Solving P - Norm Intuitionistic Fuzzy Programming Problem

In this paper, notion of p - norm generalized trapezoidal intuitionistic fuzzy numbers is introduced. A new ranking method is introduced for p - norm generalized trapezoidal intuitionistic fuzzy numbers. Also we consider linear programming problem in intuitionistic fuzzy environment. In this problem, all the coefficients and variables are represented by p - norm generalized trapezoidal intuitionistic fuzzy numbers. To overcome the limitations of the existing methods, a new method is proposed to compute the intuitionistic fuzzy optimal solution for intuitionistic fuzzy linear programming problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed approach.Comment: some erro

NEUTROSOPHIC MULTI-OBJECTIVE LINEAR PROGRAMMING

For modeling imprecise and indeterminate data for multi-objective decision making, two different methods: neutrosophic multi-objective linear/non-linear programming neutrosophic goal programming, which have been very recently proposed in the literatuire. In many economic problems, the well-known probabilities or fuzzy solutions procedures are not suitable because they cannot deal the situation when indeterminacy inherently involves in the problem. In this case we propose a new concept in optimization problem under uncertainty and indeterminacy. It is an extension of fuzzy and intuitionistic fuzzy optimization in which the degrees of indeterminacy and falsity (rejection) of objectives and constraints are simultaneously considered together with the degrees of truth membership (satisfaction/acceptance). The drawbacks of the existing neutrosophic optimization models have been presented and new framework of multi-objective optimization in neutrosophic environment has been proposed. The essence of the proposed approach is that it is capable of dealing with indeterminacy and falsity simultaneously

A NEW APPROACH ON SOLVING INTUITIONISTIC FUZZY LINEAR PROGRAMMING PROBLEM

ABSTRACT In this paper, we propose a new approach for solving Intuitionistic Fuzzy Linear Programming Problems (IFLPP) involving triangular intuitionistic fuzzy numbers (TIFN). We introduce a new algorithm for the solution of an Intuitionistic Fuzzy Linear Programming Problem without converting in to one or more classical Linear Programming Problems. Numerical examples are provided to show the efficiency of the proposed algorithm. Keywords: intuitionistic fuzzy set, fuzzy number, triangular intuitionistic fuzzy number, fuzzy linear programming problem. INTRODUCTION Modelling of real life problems involving optimization process. It is often difficult to get crisp and exact information for various parameters affecting the process and it involves high information cost. Furthermore the optimal solution of the problem depends on a limited number of constraints or conditions and thus some of the information collected is not useful. Under such situations it is highly impossible to formulate the mathematical model through the classical traditional methods. Hence in order to reduce information costs and also to construct a real model, the use of intuitionistic fuzzy number is more appropriate. Fuzzy sets are an efficient and reliable tool that allows us to handle such systems having imprecise parameters effectively. Atanossov [6] extended the fuzzy sets to the theory intuitionistic fuzzy sets. His studies emphasized that in view of handling imprecision, vagueness or uncertainty in information both the degree of belonging and degree of non-belonging should be considered as two independent properties as these are not complement of each other. Bellmann and Zade

‎Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership Functions

In real life‎, ‎structural problems can be described in linear and nonlinear forms‎. ‎This nonlinear structural problem is very challenging to solve when its all parameters are imprecise in nature‎. ‎Intuitionistic fuzzy sets were proposed to manage circumstances in which experts have some membership and non-membership value to judge an option‎. ‎Hesitant fuzzy sets were used to manage scenarios in which experts pause between many possible membership values while evaluating an alternative‎. ‎A new growing area of a generalized fuzzy set theory called intuitionistic hesitant fuzzy set (IHFS) provides useful tools for dealing with uncertainty in structural design problem that is observed in the actual world‎. ‎In this article‎, ‎we have developed a procedure to solve non-linear structural problem in an intuitionistic hesitant fuzzy (IHF) environment‎. ‎The concept of an intuitionistic hesitant fuzzy set is introduced to provide a computational basis to manage the situations in which experts assess an alternative in possible membership values and non-membership values‎. ‎This important feature is not available in the intuitionistic fuzzy optimization technique‎. ‎Here we have discussed the solution procedure of intuitionistic hesitant fuzzy optimization technique dedicatedly for linear‎, ‎exponential‎, ‎and hyperbolic types of membership and non-membership functions‎. ‎Some theoretical development based on these functions has been discussed‎. ‎A numerical illustration is given to justify the effectiveness and efficiency of the proposed method in comparison with fuzzy multi-objective nonlinear programming method and intuitionistic fuzzy multi-objective nonlinear programming method‎. ‎Finally‎, ‎based on the proposed work‎, ‎conclusions and future research directions are addressed‎

Intuitionistic fuzzy-based TOPSIS method for multi-criterion optimization problem: a novel compromise methodology

The decision-making process is characterized by some doubt or hesitation due to the existence of uncertainty among some objectives or criteria. In this sense, it is quite difficult for decision maker(s) to reach the precise/exact solutions for these objectives. In this study, a novel approach based on integrating the technique for order preference by similarity to ideal solution (TOPSIS) with the intuitionistic fuzzy set (IFS), named TOPSIS-IFS, for solving a multi-criterion optimization problem (MCOP) is proposed. In this context, the TOPSIS-IFS operates with two phases to reach the best compromise solution (BCS). First, the TOPSIS approach aims to characterize the conflicting natures among objectives by reducing these objectives into only two objectives. Second, IFS is incorporated to obtain the solution model under the concept of indeterminacy degree by defining two membership functions for each objective (i.e., satisfaction degree, dissatisfaction degree). The IFS can provide an effective framework that reflects the reality contained in any decision-making process. The proposed TOPSIS-IFS approach is validated by carrying out an illustrative example. The obtained solution by the approach is superior to those existing in the literature. Also, the TOPSIS-IFS approach has been investigated through solving the multi-objective transportation problem (MOTP) as a practical problem. Furthermore, impacts of IFS parameters are analyzed based on Taguchi method to demonstrate their effects on the BCS. Finally, this integration depicts a new philosophy in the mathematical programming field due to its interesting principles

An Inventory Model under Space Constraint in Neutrosophic Environment: A Neutrosophic Geometric Programming Approach

In this paper, an inventory model is developed without shortages where the production cost is inversely related to the set up cost and production quantity. In addition, the holding cost is considered time dependent. Here impreciseness is introduced in the storage area. The objective and constraint functions are defined by the truth (membership) degree, indeterminacy (hesitation) degree and falsity (non-membership) degree. Likewise, a non-linear programming problem with a constraint is also considered. Then these are solved by Neutrosophic Geometric Programming Technique for linear membership, hesitation and non-membership functions. Also the solution procedure for Neutrosophic Non-linear Programming Problem is proposed by using additive operator and Geometric Programming method. Numerical examples are presented to illustrate the models using the proposed procedure and the results are compared with the results obtained by other optimization techniques

Fuzzy Linear Programming with Interval Type-2 fuzzy constraints

Doctorad