Harish Garg

Multi-objective reliability-redundancy allocation problem using particle swarm optimization

This paper considers the multi-objective reliability redundancy allocation problem of a series system where the reliability of the system and the corresponding designing cost are considered as two different objectives. Due to non-stochastic uncertain and conflicting factors it is difficult to reduce the cost of the system and improve the reliability of the system simultaneously. In such situations, the decision making is difficult, and the presence of multi-objectives gives rise to multi-objective optimization problem (MOOP), which leads to Pareto optimal solutions instead of a single optimal solution. However in order to make the model more flexible and adaptable to human decision process, the optimization model can be expressed as fuzzy nonlinear programming problems with fuzzy numbers. Thus in a fuzzy environment, a fuzzy multi-objective optimization problem (FMOOP) is formulated from the original crisp optimization problem. In order to solve the resultant problem, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker regarding cost and reliability goals and then particle swarm optimization is applied to solve the resulting fuzzified MOOP under a number of constraints. The approach has been demonstrated through the case study of a pharmaceutical plant situated in the northern part of India.

A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making

The objective of this article is to extend and present an idea related to weighted aggregated operators from fuzzy to Pythagorean fuzzy sets (PFSs). The main feature of the PFS is to relax the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted averaging (PFEWA), Pythagorean fuzzy Einstein ordered weighted averaging (PFEOWA), generalized Pythagorean fuzzy Einstein weighted averaging (GPFEWA), and generalized Pythagorean fuzzy Einstein ordered weighted averaging (GPFEOWA), are proposed in this article. Some desirable properties corresponding to it have also been investigated. Furthermore, these operators are applied to decision‐making problems in which experts provide their preferences in the Pythagorean fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, a systematic comparison between the existing work and the proposed work has been given.

A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems

Graphical abstract A generalized improved score function is defined as for IFN A={a, b, c, d}. Here k1, k1?0 and k1+k2=1 such that GIS(A)?0, 1.Display Omitted HighlightsGeneralized improved score function has been present here.Interval valued intuitionistic fuzzy numbers has used for assessing preference of DM.Shortcoming of the existing score functions is overcome.Attributes weights corresponding to attributes are completely unknown.Sensitivity analysis of decision maker preferences has been assessed. The objective of this paper is divided into two folds. Firstly, a new generalized improved score function has been presented in the interval-valued intuitionistic fuzzy sets (IVIFSs) environment by incorporating the idea of weighted average of the degree of hesitation between their membership functions. Secondly, an IVIFSs based method for solving the multi-criteria decision making (MCDM) problem has been presented with completely unknown attribute weights. A ranking of the different attributes is based on the proposed generalized improved score functions and the sensitivity analysis on the ranking of the system has been done based on the decision-making parameters. An illustrative examples have been studied to show that the proposed function is more reasonable in the decision-making process than other existing functions.

A hybrid PSO-GA algorithm for constrained optimization problems

The main objective of this paper is to present a hybrid technique named as a PSO-GA for solving the constrained optimization problems. In this algorithm, particle swarm optimization (PSO) operates in the direction of improving the vector while the genetic algorithm (GA) has been used for modifying the decision vectors using genetic operators. The balance between the exploration and exploitation abilities have been further improved by incorporating the genetic operators, namely, crossover and mutation in PSO algorithm. The constraints defined in the problem are handled with the help of the parameter-free penalty function. The experimental results of constrained optimization problems are reported and compared with the typical approaches exist in the literature. As shown, the solutions obtained by the proposed approach are superior to those of existing best solutions reported in the literature. Furthermore, experimental results indicate that the proposed approach may yield better solutions to engineering problems than those obtained by using current algorithms.

A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem

The objective of the present work is divided into two folds. Firstly, an interval-valued Pythagorean fuzzy set (IVPFS) has been introduced along with their two aggregation operators, namely, interval-valued Pythagorean fuzzy weighted average and weighted geometric operators for different IVPFS. Secondly, an improved accuracy function under IVPFS environment has been developed by taking the account of the unknown hesitation degree. The proposed function has been applied to decision making problems to show the validity, practicality and effectiveness of the new approach. A systematic comparison between the existing work and the proposed work has also been given.

Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment

We present a multi-objective reliability optimization problem using intuitionistic fuzzy optimization.Reliability is considered as a triangular fuzzy number during formulation.Exponential membership and quadratic nonmembership functions are used for defining their fuzzy goals.We utilize the PSO algorithm to the solve the optimization problem.Examples are shown to illustrate the method. In designing phase of systems, design parameters such as component reliabilities and cost are normally under uncertainties. This paper presents a methodology for solving the multi-objective reliability optimization model in which parameters are considered as imprecise in terms of triangular interval data. The uncertain multi-objective optimization model is converted into deterministic multi-objective model including left, center and right interval functions. A conflicting nature between the objectives is resolved with the help of intuitionistic fuzzy programming technique by considering linear as well as the nonlinear degree of membership and non-membership functions. The resultants max-min problem has been solved with particle swarm optimization (PSO) and compared their results with genetic algorithm (GA). Finally, a numerical instance is presented to show the performance of the proposed approach.

A Novel Correlation Coefficients between Pythagorean Fuzzy Sets and Its Applications to Decision-Making Processes

Pythagorean fuzzy set (PFS) is one of the most successful in terms of representing comprehensively uncertain and vague information. Considering that the correlation coefficient plays an important role in statistics and engineering sciences, in this paper, after pointing out the weakness of the existing correlation coefficients between intuitionistic fuzzy sets (IFSs), we propose a novel correlation coefficient and weighted correlation coefficient formulation to measure the relationship between two PFSs. Pairs of membership, nonmembership, and hesitation degree as a vector representation with the two elements have been considered during formulation. Numerical examples of pattern recognition and medical diagnosis have been taken to demonstrate the efficiency of the proposed approach. Results computed by the proposed approach are compared with the existing indices.

Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making

A series of generalized Intuitionistic fuzzy Einstein aggregation operators are developed.Interaction between the membership and non-membership has been considered.Shortcoming of the existing functions is overcome.Sensitivity analysis of decision maker preferences has been assessed.A systematic comparison between the existing work and the proposed work have been given. The present paper proposes some new geometric aggregation operations on the intuitionistic fuzzy sets (IFSs) environment. Based on it, a new class of generalized geometric interaction averaging aggregation operators using Einstein norms and conorms are developed, which includes the weighted, ordered weighted and hybrid weighted averaging operators. Furthermore, desirable properties corresponding to proposed operators have been stated. Finally, a multi-criteria decision making (MCDM) problem has been illustrated to show the validity and effectiveness of the proposed operators. The computed results have been compared with the existing results.

Generalized Pythagorean Fuzzy Geometric Aggregation Operators Using Einstein t‐Norm and t‐Conorm for Multicriteria Decision‐Making Process

The objective of this paper is to present some series of geometric‐aggregated operators under Pythagorean fuzzy environment by relaxing the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted geometric, Pythagorean fuzzy Einstein ordered weighted geometric, generalized Pythagorean fuzzy Einstein weighted geometric, and generalized Pythagorean fuzzy Einstein ordered weighted geometric operators, are proposed in this paper. Some of its properties have also been investigated in details. Finally, an illustrative example for multicriteria decision‐making problems of alternatives is taken to demonstrate the effectiveness of the approach.

Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application

In this paper, some series of averaging aggregation operators have been presented under the intuitionistic fuzzy environment by considering the degrees of hesitation between the membership functions. For it, firstly, shortcoming of some existing aggregation operators has been identified and then new operational laws have been proposed for overcoming these shortcoming. Based on these operations, weighted, ordered weighted and hybrid averaging aggregation operators have been proposed by using Einstein operational laws. Furthermore, some desirable properties such as idempotency, boundedness, homogeneity etc. are studied. Finally, a multi-criteria decision making (MCDM) method has been presented based on proposed operators and compare their performance with the existing operators.