsistent information and Atanassov proposed intuitionistic fuzzy sets in 1986 as generalization of fuzzy sets. Smarandache defined neutro-sophic sets in 1995 which generalizes both fuzzy sets and intuitionistic fuzzy s...

The problem (or scenario) involving qualitative or imprecise information is not solvable by classical set theory. To overcome the shortcoming of classical set theory, Zadeh (Inf Control 8(3):338–356, 26) introduced the concept of fuzzy sets that generalizes the concept of classical sets. Fuzzy set theory allows modelling and handling of imprecise i...

Problems with qualitative, quantitative and uncertain information can be modelled better using trapezoidal intutionistic fuzzy numbers (TrIFNs) than fuzzy numbers. Due to the partial ordering of TrIFNs, many ranking methods are available in the literature for comparing fuzzy and intuitionistic fuzzy numbers (Li in Comput Math Appl 60:1557–1570, 201...

Fuzzy numbers and intuitionistic fuzzy numbers are introduced in the literature to model problems involving incomplete and imprecise numerical quantities. Researchers from all over the world have been working in ranking of intuitionistic fuzzy numbers since 1985, but till date there is no common methodology that rank any two arbitrary intuitionisti...

Any information system or decision model which consists of combinations of quantitative, qualitative, imprecise and incomplete informations can be modelled better using trapezoidal intuitionistic fuzzy numbers (TrIFNs) than interval valued intuitionistic fuzzy numbers. Ranking of TrIFNs plays an important role in intuitionistic fuzzy decision-makin...

Most of the real world problems are complex that is raised from uncertainity in the form of ambiguity. To overcome the ambiguity and impreciseness, Zadeh [20] introduced fuzzy set theory in the year 1965. The underlying power of fuzzy sets is that linguistic variables can be used rather than quantitative variables to represent imprecise concepts wh...

Modelling real life (industrial) problems using intuitionistic fuzzy numbers is inevitable in the present scenario due to their efficiency in solving problems and their accuracy in the results. Particularly, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used in describing impreciseness and incompleteness of a data. Any intuitionistic...

Fuzzy numbers and intuitionistic fuzzy numbers are introduced in the literature to model problems involving incomplete and imprecise information in expert and intelligent systems. Ranking of TrIFNs plays an important role in an information system (Decision Making) with imprecise and inadequate information and the complete ranking on the class of tr...

Fuzzy number was introduced by Dubois and Prade [10] to handle imprecise numerical quantities. Later it was generalized to intuitionistic fuzzy number by Burillo et al. [5]. Ranking intuitionistic fuzzy numbers plays an important role in decision making and information systems. All over the world many researchers have proposed different score funct...

Intuitionistic fuzzy set plays a vital role in decision making, data analysis, and artificial intelligence. Many decision-making problems consist of different types of datum, where fuzzy set theoretical approaches may fail to obtain the optimal decision. Numerous approaches for intuitionistic fuzzy decision-making problem have been introduced in th...

The intuitionistic fuzzy sets (IFSs) introduced by Atanassov are widely applied in all areas such as data analysis, artificial intelligence, decision support systems in modelling problems with incomplete and imprecise information due to their better accuracy. More precisely, trapezoidal intuitionistic fuzzy numbers (TraIFNs) are able to model incom...

L.A.Zadeh introduced the concept of fuzzy set theory as the generalization of classical set theory in 1965 and further it has been generalized to intuitionistic fuzzy sets (IFSs) by Atanassov in 1983 to model information by the membership, nonmembership and hesitancy degree more accurately than the theory of fuzzy logic. The notions of intuitionist...

The information received from a source, represented by an information system, involves quantitative, qualitative and incomplete information. Such incomplete information are fed into the intelligent system for enhancing accuracy using interval-valued intuitionistic fuzzy numbers (IVIFN). Ranking of IVIFN is an important component of any incomplete i...

In this paper, we define the concept of an intuitionistic Q-fuzzy HX group and define a new algebraic structure of intuitionistic Q-fuzzy HX group and some related properties are investigated. We also define the level subsets of an intuitionistic Q-fuzzy HX group and discussed some of its properties. Keywords: Intuitionistic fuzzy set, intuitionist...

Out of several generalizations of fuzzy set theory for various objectives, the notions of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are interesting and very useful in modeling real life problems. The ranking of fuzzy numbers was studied by many authors and it was extended to intuitionistic fuzzy sets because of its att...

Out of several generalizations of fuzzy set theory for various objectives, the notions introduced by Atanassov (1983) and Atanassov and Gargov (1989) in defining intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are interesting and very useful in modeling real life problems. Ranking of interval-valued intuitionistic fuzzy sets...

The fuzzy sets were introduced by Zadeh in 1965 and were extended to intuitionistic fuzzy sets by Atanassov (1986). A notion of a fuzzy topological group was proposed by Foster in 1979 especially he took a group and furnished it with a fuzzy topological structure. An equivalent notion of a fuzzy topological group was introduced by Ma and Yu (1984)...

The hazards associated with major accident hazard (MAH) industries are fire, explosion and toxic gas releases. Of these, toxic gas release is the worst as it has the potential to cause extensive fatalities. Qualitative and quantitative hazard analyses are essential for the identification and quantification of these hazards related to chemical indus...

The notion of fuzzy subsets was introduced by L.A.Zadeh (1965) and it was generalised to intuitionistic fuzzy subsets by K.Atanassov [1]. After the invention of intuitionistic fuzzy subsets, many real life problems are studied accurately [7, 13, 14]. The measure of fuzziness was studied in [12, 16]. The ranking of intuitionistic fuzzy numbers plays...

The notion of fuzzy sets was introduced by L.A.Zadeh and was extended to intuitionistic fuzzy subsets by K.Atanassov. The notions of fuzzy and intuitionistic fuzzy topological spaces were introduced and studied by C.L.Chang, D. Coker, K.Hur et.al. The notion of induced topology on fuzzy singletons has been introduced and it has been extended to the...

Following the introduction of fuzzy sets in 1965, a notion of fuzzy topological group was proposed by Foster in 1979: essentially he took a group and furnished it with a fuzzy topological structure. An equivalent notion of fuzzy topological group was introduced by Ma and Yu in 1984 by replacing points by fuzzy points. Recently two of the coauthors...

The authors introduce a new definition of intuitionistic fuzzy Hausdorff space and compare it with existing notions.

The notion of fuzzy sets is introduced by L. A. Zadeh [Inf. Control 8, 338–353 (1965; Zbl 0139.24606)]. The notion of fuzzy topological spaces is introduced and studied by C. L. Chang [J. Math. Anal. Appl. 24, 182–190 (1968; Zbl 0167.51001)]. The notion of fuzzy singletons is introduced by P.-M. Pu and Y.-M. Liu [J. Math. Anal. Appl. 76, 571–599 (1...

Decision-making is the most important scientific, social and economic endeavor. Many classical methods are available in the literature if the relationship between alternatives and criteria is in linguistic terms. Among them Fuzzy Analytic Hierarchy processes is a very much useful method. In this paper we are dealing with six financial investment pr...

Abstract The notion of intuitionistic fuzzy sets was introduced by K.Atanassov. The notion of intuitionistic fuzzy topological spaces was introduced and studied by D.Coker. The notion of intuitionistic fuzzy points is introduced by Gallego. In this paper the notion of induced topology on the collection of intuitionistic fuzzy singletons with respe...

The notion of fuzzy filters was studied by M. A. De Prada Vicente and M. Saralegui Aranguren [J. Math. Anal. Appl. 129, 560–568 (1988; Zbl 0647.54004)], R. Lowen [General Topology Appl. 10, 147–160 (1979; Zbl 0409.54008)] and P. V. Ramakrishnan and V. Lakshmana Gomathi Nayagam [J. Fuzzy Math. 10, No. 3, 615–625 (2002; Zbl 1016.54007)]. The notion o...

The notion of fuzzy filters was studied by Vicente and Aranguren (1988), Lowen (1979), and Ramakrishnan and Nayagam (2002). The notion of fuzzily compactness was introduced and studied by Ramakrishnan and Nayagam (2002). In this paper, an equivalent condition of fuzzily compactness is studied and a new notion of semi-Hausdorffness on fuzzy filters,...

The notion of Interval Valued Fuzzy Sets (IVF sets) was introduced by T. K. Mondal. In this paper a notion of IVF filter is introduced and studied. A new notion of Hausdorffness, which can not be defined in crisp theory of filters, is defined on IVF filters and their properties are studied.

The notion of fuzzy set was introduced by Zadeh. Fuzzy topological spaces were introduced by Chang2 and studied by many eminent authors like Lowen6&7, Wong9-11. A notion of fuzzy Hausdorff space was introduced in [8]. A different notion of fuzzy Hausdorff space was introduced in [4]. In this paper, we introduce the notion of nearly fuzzy Hausdorff...