Abstract: Fuzzy set and intuitionistic fuzzy set are dealing with the imprecision and uncertainty inherent in a complex decision problem. However, sometimes these theories are not sufficient to model indeterminate and inconsistent information encountered in real-life problems. To overcome this insufficiency, the neutrosophic set, which is useful in practical applications, is proposed, triangular neutrosophic numbers and trapezoidal neutrosophic numbers are examined, their definitions and applications are discussed. In this study, a decision making algorithm is developed using neutrosophic set processes and an application is given in fighter aircraft selection as an example of a decision making problem. The estimation of the fighter aircraft selection with the neutrosophic multiple criteria decision analysis method is examined.
Abstract: Vendor (supplier) selection is a group decision-making (GDM) process, in which, based on some predetermined criteria, the experts’ preferences are provided in order to rank and choose the most desirable suppliers. In the real business environment, our attitudes or our choices would be made in an uncertain and indecisive situation could not be expressed in a crisp framework. Intuitionistic fuzzy sets (IFSs) could handle such situations in the best way. VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems. This method, which is used to determine the compromised feasible solution with respect to the conflicting criteria, introduces a multi-criteria ranking index based on the particular measure of 'closeness' to the 'ideal solution'. Until now, there has been a little investigation of VIKOR with IFS, therefore we extended the intuitionistic fuzzy (IF) VIKOR to solve vendor selection problem under IF GDM environment. The present study intends to develop an IF VIKOR method in a GDM situation. Therefore, a model is presented to calculate the criterion weights based on entropy measure. Then, the interval-valued intuitionistic fuzzy weighted geometric (IFWG) operator utilized to obtain the total decision matrix. In the next stage, an approach based on the positive idle intuitionistic fuzzy number (PIIFN) and negative idle intuitionistic fuzzy number (NIIFN) was developed. Finally, the application of the proposed method to solve a vendor selection problem illustrated.
Abstract: The aim of this paper is to introduce the notion of
intuitionistic fuzzy positive implicative ideals with thresholds (λ, μ) of
BCI-algebras and to investigate its properties and characterizations.
Abstract: In medical investigations, uncertainty is a major
challenging problem in making decision for doctors/experts to
identify the diseases with a common set of symptoms and also has
been extensively increasing in medical diagnosis problems. The
theory of cross entropy for intuitionistic fuzzy sets (IFS) is an
effective approach in coping uncertainty in decision making for
medical diagnosis problem. The main focus of this paper is to
propose a new intuitionistic fuzzy cross entropy measure (IFCEM),
which aid in reducing the uncertainty and doctors/experts will take
their decision easily in context of patient’s disease. It is shown that
the proposed measure has some elegant properties, which
demonstrates its potency. Further, it is also exemplified in detail the
efficiency and utility of the proposed measure by using a real life
case study of diagnosis the disease in medical science.
Abstract: The applicability of Net Present Value (NPV) in an
investment project is becoming more and more popular in the field
of engineering economics. The classical NPV methodology involves
only the precise and accurate data of the investment project. In the
present communication, we give a new mathematical model for NPV
which uses the concept of intuitionistic fuzzy set theory. The proposed
model is based on triangular intuitionistic fuzzy number, which may
be known as Intuitionistic Fuzzy Net Present Value (IFNPV). The
model has been applied to an example and the results are presented.
Abstract: Based on the theory of intuitionistic fuzzy sets, the concepts of intuitionistic fuzzy subalgebras with thresholds (λ, μ) and intuitionistic fuzzy ideals with thresholds (λ, μ) of BCI-algebras are introduced and some properties of them are discussed.
Abstract: The aim of this paper is to introduce the notion of intuitionistic fuzzy implicative ideals with thresholds (λ, μ) of BCI-algebras and to investigate its properties and characterizations.
Abstract: In this paper a new concept named Intuitionistic Fuzzy
Multiset is introduced. The basic operations on Intuitionistic Fuzzy
Multisets such as union, intersection, addition, multiplication etc. are
discussed. An application of Intuitionistic Fuzzy Multiset in Medical diagnosis problem using a distance function is discussed in detail.
Abstract: In general fuzzy sets are used to analyze the fuzzy
system reliability. Here intuitionistic fuzzy set theory for analyzing
the fuzzy system reliability has been used. To analyze the fuzzy
system reliability, the reliability of each component of the system as
a triangular intuitionistic fuzzy number is considered. Triangular
intuitionistic fuzzy number and their arithmetic operations are
introduced. Expressions for computing the fuzzy reliability of a
series system and a parallel system following triangular intuitionistic
fuzzy numbers have been described. Here an imprecise reliability
model of an electric network model of dark room is taken. To
compute the imprecise reliability of the above said system, reliability
of each component of the systems is represented by triangular
intuitionistic fuzzy numbers. Respective numerical example is
presented.
Abstract: The notion of intuitionistic fuzzy sets was introduced
by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun
and S.Z. Song introduced the notion of intuitionistic fuzzy points.
In this paper we find some relations between the intuitionistic fuzzy
ideals of a semigroup S and the set of all intuitionistic fuzzy points
of S.
Abstract: Fuzzy sets theory affirmed that the linguistic value for
every contraries relation is complementary. It was stressed in the
intuitionistic fuzzy sets (IFS) that the conditions for contraries
relations, which are the fuzzy values, cannot be greater than one.
However, complementary in two contradict phenomena are not
always true. This paper proposes a new idea condition for conflicting
bifuzzy sets by relaxing the condition of intuitionistic fuzzy sets.
Here, we will critically forward examples using triangular fuzzy
number in formulating a new condition for conflicting bifuzzy sets
(CBFS). Evaluation of positive and negative in conflicting
phenomena were calculated concurrently by relaxing the condition in
IFS. The hypothetical illustration showed the applicability of the new
condition in CBFS for solving non-complement contraries
intuitionistic evaluation. This approach can be applied to any
decision making where conflicting is very much exist.
Abstract: The entropy of intuitionistic fuzzy sets is used to indicate the degree of fuzziness of an interval-valued intuitionistic fuzzy set(IvIFS). In this paper, we deal with the entropies of IvIFS. Firstly, we propose a family of entropies on IvIFS with a parameter λ ∈ [0, 1], which generalize two entropy measures defined independently by Zhang and Wei, for IvIFS, and then we prove that the
new entropy is an increasing function with respect to the parameter λ. Furthermore, a new multiple attribute decision making (MADM) method using entropy-based attribute weights is proposed to deal with the decision making situations where the alternatives on attributes are expressed by IvIFS and the attribute weights information is unknown. Finally, a numerical example is given to illustrate the applications of the proposed method.
Abstract: The primary objective of the paper is to propose a new method for solving assignment problem under uncertain situation. In the classical assignment problem (AP), zpqdenotes the cost for assigning the qth job to the pth person which is deterministic in nature. Here in some uncertain situation, we have assigned a cost in the form of composite relative degree Fpq instead of and this replaced cost is in the maximization form. In this paper, it has been solved and validated by the two proposed algorithms, a new mathematical formulation of IVIF assignment problem has been presented where the cost has been considered to be an IVIFN and the membership of elements in the set can be explained by positive and negative evidences. To determine the composite relative degree of similarity of IVIFS the concept of similarity measure and the score function is used for validating the solution which is obtained by Composite relative similarity degree method. Further, hypothetical numeric illusion is conducted to clarify the method’s effectiveness and feasibility developed in the study. Finally, conclusion and suggestion for future work are also proposed.
Abstract: In conventional reliability assessment, the reliability data of system components are treated as crisp values. The collected data have some uncertainties due to errors by human beings/machines or any other sources. These uncertainty factors will limit the understanding of system component failure due to the reason of incomplete data. In these situations, we need to generalize classical methods to fuzzy environment for studying and analyzing the systems of interest. Fuzzy set theory has been proposed to handle such vagueness by generalizing the notion of membership in a set. Essentially, in a Fuzzy Set (FS) each element is associated with a point-value selected from the unit interval [0, 1], which is termed as the grade of membership in the set. A Vague Set (VS), as well as an Intuitionistic Fuzzy Set (IFS), is a further generalization of an FS. Instead of using point-based membership as in FS, interval-based membership is used in VS. The interval-based membership in VS is more expressive in capturing vagueness of data. In the present paper, vague set theory coupled with conventional Lambda-Tau method is presented for reliability analysis of repairable systems. The methodology uses Petri nets (PN) to model the system instead of fault tree because it allows efficient simultaneous generation of minimal cuts and path sets. The presented method is illustrated with the press unit of the paper mill.
Abstract: Intuitionistic fuzzy sets as proposed by Atanassov,
have gained much attention from past and latter researchers for
applications in various fields. Similarity measures between
intuitionistic fuzzy sets were developed afterwards. However, it does
not cater the conflicting behavior of each element evaluated. We
therefore made some modification to the similarity measure of IFS
by considering conflicting concept to the model. In this paper, we
concentrate on Zhang and Fu-s similarity measures for IFSs and
some examples are given to validate these similarity measures. A
simple modification to Zhang and Fu-s similarity measures of IFSs
was proposed to find the best result according to the use of degree of
indeterminacy. Finally, we mark up with the application to real
decision making problems.