Effective decision‐making requires well‐founded optimization models and algorithms tolerant of real‐world uncertainties. In the mid‐1980s, intuitionistic fuzzy set theory emerged as another mathematical framework to deal with the uncertainty of subjective judgments and made it possible to represent hesitancy in a decision‐making problem. Nowadays, intuitionistic fuzzy multiobjective linear programming (IFMOLP) problems are a topic of extensive research, for which a considerable number of solution approaches are being developed. Among the available solution approaches, ranking function‐based approaches stand out for their simplicity to transform these problems into conventional ones. However, these approaches do not always guarantee Pareto optimal solutions. In this study, the concepts of dominance and Pareto optimality are extended to the intuitionistic fuzzy case by using lexicographic criteria for ranking triangular intuitionistic fuzzy numbers (TIFNs). Furthermore, an intuitionistic fuzzy ε‐constraint method is proposed to solve IFMOLP problems with TIFNs. The proposed method is illustrated by solving two intuitionistic fuzzy transportation problems addressed in two studies (S. Mahajan and S. K. Gupta’s, “On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions,” Ann Oper Res, vol. 296, no. 1, pp. 211–241, 2021, and Ghosh et al.’s, “Multi‐objective fully intuitionistic fuzzy fixed‐charge solid transportation problem,” Complex Intell Syst, vol. 7, no. 2, pp. 1009–1023, 2021). Results show that, in contrast with Mahajan and Gupta’s and Ghosh et al.’s methods, the proposed method guarantees Pareto optimality and also makes it possible to obtain multiple solutions to the problems.

Linear ranking functions are often used to transform fuzzy multiobjective linear programming (MOLP) problems into crisp ones. The crisp MOLP problems are then solved by using classical methods (eg, weighted sum, epsilon-constraint, etc), or fuzzy ones based on Bellman and Zadeh's decision-making model. In this paper, we show that this transformation does not guarantee Pareto optimal fuzzy solutions for the original fuzzy problems. By using lexicographic ranking criteria, we propose a fuzzy epsilon-constraint method that yields Pareto optimal fuzzy solutions of fuzzy variable and fully fuzzy MOLP problems, in which all parameters and decision variables take on LR fuzzy numbers. The proposed method is illustrated by means of three numerical examples, including a fully fuzzy multiobjective project crashing problem.

Fuzzy linear programming (FLP) problems with a wide varietyof applications in sciencesand engineering allow working with imprecise data and constraints, leading to more realistic models. The main contribution of this study is to deal with the formulation of a kind of FLP problems, known as bounded interval-valued fuzzy numbers linear programming (BIVFNLP) problems, with coefficients of decision variables in the objective function, resource vector, and coefficients of the technological matrix represented as interval-valued fuzzy numbers (IVFNs), and crisp decision variables limited to lower and upper bounds. Here, based on signed distance ranking to order IVFNs, the bounded simplex method is extended to obtain an interval-valued fuzzy optimal value for the BIVFNLP problem under consideration. Finally, one illustrative example is given to show the superiority of the proposed algorithm over the existing ones.

A “standard” map provides a simplified representation of the real world but is not able to adapt to the needs of different users having different preferences. On the contrary, adaptive maps are aimed at representing the world as seen through the eyes of the user depicting the suitability/difficulty of the paths between points of interest according to the user's preferences. Adaptive maps consider, simultaneously, multiple attributes like travel time, distance, slopes, etc. In this paper, a model for adaptive maps is presented. A generation and a visualization methods are proposed. To illustrate the results, five different adaptive maps are generated and visualized considering different attributes and preferences.

In this paper, a review of decision-making models based on the rough set theory is presented. The use of these techniques allows for the presence of uncertainty in computer models that are developed for decision making, and to formulate the decision-making models using the experiences of previous decisions made. Since the formulation of these models differs from the classical approach of decision-making models, in this paper, the models are analyzed and a method is proposed for its implementation.

Coherence measures are a tool to compare those fuzzy sets that are sensitive to their own similarity as well as to their fuzzy nature. Within this article we can find three generalizations made about the definition of coherence measures: a first one for any fuzzy set, a second one for any definition about strong negation, and a final one for an extension in those coherence measures that, as a result, do not cause a value in the unit interval, but a fuzzy set in that interval. Tools and properties are offered to create coherence measures. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 1–11, 2005.

The interface between combinatorial optimization and fuzzy sets-based methodologies is the subject of very active and increasing research. In this context we describe FANS, a fuzzy adaptive neighborhood search optimization heuristic that uses a fuzzy valuation to qualify solutions and adapts its behavior as a function of the search state. FANS may also be regarded as a local search framework. We show the application of this fuzzy sets-based heuristic to the protein structure prediction problem in two aspects: first, to analyze how the codification of the solutions affects the results, and second, to confirm that FANS is able to obtain as good results as a genetic algorithm. Both results shed some light on the application of heuristics to the protein structure prediction problem and show the benefits and power of combining basic fuzzy sets ideas with heuristic techniques. © 2002 Wiley Periodicals, Inc.

In almost every work on fuzzy sets, the existence of membership functions taking part in the considered model is assumed and it is not studied in depth whether or not such functions exist. On the other hand, generally the relationship between a certain studied characteristic and its referential set is not problematic since it is usually a matter of direct measurement. However, in a great variety of situations it is necessary to work with properties whose measurement is not obvious, but is an object of study in itself. In this work, we start by approaching the description of the cases in which the existence of a membership function can be guaranteed. Next, we consider the situations where one faces linguistic terms associated with attributes that cannot be directly measured; in such cases, the existence of a membership function cannot be assured. However, the conditions of existence and methods for the construction of those membership functions may be based on the psychological measurement theory. ©1999 John Wiley & Sons, Inc.

Genetic algorithms are adaptive methods which may be used as approximation heuristic for search and optimization problems. Genetic algorithms process a population of search space solutions with three operations: selection, crossover, and mutation. A great problem in the use of genetic algorithms is the premature convergence, a premature stagnation of the search caused by the lack of diversity in the population and a disproportionate relationship between exploitation and exploration. The crossover operator is considered one of the most determinant elements for solving this problem. In this article we present two types of crossover operators based on fuzzy connectives for real-coded genetic algorithms. The first type is designed to keep a suitable sequence between the exploration and the exploitation along the genetic algorithm's run, the dynamic fuzzy connectives-based crossover operators, the second, for generating offspring near to the best parents in order to offer diversity or convergence in a profitable way, the heuristic fuzzy connectives-based crossover operators. We combine both crossover operators for designing dynamic heuristic fuzzy connectives-based crossover operators that show a robust behavior. © 1996 John Wiley & Sons, Inc.

This article discusses the applications of fuzzy boolean programming problems for representing and reasoning with propositional knowledge. the use of the models provided by the fuzzy boolean problems are proposed to answer imprecise questions in precisely stated knowledge-based systems. Also, the advantages of using fuzzy boolean programming instead of classical ones are presented in the framework of propositional knowledge. © 1994 John Wiley & Sons, Inc.

A model is proposed for dealing with decision-making problems in which the decision maker has a vague (linguistically assessed) and incomplete information about results and external factors (a quite usual situation in real decision cases). It is assumed here that utilities are evaluated in a term set of labels and the incomplete information is supposed to be a partial linguistic assignment of probability with values on a term set of linguistic likelihoods. the first step is to discuss a well-fitted interpretation of that model. After that, basic decision rules based on fuzzy risk intervals are developed. Additionally the suitability of considering a hierarchical structure (represented by a tree) for the set of utility labels is analyzed. © 1994 John Wiley & Sons, Inc.

This article is devoted to defining some aggregation operations between linguistic labels. First, from some remarks about the meaning of label addition, a formal and general definition of a label space is introduced. After, addition, difference, and product by a positive real number are formally defined on that space. the more important properties of these operations are studied, paying special attention to the convex combination labels. the article concludes with some numerical examples. © 1993 John Wiley Sons, Inc.

Using linguistic values to assess results and information about external factors is quite usual in real decision situations. In this article we present a general model for such problems. Utilities are evaluated in a term set of labels and the information is supposed to be a linguistic evidence, that is, is to be represented by a basic assignment of probability (in the sense of Dempster-Shafer) but taking its values on a term set of linguistic likelihoods. Basic decision rules, based on fuzzy risk intervals, are developed and illustrated by several examples. the last section is devoted to analyzing the suitability of considering a hierarchical structure (represented by a tree) for the set of utility labels. © 1992 John Wiley & Sons, Inc.