Manjot Kaur

A Ranking Approach for Intuitionistic Fuzzy Numbers and its Application

To the best of our knowledge very few methods have been proposed in previous studies for comparing intuitionisticfuzzy (IF) numbers. In this paper, the limitations and the shortcomings of all these existing methods are pointed out. Inorder to overcome these limitations and shortcomings a new ranking approach—by modifying an existing rankingapproach—is proposed for comparing IF numbers. Thus, with the help of proposed the ranking approach, a newmethod is proposed to find the optimal solution of such unbalanced minimum cost flow (MCF) problems in which allthe parameters are represented by IF numbers.

Method for solving unbalanced fully fuzzy multi-objective solid minimal cost flow problems

In fuzzy single and multi-objective minimal cost flow (MCF) problems, it is assumed that there is only one conveyance which can be used for transporting the product. However, in real life problems, more than one conveyance is used for transporting the product. To the best of our knowledge untill now no method is proposed in the literature for solving such fuzzy single and multi-objective MCF problems in which more than one conveyance is used for transporting the product and all the parameters, as well as all the decision variables that are represented by fuzzy numbers. In this paper, these types of fuzzy multi-objective MCF problems are called fully fuzzy multi-objective solid minimal cost flow (SMCF) problems and a new method is proposed for solving these problems. The advantages of the proposed methods are also discussed.

A New Approach for Solving Fuzzy Maximal Flow Problems

In conventional maximal flow problems, it is assumed that decision maker is certain about the flows between different nodes. But in real life situations, there always exist uncertainty about the flows between different nodes. In such cases, the flows may be represented by fuzzy numbers. In literature, there are several methods to solve such type of problems. Till now, no one has used ranking function to solve above type of problems. In this paper, a new algorithm is proposed to find fuzzy maximal flow between source and sink by using ranking function. To illustrate the algorithm a numerical example is solved and result is explained. If there is no uncertainty about the flow between source and sink then the proposed algorithm gives the same result as in crisp maximal flow problems.

Polymer-based biocompatible fluorescent sensor for nano-molar detection of Zn2+ in aqueous medium and biological samples

Chemosensors are prepared through condensation reactions between polymeric amines and three different aldehydes; the activities of the three products were evaluated in DMF–H2O (7 : 3, v/v) solvent system. Chemosensor 2c demonstrated selectivity for Zn2+ enhancement of the fluorescence intensity at 420 nm. Upon binding of 2c with Zn2+, an approximately 9 fold enhancement in fluorescence intensity was observed due to the combined effect of ESIPT, CN isomerisation and the two-channel quenching of PET. The investigation of the photophysical properties of 2c revealed that the sensor at low pH led to a shift in the emission profile because of the presence of two types of nitrogen i.e. sp2 and sp3 nitrogens and the pH dependent fluorescence profile is due to the protonation at sp3 hybridised nitrogen that influences the charge transfer transitions of 2c. However, the salt effect has not much influence on the photophysical properties of 2c; and 2c was found to form organic nano-particles (ONP) in a DMF–H2O (1 : 99, v/v) solvent system and this material was found to detect a minimum of 40 nM concentration of Zn2+. The receptor 2c was found to be biocompatible through MTT assay and potent to detect Zn2+ in real biological conditions of microbial cells. The compounds 2a, 2b and 2c while immobilized in PVC based membrane, exhibited their selectivity for zinc ions as ion selective electrodes. These electrodes responded linearly in a wide concentration range with a lower detection limit of 10 μM. The electrodes have been successfully used as indicator electrodes in potentiometric titration of zinc ions with EDTA.

An Algorithm for Solving Fuzzy Maximal Flow Problems Using Generalized Trapezoidal Fuzzy Numbers

Kumar et al. (A new approach for solving fuzzy maximal flow problems, Lecture Notes in Computer Science, Springer-Verlag, Berlin Heidelberg 5908 (2009) 278-286) proposed a new algorithm to find the fuzzy maximal flow between source and sink by representing the flow as normal triangular fuzzy numbers. Chen (Operations on fuzzy numbers with function principal, Tamkang Journal of Management Science 6 (1985) 13-25) pointed out that in many cases it is not to possible to restrict the membership function to the normal form and proposed the concept of generalized fuzzy numbers. There are several papers in the literature in which generalized fuzzy numbers are used for solving real life problems but to the best of our knowledge, till now no one has used generalized fuzzy numbers for solving the maximal flow problems. In this paper, the existing algorithm is modified to find fuzzy maximal flow between source and sink by representing all the parameters as generalized trapezoidal fuzzy numbers. To illustrate the modified algorithm a numerical example is solved and the obtained results are compared with the existing results. If there is no uncertainty about the flow between source and sink then the proposed algorithm gives the same result as in crisp maximal flow problems.

An Improved Algorithm for Solving Fuzzy Maximal Flow Problems

Kumar et al. (A new approach for solving fuzzy maximal flow problems; Lecture Notes in Computer Science, Springer-Verlag; Berlin Heidelberg, 5908, (2009) 278-286) proposed a new algorithm for solving the fuzzy maximal flow problems. In the numerical example solved by Kumar et al., by using the proposed algorithm, there exists negative part in the obtained triangular fuzzy numbers which represents that the flow between two nodes may be negative. Although it is mathematically correct according to properties of ranking function. But in real life problems the negative quantity of the flow has no physical meaning. To overcome this shortcoming the algorithm, proposed by Kumar et al., is improved.

An algorithm for solving fuzzy maximal flow problems using generalized triangular fuzzy numbers

There are several papers in the literature in which generalized fuzzy numbers are used for solving real life problems but to the best of our knowledge, till now no one has used generalized fuzzy numbers for solving the maximal flow problems. In this paper, the existing algorithm is modified to find fuzzy maximal flow between source and sink by representing all the parameters as generalized triangular fuzzy numbers. To illustrate the modified algorithm a numerical example is solved and the obtained results are compared with the existing results. If there is no uncertainty about the flow between source and sink then the proposed algorithm gives the same result as in crisp maximal flow problems.

Fuzzy optimal solution of fuzzy transportation problems with transshipments

In this paper a new method, named as Mehars method, is proposed for solving fuzzy transportation problems with transshipments. Also, it is shown that it is better to use Mehars method as compared to the existing method.