Juan Carlos Figueroa-García

Multi-period Mixed Production Planning with uncertain demands: Fuzzy and interval fuzzy sets approach

This paper shows a general model of a Mixed Production Planning problem with fuzzy demands. The main focus is the development of a model for Production Planning using fuzzy sets in order to use classical mathematical programming techniques to reach an optimal solution over a multiple criteria context. The classical Fuzzy Linear Programming model namely the Soft Constraints Model is used to involve flexibility in the problem. Moreover, an Interval Fuzzy Set approach is used to involve uncertainty in the problem.

Distance measures for Interval Type-2 fuzzy numbers

This paper shows some distance measures for comparing Interval Type-2 fuzzy numbers. In addition, some definitions about ordering of Interval Type-2 fuzzy numbers based on their centroids, are provided. Some numerical examples are given, and some interpretation issues are explained.

Computing optimal solutions of a linear programming problem with interval type-2 fuzzy constraints

This paper presents the computation of the set of optimal solutions of a Fuzzy Linear Programming model with constraints that involve uncertainty, by means of Interval Type-2 Fuzzy sets. By applying convex optimization algorithms to a linear programming model with Interval Type-2 fuzzy constraints, an Interval Type-2 fuzzy set of optimal solutions derived from the uncertain constraints of the problem, is obtained. This set of optimal solutions is defined through four boundaries which determine its behavior. Finally, some theoretical considerations are made and explained through an application example.

A Transportation Model with Interval Type-2 Fuzzy Demands and Supplies

This paper presents a basic transportation model (TM) where its demands and supplies are defined as Interval Type-2 Fuzzy sets (IT2FS). This kind of constraints involves uncertainty to the membership function of a fuzzy set, so we called this model as Interval Type-2 Transportation Model (IT2TM). Using convex optimization techniques, a global solution of this problem can befound. To do so, we define a general model for IT2TM and then we present an application example to illustrate how the algorithm works.

On the computation of the distance between Interval Type-2 Fuzzy numbers using a-cuts

This paper presents a proposal for computing the distance between two Interval Type-2 Fuzzy numbers using its decomposition into a-cuts. This decomposition has been widely used in decision making, computation of a function of fuzzy sets, fuzzy optimization, etc, so the use of a-cuts to compare Interval Type-2 fuzzy numbers arises as an interesting method. In addition, some examples are provided and the comparison of Interval Type-2 fuzzy numbers using their centroids, is discussed.

Rule generation of fuzzy logic systems using a self-organized fuzzy neural network

Abstract This paper proposes an algorithm for creating rules of a fuzzy logic system using a neuro-fuzzy approach. The proposal is based on the results of Juang and Tsao who use a Fuzzy Neural Network (FNN) to generate rules and fuzzy sets from input data. A time series example is solved using our proposal, which is tested using statistical analysis of the residuals of the model.

A method for solving linear programming models with Interval Type-2 fuzzy constraints

This paper shows a method for solving linear programming problems that includes Interval Type-2 fuzzy constraints. The proposed method finds an optimal solution in these conditions using convex optimization techniques. Some feasibility conditions are presented, and some interpretation issues are discussed. An introductory example is solved using the proposed method, and its results are described and discussed.

Interval Type-2 Fuzzy Markov Chains

Uncertainties in fuzzy Markov chains can be treated in different ways. The use of interval type-2 fuzzy sets (IT2FS) allows describing the distributional behavior of an uncertain discrete-time Markov process through infinite type-1 fuzzy sets embedded in its Footprint of Uncertainty. In this way, a finite state fuzzy Markov chain process is defined in an interval type-2 fuzzy environment. To do so, its limiting properties and its type-reduced behavior are defined and applied to two explanatory examples.

On ordering words using the centroid and Yager index of an Interval Type-2 Fuzzy Number

Comparing words where multiple people is involved on defining the meaning of every word is a common situation in different real scenarios such as decision making, natural reasoning, etc. When multiple people express their opinions about a word/lable/concept, then an Interval Type-2 Fuzzy Number can be used to represent uncertainty involved in their opinions, so an important task is how to establish an order of every word involved. To do so, we propose to use the centroid and Yager Index Rank of an Interval Type-2 fuzzy number to establish the order of different words defined by multiple people. We provide an application example and an analysis of the results including some recommendations for practical implementations of both type reduction methods.

On Computing the Footprint of Uncertainty of an Interval Type-2 Fuzzy Set as Uncertainty Measure

This paper presents a uncertainty measure of an Interval Type-2 fuzzy set based on its Footprint of Uncertainty. The proposed measure provides information about the amount of uncertainty contained into an Interval Type-2 fuzzy set. Some relationships between the proposed measure and other well known measures of an Interval Type-2 fuzzy set as the centroid, variance, cardinality, etc. are defined and illustrated through some application examples.