C. R. Bector

Matrix Games with Fuzzy Goals and Fuzzy Linear Programming Duality

A two person zero-sum matrix game with fuzzy goals is shown to be equivalent to a primal-dual pair of fuzzy linear programming problems. Further certain difficulties with similar studies reported in the literature are also discussed.

Bi-matrix Games with Fuzzy Goals and Fuzzy

A bi-matrix game with fuzzy goal is shown to be equivalent to a (crisp) non-linear programming problem in which the objective as well as all constraint functions are linear except two constraint functions, which are quadratic. This equivalence is further extended to bi-matrix games with fuzzy pay-offs, as well as to bi-matrix games with fuzzy goals and fuzzy payoffs, whose equilibrium strategies are conceptualized by employing a suitable ranking (defuzzification) function.

Application of possibility theory to investment decisions

Carlson and Fuller (2001, Fuzzy Sets and Systems, 122, 315–326) introduced the concept of possibilistic mean, variance and covariance of fuzzy numbers. In this paper, we extend some of these results to a nonlinear type of fuzzy numbers called adaptive fuzzy numbers (see Bodjanova (2005, Information Science, 172, 73–89) for detail). We then discuss the application of these results to decision making problems in which the parameters may involve uncertainty and vagueness. As an application, we develop expression for fuzzy net present value (FNPV) of future cash flows involving adaptive fuzzy numbers by using their possibilistic moments. An illustrative numerical example is given to illustrate the results.

A note on Generalized fuzzy linear programming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach

In this short note, we point out that the paper entitled above suffers from certain mistakes.

Fuzzy EOQ model using possibilistic approach

Purpose – The purpose of this paper is to derive an economic order quantity (EOQ) for an inventory control problem where the inventory carrying cost and the order cost are uncertain, represented by fuzzy numbers. The fuzzy numbers used herein are most general so far, represented by adaptive trapezoidal fuzzy numbers. This paper attempts to use the most general form of fuzziness to represent the uncertainty of the parameters in the inventory model.Design/methodology/approach – The fuzzy EOQ formula derivation is analytical. Given the inventory cost Cc and the order cost Co as fuzzy numbers and the demand, a crisp number and instant replenishment of inventory, a fuzzy EOQ is derived. This is done by using the possibilistic mean and the possibilistic variance of the fuzzy total inventory cost. Then for practical implementation, this quantity is defuzzyfied using the middle of the maxima (MOM) of the fuzzy EOQ, in order to get the crisp value of the EOQ that minimizes the (fuzzy) total inventory cost.Findings...

Renyi’s Entropy Model for Brand Purchase Behaviour

Abstract For the Renyi’s entropy model for brand purchase behaviour, it is proved that if none of the market shares of a specified number of brands in the market is prescribed, then the entropy will be maximum when the market shares of all these brands are equal, and if the market shares of some of those brands are prescribed, then the entropy will be maximum when the market shares for the remaining brands are, equal. The maximization of entropy is also studied when some or all of the probabilities of some specified brands being selected are prescribed. Results for Shannon’s entropy model for brand purchase behaviour are deduced as a special case.

A mixed solution strategy for group multi-attribute TOPSIS model with application to supplier selection problem

Abstract In this paper we introduce a concept called (φ, λ) -mixed solution strategy for the group fuzzy TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) model using possibility concepts, objective entropy weights derived exclusively from the decision matrix, and a group decision methodology to compute criteria weights. This approach reflects both the subjective considerations of a group of decision makers and the objective information in the decision matrix. An application to the supplier selection problem illustrates the application of the proposed method.

Possibilistic characterization of (m,n) -Trapezoidal fuzzy numbers with applications

Abstract In this paper, we derive possibilistic mean, possibilistic variance, and possibilistic covariance of (m, n)-trapezoidal fuzzy numbers. Results for ordinary trapezoidal and triangular fuzzy numbers (both non-symmetric and symmetric) are derived as special cases. Furthermore, examples are provided through which we discuss weighted possibilistic moments for (m, n)-trapezoidal fuzzy numbers, using some specific weighting function.

Voting Behavior Through Entropy Approach

Abstract Under a variety of assumptions, a number of results regarding the voting behavior of voters in an election are obtained by using the Maximum Entropy Principle.