P. K. De

Ranking of trapezoidal intuitionistic fuzzy numbers

Techniques for ranking simple fuzzy numbers are abundant in nature. However, we lack effective methods for ranking intuitionistic fuzzy numbers(IFN). The aim of this paper is to introduce a new ranking procedure for trapezoidal intuitionistic fuzzy number(TRIFN). To serve the purpose, the value and ambiguity index of TRIFNs have been defined. In order to rank TRIFNs, we have defined a ranking function by taking sum of value and ambiguity index. To illustrate the the proposed ranking method a numerical example has been given.

Ranking of intuitionistic fuzzy numbers by new distance measure

Ranking of intuitionsitic fuzzy number plays a vital role in decision making and other intuitionistic fuzzy applications. In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. We first define a distance measure for interval numbers based on Lp metric and further generalize the idea for intuitionistic fuzzy number by forming interval with their respective value and ambiguity indices. Finally, some comparative results are given in tabular form.

A general formulation and solution of fuzzy multi-objective linear programming problems

The purpose of this article is to explain how a fuzzy linear programming model can be transformed into a fuzzy multi-objective linear programming model and then solved. An algorithm is developed to present our approach and fuzzy optimal solution is obtained. To demonstrate the efficiency and feasibility of the proposed approach, one numerical example has been solved.

Using goal programming approach to solve fuzzy multi-objective linear fractional programming problems

The aims of the article is to the study fuzzy multi-objective linear fractional programming (FMOLFP) problem by using goal programming approach. At first by using Charnes and Cooper [1] transformation, the FMOLFP problem is transformed to fuzzy multi-objective linear programming (FMOLP) problem. The reduced problem is formulated by goal programming approach to find out the solution of FMOLFP problem. By using our proposed GP approach some pareto optimal solution is obtained for the FMOLFP problem. A numerical example is presented to demonstrate our approach.

Solution of multi objective linear fractional programming problem by Taylor series approach

This article proposes to handle multi objective linear fractional programming (MOLFP) problems in fuzzy environment. As a generalized mean value theorem first order Taylor series approach is used to convert multi objective linear fractional programming to multi objective linear programming problem by introducing imprecise aspiration level to each objective. Then additive weighted method has been used to get its solution. It has been observed that optimality reached for different weight values of the membership function for the different objective functions. The method has been presented by an algorithm and sensitivity analysis for the fuzzy multi objective linear fractional programming (FMOLFP) problem with respect to aspiration level and tolerance limit are also presented. The present approach is demonstrated with one numerical example.

Application of ranking method to multi attribute decision making with trapezoidal intuitionistic fuzzy numbers

An approach to multi attribute group decision making with intuitionistic fuzzy setting has been described. In the present article, the application of proposed ranking method based on value and ambiguity has been studied. A multi attribute group decision making problem has been studied with an illustrative numerical example.

Algorithm for Solving Fuzzy Multiobjective Linear Fractional Programming Problem by Additive Weighted Method

In this paper attention has been paid to the study of multiobjective linear fractional programming problem (MOLFPP) by using fuzzy set theoretic approach. In this approach, MOLFPP is transformed into multiobjective linear programming problem (MOLPP) by suitable transformation. In algorithm-I, MOLFPP is transformed into MOLPP by using fuzzy set theory and the pareto optimal solution of the transformed MOLPP is obtained by applying Zimmermann’s min-operator model and simplex method. Further we have used additive weighted method to modify the above approach. Algorithm-II has been presented to find the pareto optimal solution of MOLFPP by applying additive weighted method. To demonstrate the applicability of the proposed approach, one numerical example is solved to find the pareto optimal solution by applying this two algorithms.

A study on continuity in Intuitionistic Menger Normed space

In this paper, attention has been paid to the study of Intuitionistic Menger Normed space and various properties of this space. Our first aim is to redefine the notion of Intuitionistic Menger Normed space which was earlier given by S. Kutukcu, A. Tuna, A. T. Yakut [7]. Secondly, we have studied continuity in this space. Further, continuity and boundedness of linear operators in Intuitionistic Menger normed settings has been discussed according to our new definition.