Animesh Biswas

A fuzzy programming approach for solving quadratic bilevel programming problems with fuzzy resource constraints

In this paper, a fuzzy goal programming (FGP) model is developed to solve quadratic bilevel programming problems with fuzzy resource constraints for proper distribution of decision powers to the leader and follower. In the model, formulation of the problem, concept of tolerance membership functions for measuring the degree of satisfaction of the objective of the leader and follower are defined first, under the fuzzily described system constraints. Subsequently, a quadratic programming model is constructed on the basis of degree of satisfaction of both the leader and follower. The developed model is converted into an equivalent non-linear FGP model to achieve the highest degree of satisfaction (unity) to the extent possible. In the decision process, the Taylors series approximation technique is applied to linearise the non-linear goals and to achieve the fuzzy goal objective values of the decision-makers at both the levels, by arriving at most satisfactory solution regarding the optimality of two different sets of decision variables controlled separately by each of them. An illustrative example is solved to demonstrate the efficiency of the proposed approach and the solution is compared with the solution obtained by using an existing methodology developed by Osman et al. in 2004.

A Fuzzy Goal Programming Method for Solving Chance Constrained Programming with Fuzzy Parameters

This paper develops a fuzzy goal programming methodology for solving chance constrained programming problem involving fuzzy numbers and fuzzy random variables which follow standard normal distribution. In the model formulation process, the problem is converted into an equivalent fuzzy programming problem by applying chance constrained programming technique. Then the problem is divided into equivalent sub problems by considering the tolerance limit of the fuzzy numbers relating to the system constraint having different forms of membership functions in the decision making context. Afterwards the objective and the constraints resulting from chance constraints are converted into fuzzy goals by assigning some imprecise aspiration levels. In the decision process, a fuzzy goal programming methodology is introduced to find the most satisfactory solution in the decision making environment. To demonstrate the potentiality of the proposed approach, an illustrative example, studied previously, is solved and is compared with the existing methodologies.

Using Fuzzy Goal Programming Technique to Solve Multiobjective Chance Constrained Programming Problems in a Fuzzy Environment

In this paper a fuzzy goal programming technique is presented to solve multiobjective decision making problems in a probabilistic decision making environment where the right sided parameters associated with the system constraints are exponentially distributed fuzzy random variables. In model formulation of the problem, the fuzzy chance constrained programming problem is converted into a fuzzy programming problem by using general chance constrained methodology. Then by realizing the fuzzy nature of the parameters associated with the system constraints, the problem is decomposed by considering the tolerance ranges of the parameters. The tolerance membership functions of each of the individual objectives are defined in isolation to measure the degree of achievements of the goal levels of the objectives. Then a fuzzy goal programming model is developed to achieve the highest degree of each of the defined membership functions to the extent possible. In the solution process the minsum fuzzy goal programming technique is used to find the most satisfactory decision in the decision making environment. An example is solved to illustrate the proposed methodology and the achieved solution is compared with the solution of another existing technique.

A Fuzzy Multilevel Programming Method for Hierarchical Decision Making

This paper describes a fuzzy programming method for multilevel programming problems in a large hierarchical decision making organization. In the proposed approach, first the objectives at different decision making units are described fuzzily by setting an imprecise aspiration level to each of them. Then the defined fuzzy goals for the objective functions and the control vectors of the upper-level units are characterized by membership functions for measuring the degree of satisfaction of the decision makers located at different hierarchical levels.

Exploration of transcultural properties of the reduced version of the Morningness–Eveningness Questionnaire (rMEQ) using adaptive neuro-fuzzy inference system

The reduced version of the Morningness–Eveningness Questionnaire (rMEQ) is widely used to study morningness orientation. The fuzzy analysis helps mapping outputs of the questionnaire irrespective of linguistic and cross-cultural aspects in an efficient manner. In the present study, the rMEQ was administered to a convenience sample of university students (N = 2660) in four different countries and responses have been quantified by using an adaptive neuro-fuzzy inference system for the cross-cultural comparison and then the quantified values are used to construct the proposed model. The cross-country fuzzy morningness value showed that environmental temperature has definite influence on morningness orientation but other factors may also have a role. The developed model can be universally used to analyse the morning–evening orientation of people more precisely without cross-language and cross-cultural biases and it would become a potential tool for interpretation of morningness scores and counselling of individuals.

Priority based fuzzy goal programming technique to fractional fuzzy goals using dynamic programming

This paper describes the use of preemptive priority based fuzzy goal programming method to fuzzy multiobjective fractional decision making problems under the framework of multistage dynamic programming. In the proposed approach, the membership functions for the defined objective goals with fuzzy aspiration levels are determined first without linearizing the fractional objectives which may have linear or nonlinear forms. Then the problem is solved recursively for achievement of the highest membership value (unity) by using priority based goal programming methodology at each decision stages and thereby identifying the optimal decision in the present decision making arena. A numerical example is solved to represent potentiality of the proposed approach.

Assessing Morningness of a Group of People by Using Fuzzy Expert System and Adaptive Neuro Fuzzy Inference Model

In this paper two computational systems, one is based on fuzzy logic system and other is based on adaptive neuro fuzzy inference system (ANFIS), are developed for assessing morningness of a group of people and the result is compared for finding the best system in the assessment process. In fuzzy rule based system, the linguistic terms for assessing morningness are quantified by using fuzzy logic and a fuzzy expert system is developed. On the other side, an ANFIS model is generated to assess data for training and testing the model in accordance with a preference scale adopted to quantify the responses of subjects for a reduced version of Morningness-Eveningness Questionnaire (rMEQ). The result reflects that ANFIS is able to assess morningness better than fuzzy expert inference system.

A fuzzy goal programming technique for multi-objective chance constrained programming with normally distributed fuzzy random variables and fuzzy numbers

This paper presents a fuzzy goal programming approach for modelling and solving multi-objective decision making problems having fuzzy random variables and fuzzy numbers associated with the system constraints. In the model formulation process, the problem is converted into an equivalent fuzzy programming problem by using chance constrained programming technique. The problem is then decomposed into sub problems by considering the tolerance limits of fuzzy numbers relating to the system constraints. The individual optimal solution of each objective is found to construct the membership goals. A two-phase fuzzy goal programming model is developed to achieve the highest degree of each of the defined membership goals of the objectives to the extent possible by minimising under deviational variables and thereby obtaining most satisfactory solution in the decision making environment. A numerical example is solved to illustrate the proposed approach and the achieved solutions are compared with other existing methodologies.

A fuzzy programming method for solving multiobjective chance constrained programming problems involving log-normally distributed fuzzy random variables

In this paper a fuzzy programming technique is presented to solve multiobjective chance constrained programming problem having the right sided parameters associated with system constrains follow log-normal distribution. In model formulation process the imprecise probabilistic problem is converted into an equivalent fuzzy programming model by applying chance constrained programming methodology. Then by considering fuzzy nature of parameters involved with the system constraints, the problem is decomposed on the basis of tolerance values of the parameters. The individual optimal value of each objective is found to construct the membership goals of the objectives. A priority based fuzzy goal programming approach is used for achievement of the highest membership degree to the extent possible under different priority structures to achieve the ideal point dependent solution in the decision making context. To expound the potentiality of the proposed approach, an illustrative example is solved and the solution is compared with other existing technique.

An Integrated TOPSIS Approach to MADM with Interval-Valued Intuitionistic Fuzzy Settings

In this paper, the three-parameter characterization of intuitionistic fuzzy sets and normalized hamming distance are employed to develop mathematical programming-based TOPSIS techniques in interval-valued intuitionistic fuzzy settings. A pair of linear fractional programming models are generated which are simplified for producing intervals to measure relative closeness coefficients of alternatives. Possibility degree matrix is obtained by pairwise comparisons of closeness coefficients and optimal degrees are estimated for final ranking of alternatives. The proposed approach is illustrated through a numerical example.