Q. M. Danish Lohani

Particle swam optimization based reliability-redundancy allocation in a type-2 fuzzy environment

In this paper, we have addressed the reliability-redundancy allocation problem with a particle swam optimization based technique. The parameters of the system components are actually imprecise or uncertain quantity since those are generally guessed by the designers during the design-time. Thus, important features of the designed system, viz. reliability, costs, weight etc very suitably qualifies to be considered as fuzzy quantity. Our problem formulation considers these parameters as type-2 fuzzy quantity. There are few reports where the problem has been studied under type-1 fuzzy uncertainty. As far as we know, no research has been reported where the problem has been addressed with a particle swam optimization based approach in a type-2 fuzzy environment. Suitable examples are included to demonstrate our approach. Results are compared showing that the type-2 fuzzy uncertainty based approach outperforms other recently reported results.

Fuzzy multi-objective reliability-redundancy allocation problem

Reliability is the measure of the result of the quality of the system over a long run. The reliability-redundancy allocation problem (RRAP) aims to ensure high systems reliability in the presence of optimally redundant systems components. This is one of the most important design considerations for the systems designers. Several researchers have addressed this important issue during last few decades. However, due to the embedded uncertainty in the parameters of the system components, reliability as well as the costs of the whole system fits very well to be modeled as fuzzy quantity. We therefore modeled this problem as a fuzzy multi-objective optimization problem (MORRAP) that is addressed using the popular multi-objective evolutionary algorithm, NSGA-II (non-dominated sorting genetic algorithm-II). We have considered the based MORRAP with fuzzy type-2 uncertainty. As far as we know, no research has been reported where MORRAP was considered under type-2 fuzzy uncertainty. A typical numerical example is included and results are compared showing that our approach outperforms other recently reported results.

Multiobjective Reliability Redundancy Allocation Problem With Interval Type-2 Fuzzy Uncertainty

The multiobjective reliability redundancy allocation problem (MORRAP) aims to ensure high system reliability in the presence of optimally redundant components. This is one of the most important design considerations for system designers. Due to the associated uncertainty in component parameters, precise computations of overall system reliability, cost, and weight, etc., are difficult during design time. Hence, these parameters are befitting to be modeled as fuzzy quantities. As type-1 fuzzy numbers have limitations in representing higher order uncertainties, so this paper models the component parameters viz., reliability, cost, and weight with interval type-2 fuzzy numbers. Thus, we propose a novel formulation of MORRAP, termed as interval type-2 fuzzy multiobjective optimization problem (IT2FMORRAP). A popular multiobjective evolutionary algorithm, viz., nondominated sorting genetic algorithm II, is used to solve the proposed IT2FMORRAP, for which we have developed two novel algorithms in this paper. Numerical examples are included to demonstrate the solution approach. On comparing the outcomes with earlier results, we have found that the proposed IT2FMORRAP outperforms classical as well as other type-1 fuzzy-number-based approaches.

A novel clustering algorithm based on a new similarity measure over Intuitionistic fuzzy sets

In Intuitionistic fuzzy sets(IFSs), experts assign both membership value and non-membership value to each fuzzy element x with a certain degree of hesitation. The hesitancy in the opinion of the experts appear due to incomplete information available regarding x. Therefore, precise estimation of its both membership value and non-membership value becomes highly difficult. Hence, there is a high chance that both membership value and the non-membership value assigned to x by the expert may not be absolutely correct. So, whenever we try to measure similarity between the IFSs using the various distance measures involving all the components of IFSs like membership value, non-membership value together with hesitation, then we often notice that all of them fails to describe the underlying situation completely. Therefore, the similarity measures derived from these distance measures also fails to produce good results. So, we introduce a new similarity measure by properly defining a similarity degree through the result established in this paper. The similarity measure has a central role in developing a modified λ-cutting algorithm for clustering. Here we also establish the efficacy of our modified λ-cutting algorithm while implementing it on a real world data set.

Atanassov Intuitionistic Fuzzy Domain Adaptation to contain negative transfer learning

Transfer learning framework is designed to use previously acquired knowledge to solve a new but somewhat related task (like humans do). Non-availability of sufficient and relevant information in building a learning model is a major bottleneck in this research area. However, such models are highly susceptible to negative transfer learning (NTL) during transferral of knowledge due to the hesitancy in the decision making. Negative transfer learning may cause chaotic learning and have a profound effect on their predictive precision. In this paper, we have proposed a novel Intuitionistic Fuzzy Domain Adaptation (IFDA) algorithm, which uses Yager-generating function over Atanassovs Intuitionistic fuzzy set theory in conjunction with modified Hausdorff Intuitionistic similarity metric to build a fuzzy domain adaptation algorithm which is independent of supervised machine learning technique. It exploits the hesitancy margin in intuitionistically fuzzified features by eradicating similar looking but useless instances. Therefore, it selects optimal source instances from a previous problem in bridging the knowledge gap, in order to solve a new target problem, by containing negative transfer learning.

A similarity measure for atanassov intuitionistic fuzzy sets and its application to clustering

The pattern recognition problem are mostly dealt through the process of clustering. Many important techniques used for clustering are based on similarity measures. The similarity measures are derived from distance measures. Therefore, for measuring the similarity between objects (Atanassov intuitionistic fuzzy set(AIFS)) researchers have applied several distance measures like normalized Euclidean distance measure, Hamming distance measure, etc. For a problem, the distance measure has to be judiciously selected in accordance with existing underlying nature. Hence, there does not exist any procedure of selecting a distance measure which globally works for all kind of problems. So in this paper, we have given a new similarity measure based on the distance measure of double sequence of bounded variation. We have compared results obtained through our similarity measure with the results of other similarity measure. Our results clearly depicts the efficacy of our similarity measure over other similarity measures.

Sequence spaces M ( ϕ )

Distance measures play a central role in evolving the clustering technique. Due to the rich mathematical background and natural implementation of [Formula: see text] distance measures, researchers were motivated to use them in almost every clustering process. Beside [Formula: see text] distance measures, there exist several distance measures. Sargent introduced a special type of distance measures [Formula: see text] and [Formula: see text] which is closely related to [Formula: see text]. In this paper, we generalized the Sargent sequence spaces through introduction of [Formula: see text] and [Formula: see text] sequence spaces. Moreover, it is shown that both spaces are BK-spaces, and one is a dual of another. Further, we have clustered the two-moon dataset by using an induced [Formula: see text]-distance measure (induced by the Sargent sequence space [Formula: see text]) in the k-means clustering algorithm. The clustering result established the efficacy of replacing the Euclidean distance measure by the [Formula: see text]-distance measure in the k-means algorithm.

M(\phi)

In this paper we define and study continuity, boundedness and Frechet differentiation of nonlinear operators between fuzzy 2-normed spaces FTNS. We also display here some interesting examples.

and N ( ϕ )

In the modern era of industrialization and globalization, distribution and control of goods are essential aspects for multinational corporations and strategic partners. Vendor managed inventory (VMI) is one of the well-known strategies of merchandizing between supplier and retailer. In this paper, we consider different number of suppliers and retailers to perform business under VMI system and formulate three: single-supplier and single-retailer, single-supplier and multi-retailer, and multi-supplier and multi-retailer VMI systems. The objective is to minimize the total cost of VMI system. Since it is a non-linear integer programming problem, this paper proposes a novel hybrid biogeography-based optimization algorithm to solve it. We enhance the proposed algorithm by embedding stochastic fractal search (SFS) in biogeography-based optimization (BBO). SFS algorithm is a newly developed powerful evolutionary algorithm to find global optimum much faster and efficiently. The diffusion process of SFS improved the exploitation ability of search in BBO. Our proposed algorithm is applied on all three versions of VMI systems under different constraints. We have considered suitable input data for all the different problems and obtained the results. By comparison, we show that the results outperformed for all VMI systems.

N(\phi)

Supplier selection is a process in which one supplier is selected out of given suppliers on the basis of certain features such as reliability, maintenance, delivery performance, quality etc. Nowadays, supplier selection problem is a big issue because selection of the best supplier is a multi-criteria decision making (MCDM) problem under many combating criteria. The knowledge of the decision makers (DMs) is incomplete as well as imprecise. To deal this complex situation (uncertainty and hesitation), Intuitionistic fuzzy sets (IFSs) are used to select better DMs preferences. IFS is a powerful tool as it deals with membership function, non-membership function together with hesitancy. In this paper, we propose an intuitionistic fuzzy TOPSIS decision making method using correlation coefficient to deal with MCDM problems using IFS. Intuitionistic fuzzy weighted averaging (IFWA) operator is used to aggregate each DMs opinions for valuating the importance of alternatives and criteria. The proposed method is implemented on the numerical example given in F. E. Boran, S. Genc, M. Kurt and D. Akay, [Expert Systems with Applications, 8(2009), 11 363-11 368] to demonstrate about our procedure. The results obtained by our method matches with the results of Boran. Hence, our logic is proper for handling supplier selection problem.