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 focus of the paper is to furnish the entropy measure
for a neutrosophic set and neutrosophic soft set which is a measure
of uncertainty and it permeates discourse and system. Various characterization
of entropy measures are derived. Further we exemplify
this concept by applying entropy in various real time decision making
problems.
Abstract: We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study.
Abstract: This paper treats different aspects of entropy measure
in classical information theory and statistical quantum mechanics, it
presents the possibility of extending the definition of Von Neumann
entropy to image and array processing. In the first part, we generalize
the quantum entropy using singular values of arbitrary rectangular
matrices to measure the randomness and the quality of denoising
operation, this new definition of entropy can be implemented to
compare the performance analysis of filtering methods. In the second
part, we apply the concept of pure state in quantum formalism
to generalize the maximum entropy method for narrowband and
farfield source localization problem. Several computer simulation
results are illustrated to demonstrate the effectiveness of the proposed
techniques.
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 design of weight is one of the important parts in
fuzzy decision making, as it would have a deep effect on the evaluation
results. Entropy is one of the weight measure based on objective
evaluation. Non--probabilistic-type entropy measures for fuzzy set
and interval type-2 fuzzy sets (IT2FS) have been developed and applied
to weight measure. Since the entropy for (IT2FS) for decision
making yet to be explored, this paper proposes a new objective
weight method by using entropy weight method for multiple attribute
decision making (MADM). This paper utilizes the nature of IT2FS
concept in the evaluation process to assess the attribute weight based
on the credibility of data. An example was presented to demonstrate
the feasibility of the new method in decision making. The entropy
measure of interval type-2 fuzzy sets yield flexible judgment and
could be applied in decision making environment.
Abstract: Probabilistic measures of uncertainty have been
obtained as functions of time and birth and death rates in a queuing
process. The variation of different entropy measures has been studied
in steady and non-steady processes of queuing theory.
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: In this paper, a fast motion compensation algorithm is
proposed that improves coding efficiency for video sequences with
brightness variations. We also propose a cross entropy measure
between histograms of two frames to detect brightness variations. The
framewise brightness variation parameters, a multiplier and an offset
field for image intensity, are estimated and compensated. Simulation
results show that the proposed method yields a higher peak signal to
noise ratio (PSNR) compared with the conventional method, with a
greatly reduced computational load, when the video scene contains
illumination changes.
Abstract: In present communication, we have developed the
suitable constraints for the given the mean codeword length and the
measures of entropy. This development has proved that Renyi-s
entropy gives the minimum value of the log of the harmonic mean
and the log of power mean. We have also developed an important
relation between best 1:1 code and the uniquely decipherable code by
using different measures of entropy.
Abstract: In the present communication, we have studied
different variations in the entropy measures in the different states of
queueing processes. In case of steady state queuing process, it has
been shown that as the arrival rate increases, the uncertainty
increases whereas in the case of non-steady birth-death process, it is
shown that the uncertainty varies differently. In this pattern, it first
increases and attains its maximum value and then with the passage of
time, it decreases and attains its minimum value.
Abstract: The objective of the present communication is to
develop new genuine exponentiated mean codeword lengths and to
study deeply the problem of correspondence between well known
measures of entropy and mean codeword lengths. With the help of
some standard measures of entropy, we have illustrated such a
correspondence. In literature, we usually come across many
inequalities which are frequently used in information theory.
Keeping this idea in mind, we have developed such inequalities via
coding theory approach.