Fuzzy Matrix Game: A Fast Approach using Artificial Hybrid Neural-Net Logic-Gate Switching Circuit

Introducing neuro -fuzzy concept in decision making problems, makes a new way in artificial intelligence and expert systems. Sometimes, neural networks are used to optimize certain performances. In general, knowledge acquisition becomes difficult when problem's variables, constraints, environment, decision maker's attitude and complex behavior are encountered with. A sense of fuzziness prevails in these situations; sometimes numerically and sometimes linguistically. Neural networks (or neural nets) help to overcome this problem. Neural networks are explicitly and implicitly hyped to draw out fuzzy rules from numerical information and linguistic information. Logic-gate and switching circuit mobilize the fuzzy data in crisp environment and can be used in artificial neural network, also. Game theory has a tremendous scope in decision making; and consequently decision makers' hesitant characters play an important role in it. In this paper, a game situation is clarified under artificial neural network through logic-gate switching circuit in hesitant fuzzy environment with a suitable example; and this concept can be applied in future for real-life situations.

Best Reply Player Against Mixed Evolutionarily Stable Strategy User

We consider matrix games with two phenotypes (players): one following a mixed evolutionarily stable strategy and another one that always plays a best reply against the action played by its opponent in the previous round (best reply player, BR). We focus on iterated games and well-mixed games with repetition (that is, the mean number of repetitions is positive, but not infinite). In both interaction schemes, there are conditions on the payoff matrix guaranteeing that the best reply player can replace the mixed ESS player. This is possible because best reply players in pairs, individually following their own selfish strategies, develop cycles where the bigger payoff can compensate their disadvantage compared with the ESS players. Well-mixed interaction is one of the basic assumptions of classical evolutionary matrix game theory. However, if the players repeat the game with certain probability, then they can react to their opponents’ behavior. Our main result is that the classical mixed ESS loses its general stability in the well-mixed population games with repetition in the sense that it can happen to be overrun by the BR player.

Evaluating the Effectiveness of an Intrusion Detection System Based on Matrix Games and Fuzzy Sets

We consider a problem formulated as a matrix game in which the gain of officials using a specific intrusion detection system (criminal actions) of intruders (player 1) is the probability of timely detection of these criminal actions (player 2). As a rule, it is not possible to unambiguously set the probability of timely detection of criminal actions, so it is proposed to use the apparatus of fuzzy set theory to evaluate it. Reviewed and discussed the basic concepts of fuzzy set theory, and an example of practical application of this theory to assess the efficiency of the detection system of criminal damage. Application of fuzzy set theory in assessing the possible actions of an attacker can detect existing vulnerabilities in information security of automated systems continue to spend improving the detection of criminal acts (hackers) to prevent the possibility of applying economic and other damage to the company.

Two-person game with hesitant fuzzy payoff: An application in MADM

Hesitant Fuzzy Set (HFS) permits the membership function having a collection of probable values which are more effective for modelling the real-life problems. Multiple Attribute Decision Making (MADM) process apparently assesses multiple conflicting attribute in decision making. In traditional decision making problems, each player is moving independently whereas in reality it is seen that each player aims to maximize personal profit which causes a negative impact on other player. MADM problem treats with candidate to the best alternative corresponding to the several attributes. Here, we present an MADM problem under hesitant fuzzy information and then transforming it into two-person matrix game, referred to herein as MADM game. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is one of the prominent approach for solving the MADM problems. In this work, we develop the TOPSIS based on Ordered Weighted Aggregation (OWA) operator and hybrid hesitant fuzzy normalized Euclidean distance. Then the two approaches, namely Hybrid Hesitant Fuzzy Ordered Weighted Aggregation-TOPSIS (HHFOWA-TOPSIS) and the Linear Programming Problem (LPP) are applied to solve the formulated MADM game. For solving MADM game, we apply LPP by considering the various values of $\alpha, \psi$, and HHFOWA-TOPSIS for finding the optimal alternative according to their scores. An investment selection problem is included to explain the feasibility and superiority of our formulated approaches. A comparison analysis is drawn among the obtained results which are derived from the two approaches. LPP and HHFOWA-TOPSIS provide the best alternative for the proposed problem. Finally, conclusions about our findings and outlooks are described.

Nash Equilibrium Points for Generalized Matrix Game Model with Interval Payoffs

Game theory-based models are widely used to solve multiple competitive problems such as oligopolistic competitions, marketing of new products, promotion of existing products competitions, and election presage. The payoffs of these competitive models have been conventionally considered as deterministic. However, these payoffs have ambiguity due to the uncertainty in the data sets. Interval analysis-based approaches are found to be efficient to tackle such uncertainty in data sets. In these approaches, the payoffs of the game model lie in some closed interval, which are estimated by previous information. The present paper considers a multiple player game model in which payoffs are uncertain and varies in a closed intervals. The necessary and sufficient conditions are explained to discuss the existence of Nash equilibrium point of such game models. Moreover, Nash equilibrium point of the model is obtained by solving a crisp bi-linear optimization problem. The developed methodology is further applied for obtaining the possible optimal strategy to win the parliament election presage problem.

A q-rung orthopair fuzzy non-cooperative game method for competitive strategy group decision-making problems based on a hybrid dynamic experts’ weight determining model

How to select the optimal strategy to compete with rivals is one of the hottest issues in the multi-attribute decision-making (MADM) field. However, most of MADM methods not only neglect the characteristics of competitors’ behaviors but also just obtain a simple strategy ranking result cannot reflect the feasibility of each strategy. To overcome these drawbacks, a two-person non-cooperative matrix game method based on a hybrid dynamic expert weight determination model is proposed for coping with intricate competitive strategy group decision-making problems within q-rung orthopair fuzzy environment. At the beginning, a novel dynamic expert weight calculation model, considering objective individual and subjective evaluation information simultaneously, is devised by integrating the superiorities of a credibility analysis scale and a Hausdorff distance measure for q-rung orthopair fuzzy sets (q-ROFSs). The expert weights obtained by the above model can vary with subjective evaluation information provided by experts, which are closer to the actual practices. Subsequently, a two-person non-cooperative fuzzy matrix game is formulated to determine the optimal mixed strategies for competitors, which can present the specific feasibility and divergence degree of each competitive strategy and be less impacted by the number of strategies. Finally, an illustrative example, several comparative analyses and sensitivity analyses are conducted to validate the reasonability and effectiveness of the proposed approach. The experimental results demonstrate that the proposed approach as a CSGDM method with high efficiency, low computation complexity and little calculation burden.

Allelopathy as an evolutionarily stable strategy

In plants, most competition is resource competition, where one plant simply pre-empts the resources away from its neighbours. Interference competition, as the name implies, is a form of direct interference to prevent resource access. Interference competition is common among animals who can physically fight, but in plants, one of the main mechanisms of interference competition is Allelopathy. allelopathic plants release of cytotoxic chemicals into the environment which can increase their ability to compete with surrounding organisms for limited resources. The circumstances and conditions favoring the development and maintenance of allelochemicals, however, is not well understood. Particularly, it seems strange that, despite the obvious benefits of allelopathy, it seems to have only rarely evolved. To gain insight into the cost and benefit of allelopathy, we have developed a 2x2 matrix game to model the interaction between plants that produce allelochemicals and plants that do not. Production of an allelochemical introduces novel cost associated with synthesis and detoxifying a toxic chemical but may also convey a competitive advantage. A plant that does not produce an allelochemical will suffer the cost of encountering one. Our model predicts three cases in which the evolutionarily stable strategies are different. In the first, the non-allelopathic plant is a stronger competitor, and not producing allelochemicals is the evolutionarily stable strategy. In the second, the allelopathic plant is the better competitor and production of allelochemicals is the more beneficial strategy. In the last case, neither is the evolutionarily stable strategy. Instead, there are alternating stable states, depending on whether the allelopathic or non-allelopathic plant arrived first. The generated model reveals circumstances leading to the evolution of allelochemicals and sheds light on utilizing allelochemicals as part of weed management strategies. In particular, the wide region of alternative stable states in most parameterizations, combined with the fact that the absence of allelopathy is likely the ancestral state, provides an elegant answer to the question of why allelopathy rarely evolves despite its obvious benefits. Allelopathic plants can indeed outcompete non-allelopathic plants, but this benefit is simply not great enough to allow them to go to fixation and spread through the population. Thus, most populations would remain purely non-allelopathic.

A new method to solve intuitionistic fuzzy matrix game based on the evaluation of different experts

In the word of uncertain competitive situations everything is in the state of flux. Under such situations knowing the exact outcomes of mixed strategies adopted by a player is nearly impossible. It is highly rational to assume that no two experts will project the similar fuzzy payoffs for mix of strategies used. Aggregation of expert’s judgement becomes utmost important before solving such competitive situations. Considering this the present paper proposes a method to solve intuitionistic fuzzy game problems by using aggregation operators on payoff judgments of more than one expert. The proposed method significantly adds to the existing literature by overcoming the limitation of Li’s existing method that considers only one expert’s opinion for solving intuitionistic fuzzy game problems. Illustrative example has been given for showing the superiority of the proposed method.