Hiroe Tsubaki

Random fuzzy multi-objective linear programming: Optimization of possibilistic value at risk (pVaR)

This paper considers multiobjective linear programming problems (MOLPP) where random fuzzy variables are contained in objective functions and constraints. A new decision making model optimizing possibilistic value at risk (pVaR) is proposed by incorporating the concept of value at risk (VaR) into possibility theory. It is shown that the original MOLPPs involving random fuzzy variables are transformed into deterministic problems. An interactive algorithm is presented to derive a satisficing solution for a decision maker (DM) from among a set of Pareto optimal solutions. Each Pareto optimal solution that is a candidate of the satisficing solution is exactly obtained by using convex programming techniques. A simple numerical example is provided to show the applicability of the proposed methodology to real-world problems with multiple objectives in uncertain environments.

Random fuzzy bilevel linear programming through possibility-based value at risk model

This article considers bilevel linear programming problems where random fuzzy variables are contained in objective functions and constraints. In order to construct a new optimization criterion under fuzziness and randomness, the concept of value at risk and possibility theory are incorporated. The purpose of the proposed decision making model is to optimize possibility-based values at risk. It is shown that the original bilevel programming problems involving random fuzzy variables are transformed into deterministic problems. The characteristic of the proposed model is that the corresponding Stackelberg problem is exactly solved by using nonlinear bilevel programming techniques under some convexity properties. A simple numerical example is provided to show the applicability of the proposed methodology to real-world hierarchical problems.

Tour route planning problem for sightseeing with the multiroute under several uncertain conditions

This paper proposes a route planning problem for sightseeing with fuzzy random variables based on constraints of required traveling times and satisfactions of the total sightseeing activity. In general, traveling times among sightseeing places and the satisfactions of activities depend on weather and climate conditions. Tourists will like to do their favorable route planning without drastically changing the tour route of usual condition such as fine even if the weather condition changes for the worse. Therefore, the fuzzy random variables for traveling times and satisfactions of activities derived from uncertainty conditions are introduced, and a new route planning problem is proposed to obtain the favorable route similar to the optimal route under the usual condition. As a basic case of fuzzy numbers, interval values and the order relation are introduced. From the order relation, the proposed model is transformed into an extended model of network optimization problems. A numerical example is provided to compare the proposed model with standard route planning problems for sightseeing.

A Constructing Algorithm for Appropriate Piecewise Linear Membership Function based on Statistics and Information Theory

Abstract This paper proposes a constructing algorithm for an appropriate membership function to integrate the fuzzy Shannon entropy with a piecewise linear function into subjective intervals estimation by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in real-world decision making. The main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the initial mathematical programming problem efficiently using previous constructing approaches. In this paper, introducing some natural assumptions in the real-world and performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each appropriate membership value is developed.

Analysis of impact of geographic characteristics on suicide rate and visualization of result with Geographic Information System.

The aim of our study was to understand the geographic characteristics of Japanese communities and the impact of these characteristics on suicide rates.

An Interactive Algorithm to Construct an Appropriate Nonlinear Membership Function Using Information Theory and Statistical Method

Abstract This paper develops a constructing algorithm for an appropriate membership function as objectively as possible. It is important to set an appropriate membership function for real-world decision making. The main academic contribution of our proposed algorithm is to integrate a general continuous and nonlinear function with fuzzy Shannon entropy into subjective interval estimation by a heuristic method under a given probability density function based on real-world data. Two main steps of our proposed approach are to set membership values a decision maker confidently judges whether an element is included in the given set or not and to obtain other values objectively by solving a mathematical programming problem with fuzzy Shannon entropy. It is difficult to solve the problem efficiently using previous constructing approaches due to nonlinear function. In this paper, the given nonlinear membership function is approximately transformed into a piecewise linear membership function, and the appropriate values are determined. Furthermore, by introducing natural assumptions in the real-world and interactively adjusting the membership values, an algorithm to obtain the optimal condition of each appropriate membership value is developed.

Versatile route planning for sightseeing with tourist's satisfaction dependent on fatigue degree

This paper proposes a versatile route planning problem for sightseeing with fuzzy random variables based on constraints of required traveling times and total satisfaction of sightseeing activities. In general, traveling times among sightseeing places and the satisfactions of activities depend on weather and climate conditions. Furthermore, the satisfactions of activities are also dependent on the tourists fatigue degree. Therefore, the fuzzy random variables for traveling times and satisfactions of activities dependent on the fatigue degree under uncertainty are introduced. Tourists will like to do their favorable route planning without drastically changing the tour route of usual condition such as fine even if the weather condition changes for the worse. A new route planning problem is proposed to obtain the favorable route similar to the optimal route under the usual condition. As a basic case of fuzzy numbers, interval values and the order relation are introduced. From the order relation, the proposed model is transformed into an extended model of network optimization problems. A numerical example is provided to compare the proposed model with standard route planning problems for sightseeing.

The Grammar of Technology Development

Grammar of technology development is a trans-disciplinary description of common approaches to well-controlled technology developments in which the most effective method for development is systematically selected. Here technology development involves the following four sequential activities for both a real society and the corresponding virtual society using appropriate engineering models: 1) Value selection of targets by defining the expected recognized quality elements. 2) Translation of the recognized quality elements occurring in societies into functional quality elements that designers and engineers can specify concrete parameters in their engineering models. 3) Optimization of design parameters of the engineering models to ascertain their usability. 4) Value injection into the real society to harmonize realized functional qualities and corresponding recognized quality.

A Route Recommendation System for Sightseeing with Network Optimization and Conditional Probability

This paper proposes a route recommendation system for sightseeing based on a network optimization problem. Traveling and sightseeing times are randomly changed dependent on current traffic and congestion conditions, and hence, Time-Expanded Network (TEN) to contain a copy to the set of nodes in the underlying static network for each discrete time step is introduced. In addition, in order to select the next sightseeing site, conditional probabilities are introduced, which are calculated by current conditions, statistical and Web data. Our proposed model is formulated as a nonlinear and discrete optimization problem, and it is hard to solve it directly and efficiently. Therefore, an efficient algorithm is also developed based on dynamic programming and transformation of the main problem into the recursive equation.

Route planning problem with groups of sightseeing sites classified by tourist's sensitivity under Time-Expanded Network

This paper proposes a sightseeing route planning problem with time-dependent traveling times among sightseeing sites. Since traveling times are dependent on the time of day, Time-Expanded Network (TEN), which contains a copy to the set of nodes in the underlying static network for each discrete time step, is introduced. In addition, it is hard to set satisfaction values at sightseeing sites numerically due to tourists ambiguous sensitivity, but it is not difficult to classify sightseeing sites into several groups by the tourist. Therefore, the objective function of our proposed model is set to maximize the total visiting sightseeing sites in each group. The problem is a multiobjective programming problem, and hence, a principle of compromise is introduced to solve our proposed problem in network optimization. Furthermore, a strict algorithm is also developed to equivalently transform the main problem into the existing TEN-based problem.